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<h2>HL Paper 2</h2><div class="specification">
<p>Two identical positive point charges X and Y are placed 0.30 m apart on a horizontal line. O is the point midway between X and Y. The charge on X and the charge on Y is +4.0 µC.</p>
</div>
<div class="specification">
<p>A positive charge Z is released from rest 0.010 m from O on the line between X and Y. Z then begins to oscillate about point O.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the electric potential at O.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the axes, the variation of the electric potential <em>V</em> with distance between X and Y.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the direction of the resultant force acting on Z as it oscillates.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce whether the motion of Z is simple harmonic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>k</mi><mi>Q</mi></mrow><mi>r</mi></mfrac></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfenced><mfenced><mrow><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfenced></mrow><mrow><mn>0</mn><mo>.</mo><mn>15</mn></mrow></mfrac></math> <em><strong>OR</strong> </em>240 «kV» for one charge calculated ✓</p>
<p>480 «kV» for both ✓</p>
<p> </p>
<p><em><strong>MP1</strong> can be seen or implied from calculation.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP2</strong> for <strong>MP3</strong>.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>symmetric curve around 0 with potential always positive, “bowl shape up” and curve not touching the horizontal axis. ✓</p>
<p>clear asymptotes at X and Y ✓</p>
<p> </p>
<p><img src="data:image/png;base64,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"></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>force is towards O ✓</p>
<p>always ✓</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>motion is not SHM ✓</p>
<p>«because SHM requires force proportional to r and» this force depends on <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msup><mi>r</mi><mn>2</mn></msup></mfrac></math> ✓</p>
<p><em><strong><br>ALTERNATIVE 2</strong></em></p>
<p>motion is not SHM ✓</p>
<p>energy-distance «graph must be parabolic for SHM and this» graph is not parabolic ✓</p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was generally well approached. Two common errors were either starting with the wrong equation (electric potential energy or Coulomb's law) or subtracting the potentials rather than adding them.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very few candidates drew a graph that was awarded two marks. Many had a generally correct shape, but common errors were drawing the graph touching the x-axis at O and drawing a general parabola with no clear asymptotes.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates were able to identify the direction of the force on the particle at position Z, but a common error was to miss that the question was about the direction as the particle was oscillating. Examiners were looking for a clear understanding that the force was always directed toward the equilibrium position, and not just at the moment shown in the diagram.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was a challenging question for candidates. Most simply assumed that because the charge was oscillating that this meant the motion was simple harmonic. Some did recognize that it was not, and most of those candidates correctly identified that the relationship between force and displacement was an inverse square.</p>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph shows the variation with diffraction angle of the intensity of light after it has passed through four parallel slits.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>The number of slits is increased but their separation and width stay the same. All slits are illuminated.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by the Doppler effect.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A plate performs simple harmonic oscillations with a frequency of 39 Hz and an amplitude of 8.0 cm.</p>
<p>Show that the maximum speed of the oscillating plate is about 20 m s<sup>−1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sound of frequency 2400 Hz is emitted from a stationary source towards the oscillating plate in (b). The speed of sound is 340 m s<sup>−1</sup>.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Determine the maximum frequency of the sound that is received back at the source after reflection at the plate.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what will happen to the angular position of the primary maxima.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what will happen to the width of the primary maxima.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what will happen to the intensity of the secondary maxima.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the change in the observed frequency ✓</p>
<p>when there is relative motion between the source and the observer ✓</p>
<p> </p>
<p><em>Do not award<strong> MP1</strong> if they refer to wavelength.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi mathvariant="normal">π</mi><mi>f</mi><mi>A</mi></math> ✓</p>
<p>maximum speed is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>39</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>080</mn><mo>=</mo><mn>19</mn><mo>.</mo><mn>6</mn></math> «m s<sup>−1</sup>» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>frequency at plate <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2400</mn><mo>×</mo><mfrac><mrow><mn>340</mn><mo>+</mo><mn>19</mn><mo>.</mo><mn>6</mn></mrow><mn>340</mn></mfrac></math>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2538</mn><mo> </mo></math>Hz»</p>
<p>at source <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2538</mn><mo>×</mo><mfrac><mn>340</mn><mrow><mn>340</mn><mo>-</mo><mn>19</mn><mo>.</mo><mn>6</mn></mrow></mfrac><mo>=</mo><mn>2694</mn><mo>≈</mo><mn>2700</mn></math> «Hz» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Award <strong>[1]</strong> mark when the effect is only applied once.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>stays the same ✓</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>decreases ✓</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>decreases ✓</p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Police use radar to detect speeding cars. A police officer stands at the side of the road and points a radar device at an approaching car. The device emits microwaves which reflect off the car and return to the device. A change in frequency between the emitted and received microwaves is measured at the radar device.</p>
<p>The frequency change Δ<em>f</em> is given by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\Delta f = \frac{{2fv}}{c}">
<mi mathvariant="normal">Δ</mi>
<mi>f</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>f</mi>
<mi>v</mi>
</mrow>
<mi>c</mi>
</mfrac>
</math></span></p>
<p>where <em>f</em> is the transmitter frequency, <em>v</em> is the speed of the car and <em>c</em> is the wave speed.</p>
<p>The following data are available.</p>
Transmitter frequency <em>f</em>
= 40 GHz
Δ<em>f</em>
= 9.5 kHz
Maximum speed allowed
= 28 m s<sup>–1</sup>
<p> </p>
<p>(i) Explain the reason for the frequency change.</p>
<p>(ii) Suggest why there is a factor of 2 in the frequency-change equation.</p>
<p>(iii) Determine whether the speed of the car is below the maximum speed allowed.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Airports use radar to track the position of aircraft. The waves are reflected from the aircraft and detected by a large circular receiver. The receiver must be able to resolve the radar images of two aircraft flying close to each other.</p>
<p>The following data are available.</p>
Diameter of circular radar receiver
= 9.3 m
Wavelength of radar
= 2.5 cm
Distance of two aircraft from the airport
= 31 km
<p> </p>
<p>Calculate the minimum distance between the two aircraft when their images can just be resolved.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>i<br>mention of Doppler effect<br><em><strong>OR</strong></em><br>«relative» motion between source and observer produces frequency/wavelength change<br><em>Accept answers which refer to a double frequency shift.</em><br><em>Award <strong>[0]</strong> if there is any suggestion that the wave speed is changed in the process.</em><br><br>the reflected waves come from an approaching “source” <br><em><strong>OR</strong></em><br>the incident waves strike an approaching “observer”</p>
<p>increased frequency received «by the device <em><strong>or</strong></em> by the car»</p>
<p><br><br>ii<br>the car is a moving “observer” and then a moving “source”, so the Doppler effect occurs twice<br><em><strong>OR</strong></em><br>the reflected radar appears to come from a “virtual image” of the device travelling at 2 v towards the device</p>
<p> </p>
<p>iii<br><strong>ALTERNATIVE 1</strong><br><em>For both alternatives, allow ecf to conclusion if v <strong>OR</strong> Δf are incorrectly calculated.</em></p>
<p><em>v</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\left( {3 \times {{10}^8}} \right) \times \left( {9.5 \times {{10}^3}} \right)}}{{\left( {40 \times {{10}^9}} \right) \times 2}} = ">
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>9.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>40</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>9</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 36 «ms<sup>–1</sup>»</p>
<p>«36> 28» so car exceeded limit<br><em>There must be a sense of a conclusion even if numbers are not quoted.</em></p>
<p><strong>ALTERNATIVE 2</strong><br><em>reverse argument using speed limit.</em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\Delta f = ">
<mi mathvariant="normal">Δ</mi>
<mi>f</mi>
<mo>=</mo>
</math></span> «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2 \times 40 \times {{10}^9} \times 28}}{{3 \times {{10}^8}}} = ">
<mfrac>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>40</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>9</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>28</mn>
</mrow>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 7500 «Hz»</p>
<p>« 9500> 7500» so car exceeded limit<br><em>There must be a sense of a conclusion even if numbers are not quoted.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{{31 \times {{10}^3} \times 1.22 \times 2.5 \times {{10}^{ - 2}}}}{{9.3}}">
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>31</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>1.22</mn>
<mo>×</mo>
<mn>2.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>9.3</mn>
</mrow>
</mfrac>
</math></span><em><br>Award <strong>[2]</strong> for a bald correct answer.</em><br><em>Award <strong>[1 max]</strong> for POT error.</em></p>
<p>100 «m»<br><em>Award <strong>[1 max]</strong> for 83m (omits 1.22).</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A student is investigating a method to measure the mass of a wooden block by timing the period of its oscillations on a spring.</p>
</div>
<div class="specification">
<p>A 0.52 kg mass performs simple harmonic motion with a period of 0.86 s when attached to the spring. A wooden block attached to the same spring oscillates with a period of 0.74 s.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>With the block stationary a longitudinal wave is made to travel through the original spring from left to right. The diagram shows the variation with distance <em>x</em> of the displacement <em>y</em> of the coils of the spring at an instant of time.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">A point on the graph has been labelled that represents a point P on the spring.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the conditions required for an object to perform simple harmonic motion (SHM).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the mass of the wooden block.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In carrying out the experiment the student displaced the block horizontally by 4.8 cm from the equilibrium position. Determine the total energy in the oscillation of the wooden block.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second identical spring is placed in parallel and the experiment in (b) is repeated. Suggest how this change affects the fractional uncertainty in the mass of the block.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the direction of motion of P on the spring.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain whether P is at the centre of a compression or the centre of a rarefaction.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>acceleration/restoring force is proportional to displacement<br>and in the opposite direction/directed towards equilibrium</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{T_1^2}}{{T_2^2}} = \frac{{{m_1}}}{{{m_2}}}">
<mfrac>
<mrow>
<msubsup>
<mi>T</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<msubsup>
<mi>T</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>mass = 0.38 / 0.39 «kg»</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>«use of <em>T <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 2\pi \sqrt {\frac{m}{k}} ">
<mo>=</mo>
<mn>2</mn>
<mi>π</mi>
<msqrt>
<mfrac>
<mi>m</mi>
<mi>k</mi>
</mfrac>
</msqrt>
</math></span></em>» <em>k</em> = 28 «Nm<sup>–1</sup>»</p>
<p>«use of <em>T <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 2\pi \sqrt {\frac{m}{k}} ">
<mo>=</mo>
<mn>2</mn>
<mi>π</mi>
<msqrt>
<mfrac>
<mi>m</mi>
<mi>k</mi>
</mfrac>
</msqrt>
</math></span></em>» <em>m</em> = 0.38 / 0.39 «kg»</p>
<p> </p>
<p><em>Allow ECF from MP1.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>ω </em>= «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{{0.74}}">
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mn>0.74</mn>
</mrow>
</mfrac>
</math></span>» <em>= </em>8.5 «rads<sup>–1</sup>»</p>
<p>total energy = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2} \times 0.39 \times {8.5^2} \times {(4.8 \times {10^{ - 2}})^2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>0.39</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>8.5</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>4.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p>= 0.032 «J»</p>
<p> </p>
<p><em>Allow ECF from (b) and incorrect ω.</em></p>
<p><em>Allow answer using k from part (b).</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>spring constant/k/stiffness would increase<br><em>T</em> would be smaller<br>fractional uncertainty in <em>T</em> would be greater, so fractional uncertainty of mass of block would be greater</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>left</p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>coils to the right of P move right and the coils to the left move left</p>
<p>hence P at centre of rarefaction</p>
<p> </p>
<p><em>Do not allow a bald statement of rarefaction or answers that don’t include reference to the movement of coils.</em></p>
<p><em>Allow ECF from MP1 if the movement of the coils imply a compression.</em></p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A student investigates how light can be used to measure the speed of a toy train.</p>
<p style="text-align: center;"><img 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"><img src="blob:https://questionbank.ibo.org/55ba542d-3306-4ee7-8386-825edadb928d"></p>
<p>Light from a laser is incident on a double slit. The light from the slits is detected by a light sensor attached to the train.</p>
<p>The graph shows the variation with time of the output voltage from the light sensor as the train moves parallel to the slits. The output voltage is proportional to the intensity of light incident on the sensor.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: center;"><img src="blob:https://questionbank.ibo.org/4e0f3fdc-c845-43ef-ba7c-39bab20625cf"></p>
<p> </p>
</div>
<div class="specification">
<p>As the train continues to move, the first diffraction minimum is observed when the light sensor is at a distance of 0.13 m from the centre of the fringe pattern.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>A student investigates how light can be used to measure the speed of a toy train.</p>
<p style="text-align: center;"><img 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"></p>
<p>Light from a laser is incident on a double slit. The light from the slits is detected by a light sensor attached to the train.</p>
<p>The graph shows the variation with time of the output voltage from the light sensor as the train moves parallel to the slits. The output voltage is proportional to the intensity of light incident on the sensor.</p>
<p style="text-align: center;"><img 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"></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, with reference to the light passing through the slits, why a series of voltage peaks occurs.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The slits are separated by 1.5 mm and the laser light has a wavelength of 6.3 x 10<sup>–7</sup> m. The slits are 5.0 m from the train track. Calculate the separation between two adjacent positions of the train when the output voltage is at a maximum.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the speed of the train.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the width of one of the slits.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest the variation in the output voltage from the light sensor that will be observed as the train moves beyond the first diffraction minimum.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In another experiment the student replaces the light sensor with a sound sensor. The train travels away from a loudspeaker that is emitting sound waves of constant amplitude and frequency towards a reflecting barrier.</p>
<p><img 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"></p>
<p>The graph shows the variation with time of the output voltage from the sounds sensor.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAmUAAAF7CAYAAACTu/xRAAAgAElEQVR4Ae2dD5BdVZ3nfx0sRx2MilAmLSAilYAFAiH0sANMYmQTQ+GEDYIrG4QlAR0NuLCEaGD8SyIQCgoSnR2UTBCGGQVSpGSMxJhKhqSWacNfKUhS/BXs4AqUk8mCWkt66/u6T97t16+735973z1/Pqeq696+7757zvn8zrv3e3/nd87p6u/v7zcSBCAAAQhAAAIQgECpBMaVmjuZQwACEIAABCAAAQhUCCDKaAgQgAAEIAABCEDAAwKIMg+MQBEgAAEIQAACEIAAoow2AAEIQAACEIAABDwggCjzwAgUAQIQgAAEIAABCCDKaAMQgAAEIAABCEDAAwKIMg+MQBEgAAEIQAACEIAAoow2AAEIQAACEIAABDwggCjzwAgUAQIQgAAEIAABCCDKaAMQgAAEIAABCEDAAwKIMg+MQBEgAAEIQAACEIAAoow2AAEIQAACEIAABDwggCjzwAgUAQIQgAAEIAABCCDKEmsDL7/8sr355puJ1ZrqQgACEIAABPwngCjz30a5lVBi7JBDDrF169bldk0uBAEIQAACEIBAPgQQZflwDOIqToxde+21eMuCsBiFhAAEIACBlAggyhKxtrxkEmNK06dPx1uWiN2pJgQgAAEIhEMAURaOrdoqqbxkEmNKCxYsqAg0YsvaQsqXIQABCEAAArkSQJTlitPPizkvmcSY0qRJk/CW+WkqSgUBCEAAAgkTQJQlYHznJZMYcwlvmSPBFgIQgAAEIOAHAUSZH3YorBS1XjKXEd4yR4ItBCAAAQhAwA8CiDI/7FBYKep5yVxmeMscCbYQgAAEIACB8gkgysq3QaEl0IhLF0tWm5Hzlj344IO1H/E/BCAAAQhAAAIdJtDV39/f3+E8ya6DBHbu3FkJ7HdZdnV1Wdbkr7/+euWjAw44wJ3CFgIQgAAEIACBEgggykqAXmaWtaKszLKQNwQgAAEIQAACVQJ0X1ZZsAcBCEAAAhCAAARKI4AoKw09GUMAAhCAAAQgAIEqAURZlQV7EIAABCAAAQhAoDQCiLLS0JMxBCAAAQhAAAIQqBJAlFVZsAcBCEAAAhCAAARKI4AoKw09GUMAAhCAAAQgAIEqgQ6Kst228+e32JLbt9veav457e21PTsfsBuW3GU787/40DLu3W6rZh1hs1a5enQw76El4T8IQAACEIAABCIi0DlRtnub3Xb+tfbwW0XQe916b7vKFj38hyIuPsY1y8x7jKLxMQQgAAEIQAACwRDonCgLBgkFhQAEIAABCEAAAp0n0IAo2207N66yxR/vNs0G39U1yxav2mg797h+wldt4+Kp1tW9xDbudsfMbPdGW9zdZd2LN9pu7R/5Cbt+1y5bP/8o269y7v8Z+N6s79rGh75r53fr2l3W9fHFdvvDuwa7OPfa7o1LrLtrqi3e+GqGTjZPXeeT9onrHzZbP98m71d77sDX9u5cZbO6zrFVO2u8aZVyZr6zZ6dtXLXYPl6p60B5Vm3caXsyuVd3VY76ee/d9bCtueF863bXGcZNV1GX7k376t59/g12TyXvTHnMbO+uXrt98axB/t328cWrbOPO3dVisAcBCEAAAhCAQPAExhBlu237qsts+rzNNuG6h+2t/n57q+9rNmHzl23yp262h/cJszE4jJ9h123/hV05caLNvO1pe6tvmc0YP5j1+oU27+/MvvTwH62//99txyX72eqpF9mND/9+jIu6jw+0Gdf9zH5x5QlmM2+zHW9ts+tmHOg+3Lcdd8Rf2mdmPmI/2vJCJqZtr+3etsHusJk2a+oBZnuetFVfOsvmbT7UrutTef5ofdcdapvnTbdP3dBbR5iNkPeeXrvx3M/b2v0utoff6q+sNflW3xW23x0X2+f/17bB6/zJfrNmiU0//0mbtvHfrb//Ldv51YPsJ1dfb5v2ldps72/W2EUnzLeNE75mfZVrbbe/m7zV5k1fYmt+86fMmexCAAIQgAAEIBAygdFF2e5t9g9X99rsld+yL/dMNJ08buLJdtmKm+3KHcttyY93ZgROixgmfslWLrvIeia+3czG26S5l9vfXvmK3fjjRyxXX9C4w+yUz0yx9Xess0f3icnXbdsD683OO82mjjfb3XuXXf3zaZnyvN0m9vyNrbjzAtux6Ab7ca2XrW6V99ru3vvsxh0z7fz5/8kmDhIeN/FUu+C8Kbbp509anxyKu7fYLQs32+yVX7MLjhwvsrb/kefZiju/ahP3XfdV23TLMlt1zGV21ZdPHrzWeDvywuvszvMesoW3bMmX0b582YEABCAAAQhAoNMERhFlg16kXUfZyUd/oCLI9hVu/26bfIzZr3b01fEe7TursZ1jptjRFUHmTt/fDp58uO26Y4Nty3aHuo9b3r7Djpj1X+3CHf9oP+59vXKVvb/5V/vHOybY5edMsfE2INB2DSvPONv/4CPsGHvOdrxcvxNzaJHG2fgZy6yv7xrreeVfbc2aNbZmzT22avEcmzz/7sFTR2Lr8ho8bfcT9sAdD9vE4w6zCUMsVRSjoTXhPwhAAAIQgAAEOkdgyKN+aLZ/sldeeMZ2DT045L9dj71gr2TCyIZ82O4/u56xF17Jt3tu3Af/yv7beWZ3PPCE7bY/2DMP/LOtOmau/fXx7zXb+6q98FjfKKXus8deeLUxz6C6Qc8/1t49+Vxb8W+vVbxg7511vW277WyzXz1jL+/z1I2SXeajXdd/wt6zLzZNsXfvzAi8zInsQgACEIAABCAQLIG3jVzyt9uEw46wifbMiKc4D87LI57RxgcTj7DDJrzdLNeLH2BTZ800m7fBtn11gr3wo0ds5me+ZUdUpOmBdthx3WaPjVTmbjvusANtnGUHHNQ79w+288ffsvk/n2b3vnyjzf2gumWVNCjgOTM7YvD/RjeKw9to6y48cqi3stGvcx4EIAABCEAAAkEQGMVTNs7GTz3Nzpv4tG198rdDPUR7+mzHr8yOmdxt+9tAV1rLtR3mOdpjL+94ziZW4rzeNth12PLVa744WCdbb//yg3+2H62fYp855bBBsTMg2Cb+6hF7clfWQ7fX9rz8jP3KDrfJB+9fc716/w6U32q7Qff+X/v9q38c/IJjW9sl6vIaPG38x2zWed32q61P2a4hHsnf28M3nGFds1YVP1luvSpyDAIQgAAEIACB3AmMIsoUdz/V/vs1PbZu4dfs5t7BaSrUNXfJl+36yYts2TmTbJy9w4445ZM2c9dP7PZ7nhqIMduz3dYsvc6uz/Z9VuLQ3jVQgTf22L4evF2r7dtL7xucYkOjPRfbvDtOspWXnmKV8PfKqMk+u+P2f7HtlS/ttp1rbrRvawqMfSkrDP9ge/b8v32fDNsZP8XOuXyC3bjo27Z+5iftlCPeMXjKOBvfc65d858328Il37feijDba3u232GXzFttk5dfYedMcudmr1qb9/iKN27i+h/Z6k2/GRCze3dZ781fs4Wrnqx+cfwpdunKk+yOb99oayrTW2hlgPts6bdXZ7qMD7Tply6x2eu+bktu3joozFT/6+2KRWbLl821SaNbsJofexCAAAQgAAEIeE1gjEe6RvrdZJvunGavLD7B9lNc07v/p+2YdrPt+MmX7YT9B74+btKnbcX6C82uPsberXM+9Q/2H2ddYbfOrI4jtHGH2+zF59mfNE/Zn19oP37mzQEw08+z8058zpZO2s+6ut5jMzYfbbdvWlbt9hs3yc5Z8Q92ud1gR71b55xtt/3HTPvbW8/OgH2HHTH7Ivvqn662yfsdbmf9+Jmhnr3MmWbvteP/eq7NtKPtws9/YrDrcvCE/Y+2C797r9057de2uPvPrKtrP3v33zxl0+7cZD+5osfq+8lq837O9p9+if1k9XH2vz9x8ACzg79i/3rI+XbfvVdmRla+3T44d5ltWnKQrZ3+nkpek5a+aDMuudRmZso77oNn2s2bbrZpr3zLuvdTPNl7bPraA+ySbd+3y094b+ZMdiEAAQhAAAIQCJlAV39/f385FRicePWxL9qOdRfi8Rk0gia5nT39GVu8/ZrqXG45GkgT9JZm8hzrwaUgAAEIQAACsREYw1MWW3U9qk9lJYFj7PxVT+6bVmTvrq1289Lv2Z8uP9N63OS6HhWZokAAAhCAAAQgUBwBRFlxbEe/8vhT7H/85Jt2zObPDnT5dnXZfifcam/N+Xu76/KRukpHvySfQgACEIAABCAQLoESuy/DhRZyyem+DNl6lB0CEIAABGImgKcsZutSNwhAAAIQgAAEgiGAKAvGVBQUAhCAAAQgAIGYCSDKYrYudYMABCAAAQhAIBgCiLJgTEVBIQABCEAAAhCImQCiLGbrUjcIQAACEIAABIIhgCgLxlQUFAIQgAAEIACBmAkgymK2LnWDAAQgAAEIQCAYAoiyYExFQSEAAQhAAAIQiJkAoixm61I3CEAAAhCAAASCIYAoC8ZU+RW0p6fHNLP/smXLbOvWrfldmCsVTuD111+3H/7wh3bmmWdWbOhsedFFF9maNWvszTffLLwMZJAPAdlq/fr1Jtvp9+hsKduuXLnSZGtSOAR27txZuafKlll76j6rz0jhENBvT79B95uUDTuVEGWdIu1RPr29vdbf32+nn366rV27tvJQePnllz0qIUWpR0AP8AsvvLDy0apVqyo2dLb8+te/bn19fTZt2jR77LHH6n2dYx4R0EP6s5/9rG3bts2+9KUvDbGlbNvd3W2f/OQnK0Lbo2JTlDoEJK6vvPLKyp9+f2+88cY+e2pfx9znvDTVAejZIb3c6ren3+DPfvazii2XLFnSuVL2k5IiYKY2NjQ98MAD/SeeeGL/Sy+9NPQD/vOGwIoVK/oXLFjQ/9prr41aph07dlRsKZuS/CSwZcuWio0effTRUQv4xhtv9C9atKjyp32SfwR0z9S989577x2zcLfffjv32TEplXeCL7+34U/o8piQcwcI1BNlylYP8zlz5iDMOmCDZrNwgqzRB7POk4Br5EHRbFk4vz0CTpA18wLk7N9eznw7bwJOkMmmjaZW7N/otTmvdQLunqnfWtmpSwXonF+OnMomoFiHkUyu+LLLLrus4rI94IADyi4q+ZtV4scefPBBu+WWW+yd73xnw0wUEyEX/E033WQnn3xyw9/jxOIIqMty3rx5lS7Jgw8+uKmM1P116KGH2sKFC5v6HicXQ0DdkOp+XrRoUdO/L4Uh3H333U3/poupCVcVAcWP7d692zraTTkCekTZCGBiPTyaKFOd1Z++bt06+/73vx8rgmDqpdiwiy++2DZv3tyUIHMVVJzg3LlzEdkOSIlbPcQVW3Trrbfacccd13RJ2hEBTWfGF8Yk0K5I9kkEjFnZyE/wTSQT6B95g2u2enqIv+997yPAuFlwOZ+vh7AEmR7izXjIssWQN+YrX/mKXXvttdnD7JdAQB5LeblaEWQqrtrA9ddfX/FkMyqzBANmstRDXF7P+fPnZ442t6vvapAOg3Ka45b32fotXX311aaBUq3eZ/MuE56yvIl6fr2xPGUqvhrq+9//fnvttdeMbsxyDKppL+TpysOdrikXzj77bJs5c2Y5lUk8Vz14v/GNb9g//dM/tX3jz7NdJG6WlqrvPJ533nmnTZo0qaVruC+57uxWPeHuOmxbJyCP50knnVTpUWj9Kvl+E09ZvjyjuJqE2L333ouHpSRrSoype+MLX/hCLiVQ3IveBvVAIXWegASZbJDHm7jE9X333ce8V503YyXH2267zT73uc+1Lch0MYk6zUmn+DJS5wnoZUnCePbs2Z3PfJQc8ZSNAifGjxrxlKneeb4RxsixyDoV8fZWxDWLZBDLtdXVtWHDhkrXY1510oCc1atXE/eZF9AGr1NED0IR12ywOsmfJkHcykCNosHhKSuacKDX11u94pF+8IMfBFqDMIutN7dNmzbl/vZ26aWXVjyfeMs61y7EWh7KBQsW5JqpRtP+7ne/YzWOXKmOfbG77rrLVqxYkWtIh3oldE1dm9Q5Am4lGx9HpiPKOtcOgstJbl0JBAkFUmcISARLDOfR1ZUtsYL+p0+fXhlZmz3OfnEEHnnkkQrzdmOP6pVQb/jylpE6Q0AerUsuucTOPffc3DPUNXVt5UHqDIHly5dXvGSdya25XBBlzfFK6mznLbvnnnuSqndZldVNWTeLomIc5LHRSEy8ZZ2xsGw5Z86cQjLTG/7jjz/OC1MhdIdftAgvmcvFecvuv/9+d4htgQTciFcfvWSqNqKsQOPHcGl5V6666ire4jpgTHfjz9tL5oouj82xxx5r8uCQiiXQiRu/PKq8MBVrR11dLzEa9VqEl8yVXiOjNbiHFyZHpLit7rMarOFrQpT5ahlPysVbXGcM4W78Cj4tMl1wwQV0exUJePDauvF/8YtfLDQnXpgKxbvv4lpRQ6x1Lywq8cJUFNmh1y26N2Jobq39hyhrjVtS33JvcUlVusOVlfdKXqxml99ptpiu20vTbpCKIeBu/KeeemoxGQxeVSJh6dKllbjPQjNK/OLf+973CuuGzqLlhSlLo5h9dRFrYEVRvRF5lBpRlgfFyK+ht7ju7m5GexVoZwVt66bciSTXvea6IhVDQINjJJY6ceM//fTTK11rxdSEq+rlpa+vr+n1LVshN2XKlEqcIC9MrdBr7DvqIj7llFMaO7mksxBlJYEPLVs9yDXzNCl/AvKsaNSlbsqdSOoiVYwMqRgCYiux1ImkZZskGhghXQxtvbx0Kv5IIl55bdy4sZjKJH5VxXnKudDqUmedwoco6xTpwPNx8SsEouZvyE671NVFqpuTC0bPv0bpXtF5Vjp549eampqklpQ/AQnsouM8s6WWF2fNmjXZQ+znRGDLli1eLac0UrUQZSOR4fgQAopf0ZQKjNwbgiWXf3QT7rRLXQvP//SnP82l/FykSkBejk55VlyuM2bMwPPpYOS4dZ6VouM8s0V2nk+6MLNU8tmXwNZvxfeEKPPdQh6VT+vu0YWZr0HK8KyoBmeccUZlqhM8n/naswyBjeczXxu6q5XlWaEL01kgv20ZArvV0iPKWiWX4PemTp3Kgzxnu5fhWVEV5PnUxKY7duzIuUbpXq4sgS3i8nxKRJDyI1CWZ4UuzPxs6K5UlsB2+TezRZQ1Qyvxc+nCzL8BaA6kTnddulrwIHck8tmWJbBVerow87Ghu0qZnhW6MJ0V8tuWJbBbqQGirBVqCX+HLsz8jO9GXU6ePDm/izZxJR7kTcBq4NQyui5dsVzcE7FIjkh72yeeeMJOO+209i7SxrfpwmwDXs1XyxTYNUVp6F9EWUOYOMkR+OhHP8ocVw5Gm9tt27Z1bD6rekV1sUhMp1CPTnPHJLDXrl1b6nB7HuTN2Wy0s8sU2CqXvOfyopPaJyCBrV6BUBKiLBRLeVJOHuT5GUKiTHF6ZSZ5Ax566KEyixBF3k5gl1kZHuT50PdBYMt7rrkLVRZSewQksD/2sY+1d5EOfhtR1kHYsWTFgzwfS2qh97JFGQ/yfGy5YcOG0m3JgzwfW/ogsDWR7KJFi+zpp5/Op1KJXsUHgd0sekRZs8Q4H9d6Dm1AcQ4a/ajBE2UmHuT50F++fHnpoowHeT629MGDrZro5ZcpiNqzqQ8Cu9kaIMqaJcb5xoO8/UbgS5wDD/L2bemLwFZNeJC3b08fPNiqBfG77dvSF4HdTE0QZc3Q4twKAR7k7TcEBfH6Eudw0kkn2aOPPtp+pRK9gi8CW/h5kLfXCDXoxQcPtmrBiNr2bKlva+1S/SZCSoiykKzlUVl5kLduDM2iryBeeRx9SEcffbQpJorUGgGfBDYP8tZs6L715JNPljoVhiuH22pEbW9vr/uXbRMEND2M1vh1v4kmvlrqqYiyUvGHmzkP8tZtp/VDtY6oPI4+pEmTJllfX58xx1Xz1vBNYKsGWkD7qaeear4yfKMyEvn444/3hoTKwujo1swhMavu/NASoiw0i3lSXj3INS8TQ7abN4i6CmfPnt38Fwv8Bg/y1uBqmSqfBLZqoRG9iqUhNU9AAzamTJnS/BcL+sZRRx1lKhOpeQISsz4J7EZrgChrlBTnDSPAkO1hSBo68Pjjj5s8jT4lPciZRLZ5iyie7NRTT23+iwV+g7iy1uCq/fsmsN0atfw2m7epxKxEbWgJURaaxTwqL3FlzRvDdXfJ0+hT0oOcuLLmLeJTPJkrvYuhoTvaEWlsq3iyY489trGTO3iWuuBUNlLjBHwasNF4qQfORJQ1S4zz9xEgrmwfioZ31N0lD6NvSQ9yuqObs4oT2L4M2MiWnu7oLI3G9n3t7lIX3Pbt2xurBGdVCLzwwgtBxpOp8IgyGnHLBFxcmR5OpMYIqLvLt65LV3K6ox2JxrYvvfSSd91druTElTkSjW997e760Ic+xHrDjZuxcqZiKn3rjWi0CoiyRklxXl0CepDL+0NqjIC6IXyZn6y2xHRH1xIZ/X/Z0rd4Mlfiww47jKkUHIwGtj53d9Ed3YABa04JcX4yVwVEmSPBtiUC8vrI+0NqjIDexn3s7lLpZUsNQiA1RkDdXR/5yEcaO7nDZzkvNqOjGwPve3eXuqNffPHFxiqT+FmuzTsxGxoORFloFvOsvPL6EITamFHc27gv85PVlloPck1qS3d0LZn6/2/atMnr0V3yYv/617+uX3iODiHge3fXkUceyaobQyw28j9axH369Okjn+D5J4gyzw3ke/Hk9WEencas5PvbuGqhKQEUK0UanYAb2Vj2gvKjlVLd0XixRyNU/UwTjfq8HA9e7Kqtxtp79tlnTW0/1IQoC9VynpRbXh+tFcc8OmMbxPe3cdVAMVJ4Pse2pbqS1KXkczr88MOxZQMGUneXRh773N2FF7sBQw6eomlqfB1M1UgtEGWNUOKcUQloHh15gUijE/D9bVylV4wUw+9Ht6M+1aoM6lLyOeHFbsw66uL1cZqa2tLjxa4lUv9/hWAccsgh9T8M4CiiLAAj+V5EvcXhKRvdSiG8jasGDL8f3Y7uUx9XZXBlc1vnxXZdre4426EEnnvuuSC6u/BiD7Vbvf/0HPJtVYZ65RztGKJsNDp81hABDb9n1N7oqEJ5G3ddOG4E0+i1SvdTvY3rZcT31NPTw+LkYxhJo2jV1et7wos9toXUY+Pjqgxjl7x6BqKsyoK9FgkQ7zA2OL2NhxLnoJFLjNob2abubXzkM/z5hDVNx7aFRtEeeuihY59Y8hl4scc2gH6bIbwsjVYTRNlodPisYQLEO4yOSm/jvk4aW1tyjVySiCTVJxDS2zhe7Po2dEdd167Po2hdWfFiOxIjb7V+r9p8yAlRFrL1PCo78Q6jGyOUt3HVQl05EpGk+gRCeht3Xuz6NeGoRtGGNKcVXuyR26zmV9QoWjxlIzPik4QIEO8wsrFdfFYIb+OqhbpyJCJJ9QkofjKkt3F5sSUkScMJhDanFV7s4TZ0RzS/YgijaF15R9riKRuJDMebIqB4B035QBpOQPFZIb2NO/HoxOTwGqV9JJQgf2clBT4zZY2jMXSrOflCifVUyfFiD7Vf9r/QbJkte3YfUZalwX7LBBTvINcxS/QMRxjKkPtsyekmydKo7ocU5O9Kre4cPGWOxtCtPMIhzWmFF3uo/bL/9fX1ebsWbbacY+0jysYixOcNE5DrmCV6huMKZch9tuR0k2RpVPdDCvJ3pSbY35EYunWeYF/Xoh1a2oH/nBebl9/hdBRWcNBBBw3/ILAjiLLADOZzcdUNQDfJcAuFFOTvSk83iSMxdBtSkL8rOcH+jsTQbWhhBa708mLz8utoVLehhRVUSz50D1E2lAf/tUFgwoQJdJPU8HNvtO4Nt+Zjb/+lm6S+aUIL8ne1ULC/m/7BHUt9G2JYgWwmLzbr0w5tvSGGFQytQfU/RFmVBXttEqCbZDhAvdGGFOTvauBEpBOV7njq21Dfxj/84Q+bpn8gVQmEGFag0n/gAx9gfdqqGSt7IYYV1FRh37+Isn0o2GmXAN0kwwmGPCKIbpKh9pSnSR6nEJMWT9f0D6QqgRDDClR6RrpXbej2QgwrcGWv3SLKaonwf1sE6CYZim/79u3BjghSjCDdJFV7ytMkj1OICVsOtZrzADuP8NBP/f7PjXT3u5SdLZ3iA0OaO3A0Ooiy0ejwWdMENCcS3SRVbM8//3zlzbZ6JJw9JgQeait5muRxCjFp2gcmBK5aLtSwAlcDjXRnmhNHw2z58uXBz+TvaoMocyTY5kKgu7ubbpIMScUguTXrMoeD2FU3iUQlaYBAyF3RbtoHNw1E6jYN2ZaynQbiMNJ9oBUrrGDOnDnRNGlEWTSm9KMidJNU7RD6iCCJSYlK0gCB0CYarbWbYgRfffXV2sNJ/h/6RKOK333llVeStF1tpdWme3p6ag8H+z+iLFjT+Vlwukmqdvnd735n6s4NObFu4oD1nIfJeZxCtClTKVStFvpEo4qfIt5zwJ6a2iTUsIJqi6zuIcqqLNjLgYB7aLmHWA6XDPYSikFSd27ISaJS4jL1pLfxEKc2ydpNEwJr4AnJKh5geZtCTXr5VRwVySzUqU1Gsh2ibCQyHG+ZAN0kA+hCj1tRLYgRrNpSnqaQ04EHHkiMoFllEt1QpzZx7U8vv4qj4uXXKgMeFGMXS0KUxWJJj+pBN8mAMUKPQVItiBEcsKVikDRpZ8iJGMEB64U8tUm2/cnTp6kgUk9r1661EKc2GcluiLKRyHC8ZQJ6eOkhlnJy8yC57txQWRAjOGC50GOQXPsjRtDst7/9bRQxSHr5VTxVykmDqTQ9SEwJURaTNT2py0EHHWR6iKWcQp8HydnOiUonMt3x1LahLq9UaydiBAdikOQBDj0RI2iVaUFisGW2LSLKsjTYz4UAyy1ZZWRU6DFIrjGkvtxSyMsrORu6rWIE5SlKOcm7ovi60BMxglaZFmTChAmhm3JI+RFlQ3DwT14EUl9uKYYYJNcW9Caa8ovCCeAAACAASURBVESVGnkZ6vJKzoZuK1tqtFrKKZYYJGIEB15+Y1leyf0mEWWOBNtcCeghlvJElQrAVTduDElvoikv6RLTPEjyrqS83FJsMUipv/zGMJiq9hmBKKslwv+5ENBkfikHoca0FpveRFMe5RXTPEhulFqqMYLy+MY0fYJeflNda9hNB+LiXnN5cHlwEUSZB0aIsQgpB6HqZhHTWmyKEUx5okp5V2J6kKccI6iliUKeNLb2WaGX31RjBGOY0LnWnvofUVaPCsfaJpByEKq8SjHd+NUYUp6oMpYYJPejTjlGUBM6xxSDlHKMYAyTc7vfZHaLKMvSYD83AikHoarbNpaRl65BSGSmGCMYWwyS7KkYwVQXs44tBkkvv6nGe4a+qLy7t9ZuEWW1RPg/NwKpTlSp9QXVfRtTSnWVBq37GVPXpdpkqotZuzi6mGKQFCMoT26KKabBVFn7IcqyNNjPlUCqE1U+//zzUcyDlG0Mqa7SoHid0BeVz9pR+6mu0hDLhM619tSM9il6y2IaTJW1KaIsS4P9XAmkOlGlZn9X921MSdN7pDgCUyMvFbcTU3KeIuc5iqluo9VFIy9js6XqK0+uPLoppdgGU2VthyjL0mA/VwIpBqHGNPt7tjGkOgJTHgjF7cSWUhyBqTi62GZ/V7tM8eVX8a2xDaZy9xhEmSPBNncCKQah6mYRy+zvtQ1CIzAlOlNKsY28dLbTC1NqqzTENvIya8vUVmmQLWMbTOXsiShzJNjmTiDFINSYZn+vbRCpjcCMceSls2mKqzTENvLS2VIvv6mt0hDTMnbOjm6LKHMk2BZCILUg1BhHXrqGoTfTlFZpiHHkpbNlaqs0xDr7u+ypl99f/vKXllKMYKwjL2VPRJm7S7EthEBqQagxjrx0DUMjMCU6U0nPPvtsdCMvne00AjOlVRpinf3d2VMvvxpdmkqKdeSl7IcoS6UVl1TP1IJQYxx56ZqORmBKdKaSYp0xXPbTCMwTTzzRnAcpdpvGbEvZTi+/qcQIxjzyUrZElMV+Nyq5fimNwIx15KVrQoopk+hMJSlOJ8aRl85+GoGZyioNikGKceSls6VeflNZpSHGZeycHbVFlGVpsJ87gXe9613JTGwY88hL1zBSGYGp+BzF6SheJ9akFyZ5kFJIepDHtOZlrc1SsmWMy9hl7Ykoy9JgP3cCmkQ1lWVAYh556RpGKiMwFZ+jOJ2YkzxH8iClkBSDpDi6WFNKIzAV16r41lgToixWy3pUr1TWwIz9ZqEmlcoITMXnxLbmZe0tIZURmIpBUvycW8mglkMM/6c0AlNxrYpvjTUhymK1rEf10mSqKSwD0tvbG/XNQk0qlRGYis9RnE7MKZURmLGPvHRtNJURmIprjXU2f9kSUeZaNNvCCBx55JGmhZ1jT+qmjflmIfulMgIz9tF6smUqIzBTsKXsmcIITA2mUlxrzAlRFrN1Panb4YcfbrEvA5LCzULNKZURmLGPvHS3hhRGYMY+8tLZMoURmPJ6xv7iiyhzLZptYQRSWAMzhZuFayCxj8BMYeSls2UKo/ZiH3mZki1jH3kpWyLKXItmWxiBFEZgpnCzcA1Eb6oSobGmFEZeOtulMAIz9pGXzpYpjMBMYTAVosy1aLaFEoh9BKZuFuqmTSHFPgIzhZGXrp3GPgIzhZGXzpYpjMD8/e9/H/1gKkSZa9FsCyUQ+wjMmNe8rG0YsY/ATGHkpbNp7CMwUxl56ewZ+wjMmNe8dDZElDkSbAslEPsIzJjXvKxtGLGPwExltJ7sGvsIzJRsKXvGPAIz9jUv3X0WUeZIsC2UQMxrYMa+5mVtw4h9BObOnTujXvOy1p4xj8BMZeSls2nMIzBTGUyFKHOtmW2hBGIegambhbpnU0oxj8DUfHMxr3lZ205jHoGZyshLZ9OYbSmvp+JZY0+Istgt7En99JCLdQ3MFNa8rG1GsY7AlJcs9jUva20Z8wjMVEZeOpvGPAJTXs+Y17x0NkSUORJsCyegh50eerGllEZeOtvFOgJTy4HFvuals6HbxjoCM6WRl86WMY/AlNcz5jUvnQ0RZY4E28IJ6GEX4xqYKY28dI0k1hGYzz77bPRrXjobum2sIzBTG3np7BnrCMwURl7Khogy15LZFk5AQagxroGZ0shL10g+9KEPmcRobCm10XqyX6wjMFO0pewZ4wjMVJaxk/0QZbE9VTyuT4wjMFMbeemal1ZpkBiNLaWy5mWt3WIcgZnayEtnU8V7aq69mFIqIy9lM0RZTC3X87rEOAIzxZGXrplplQaJ0liS1rxUSmnkpbOdYgTlWYoppTby0tlOMYKx2TKlZewQZa4lsy2cQIwjMFMceekaiqYBkSiNJWnNS3mMUkyKEZRnKaaUSgxSrc0UIyiPb0wppcFUiLKYWm4AdYltBOZDDz2UzJqXtc1LqzRIlMaStOaluthTTBrVJs9SLCmV2d/r2UsxgkrO81vvnNCOpTSYClEWWusMvLyxBaFqio/UplBwTVALsOsNNpakOBzN2ZViUhySPEuxpJRikOrZTB5feX5jSSkNpkKUxdJqA6lHbEGoqc3+nm1mihGMaQSm4nAUj5Nq0ioN8jDFkGTLFGZ/H8lW8vjK8xtDSm0wFaIshlYbUB1iCkJNcfb3bFOLbQSm4nAUj5Nq0gtTLF2Yqcz+PlJblcc3lom6UxtMhSgbqVVzvBACMQWhpjj7e22jiCVG0HmIXDxObT1T+D+mVRoef/xx01x6qaaYVmlIbTAVoizVX21J9XYPvRiCUFOc/b222cSySoPexlMdeelsGlOMYEoxSM5+2W1MMYKpDaZClGVbMvsdIRBLEKriVlIdrecaSiyrNKQegyR7xhIjmFoMkvst1m5jiRFMbTAVoqy2JfN/4QRimagy9RgkNZRYVmlIPQZJtowlRjC1GKSRbtixxAimNpgKUTZSi+Z4YQRimKjSdb+67tjCYHl+YXlXYpioUjFImqsr9aRVGkIPEE8tBmmkNhtDjGCKg6kQZSO1aI4XRkAPPz0EQ04pz/6etZtbksiJ1OxnIe0rBkmehdTTscceaxrAEnJSDFLqYQWyXwwxgprWI7V5IBFlId99Ai27Hn6hL2ZNPFm18YUeI0gMUtWWihHUAJaQk7wr8uCmnmKIEdSEzqm9LCHKUv/lllT/0BezVgzSRz7ykZLo+ZWtvBISqaGmF1980bSOJ2kgRjBkW8pjq9+m8+CmbNMYYgTVFlOb0BlRlvKvtsS66yGoh2GoiRikquUkTvUgDDX99re/Na3jSbLK5LkhxwgSVjC0FYc+j6CW/kptQmdE2dA2zH8dIqCHoB6GoSZikKqWCz1GkBikqi3dwBU3mW71kzD2Ul5Uvp6FQl5r2C0q79pkvfrFeAxRFqNVA6hTyFMpKGZF3a+kAQKhxwjKM0QMUrU1K0ZQ00qEmPTbJKygajn9NhWXFWLSkl89PT0hFr2tMiPK2sLHl1slEPJUChqdplFqpCqBUKdScB4hYpCqtgx5HkHCCqp21F7Iaw2nOrUJomxoG+a/DhFwD0H3UOxQtrlkw/JKwzGGOpUCyysNt6XmEdy+ffvwDwI4QljBUCMpHktxWSGm1JZXcjZClDkSbDtOQN0kclGHlpgOY7jFQp1KQbaUZ4hUJaCFvHt7e6sHAtkjrGC4oRSPpeWWNO1LaElhBanNUSYbIcpCa6kRlTfUGadTHBE0VrMLdVoMeYTkGSJVCWgqBS1tE9qEwIQVVG2Y3VNcVmgj3V3bcz0q2frEvo8oi93CHtcvxBmn9capN8/URgSN1YxC7SaRR0ieIdJQAppKQdNLhJQIK6hvLY10D21C4JSnNkGU1W/HHO0AAQX7h9ZNojfOFEcEjdUcQuwm0du4PELyDJGGEgjR80lYwVAbuv+wpSMRxhZRFoadoixliN0keuNkotH6zTG0bhK9jcsjRBpOQNNKhBbsT1jBcDvqiLzYoU0IrLaX6tQmiLL67ZijHSIQWjcJb+MjN4zQukmw5ci2DC3Yn7CCkW3pQi1CCvZPOawAUTZyW+aTDhAIzbXO2/jIjSI0W6b8Nj6yFQc+Cc2LTVjB6BbVSPdQgv1TDytAlI3elvm0YAJyUWs+mhASb+OjWym0YP+U38ZHt+TApyF5sR999FHCCkYxqka6hxLsv2PHjqTDChBlozRkPiqewFFHHRVMvANv46O3h5CC/VN/Gx/dkgOfhuT51Ez+Ki+pPoGQbKmZ/FO2JaKsfhvmaIcIuHloQpjZnyD/sRtFKMH+qb+Nj21JqwRahxLsr5n85akl1ScQkhdbPScf+9jH6lckgaOIsgSM7HsVQ5nZ/8EHH0z6Da6RdqRgf3Ul+Z5SfxtvxD6hBPu7mfxdQHsjdUvtnJC82KnO5O/aJKLMkWBbGgHFOzzxxBOl5d9oxryNj01K3Q7qSvI9pf423oh9XLC/717sF154wbT2Kml0AvJiP/XUU6OfVPKnrq25HpSSi1NK9oiyUrCTaZaAZvbX9AQ+J97GG7POpEmTTOLVLZPS2Lc6f1bqb+ONElewv+/r027bts3U7kijE5g6darpPuZzevrpp009JyknRFnK1vek7pMnTzZNNeFz4m28cessWLDA6yV63HxNKb+NN2rNELzYGkX70Y9+tNEqJXveYYcdZhs2bPC6/orbVZtLOSHKUra+J3V38Q4+v8XxNt54Yzn11FO99nxqFO2ZZ57ZeIUSPtN3L7a6u1gqq7EGKm+i7wvNE7drhihrrD1zVsEETjvtNJM3ytd033338TbeoHF8n3uOOa0aNKSZ+e7FVtcqS2U1bk+x0shjH5NCHojbRZT52DaTLJPe4uSN8jG54FMWrm7MOr7PPacunJTnQWrMigNn+e7F1gCh1Lu7mrGn2r1GHvuYtBatQh9SH0WLp8zH1plgmRQTIm+Uj4ng0+as4mK1XOxWc98u9mzX3UVgeOOc5cX2dSCOurvUxUpqjIDm//J1BRW1MYU+pJ4QZam3AE/q77xQzivlSbEqxVB3F2/jzVlEMVs+Dr+nu6s5O+rs448/3nycRNZ1d6mLldQYgUMPPdTbQVUSiwp9SD0hylJvAR7VX0Oh5ZXyLdHd1bxFNPzex+5ouruat6W6o330Yis2iu6u5uwpL/acOXO8nBpDI/DV1lJPiLLUW4BH9Zc3yrfZ4Onuaq2B+NodTXdX8/b0tTtaApvurubt6WN3tEbeSyy6ttZ8reL5BqIsHlsGXxMFofo2j448d4zuar5pue5on+LK6O5q3o7uGz52R0tgp7xGorNNs1t1R/sWV6Z4MolFEqMvaQMeEXDz6PgUV0Y8WesNxLcHOd1drdvSt+5oBHbrtlQXoW+TdUskSiySEGW0Ac8ILF261KtYJOLJWm8gvj3I6e5q3Za+dUcjsFu3pY9xZcSTVe1J92WVBXseEPDpQU48WXsNwrcH+Zo1a+juatGk6o7u7u72JkAcgd2iIQe/pq5CX7owiScbaktE2VAe/FcyAZ8e5MSTtdcYfIorcwL7uOOOa69SCX/bpwBx4snaa4innHKKiaEPSeKQeLKqJRBlVRbseUDApwf55s2buVm02SY+97nPmRaMLjshsNu3gGJ+1q1b1/6F2ryCBLaW42F+stZBip0YKjav7CRxKJFIGiCAKKMleEfAlwc561223zR8eZAjsNu35ZQpU7x4kDuBnfpyPO1YVOw0x9sjjzzSzmXa/i4CezhCRNlwJhwpmYAPD3LFOSiGxnnuSkYSbPa+PMgR2O03IV8e5Ajs9m2pK8yePbv0eSER2MNtiSgbzoQjJRPw4UFOnEM+jcCHB/ljjz2GwM7HnF48yBHY+Rizp6fHfvjDH+ZzsRavgsAeDg5RNpwJR0om4MODXCP1iHPIpyHojVw337KSRuoRSJwP/bIf5AjsfOyoq7heAPUKlJUQ2MPJI8qGM+GIBwTOPvvs0h7kjNTLtwHoQa6bb1kJgZ0feT3I1a0vcVRG2rJli82dO7eMrKPMU/G7ZU2NgcCu36QQZfW5cLRkApqv7KqrripldJAW0tYktqR8CJT5INcyT319fcZUGPnYUleRKJL3sYyk7jatkUvKh4B6A/TSUkZCYNenjiirz4WjJRPQrNNljQ66++67bdq0aSUTiCt7Pch1E+502rhxo8kbQMqPgNabLONB7tZR1XJspHwI6GVFLy2ObT5XbewqEtgzZsxo7OSEzkKUJWTs0KpaRhemG6KtwQak/Ajo5ltGUDFdl/nZ0F3JPcg7HYuEwHYWyHerlxax7WSi63Jk2oiykdnwSckEyujC3LRpU6XrUoMNSPkRKKMLk67L/OxXeyU9yNevX197uND/V65caTNnziw0jxQvXkYXJl2XI7c0RNnIbPikZAJldGHKm3P66aeXXPM4s1cX5k9/+tOOVQ7PSnGozzzzzI56Pp1nha7L/G3aac+nVhGg63JkOyLKRmbDJx4QuOCCC2z16tUdKYm6YwgKLw71GWec0dHBG/KsSDyQ8ifgPJ9bt27N/+J1rohnpQ6UHA8tXLiwY55PrSJw7LHH7puSI8dqRHEpRFkUZoy3Em4iWcV6FZ3UHUNQeHGU5flctGhRRxZCllhgRYbibKkrf/GLX+zItDXyrFxyySUmUU8qhoCL+ezEWphr1641xQuT6hNAlNXnwlFPCCi2a8WKFXb//fcXWiLnUsezUihmmzNnjn3ve98rNhMz041fooFUHAEX81n0C5MWrJaYl6gnFUNAnk95r4peC1NtZfny5XbqqacWU5EIroooi8CIsVdBwb3qiiryLU43/unTp+NSL7gxnXzyyZUu4iJH7nHjL9iIg5eXSOrEC5NEvMQ8qVgCChWRYCoy3XXXXZU2w0CqkSkjykZmwyeeEFBwrwRTkW9x3Pg7Z+yvfOUrds899xSWITf+wtAOu3DRL0xu5QCJeVKxBIp+YaI3ojH7Icoa48RZJRPQm3JRb3EuWJkbf2eMrLUwtVpDEd1euqbij84999zOVCbxXNwL07p16wohIYFNN3QhaOteVC9MP/jBD+p+1u5BtRF6I8amiCgbmxFneEDACSYnoPIsksSeYlZInSHg4gT1wM07aZ45dakRf5Q32ZGvp5U3NMVB3uEF6uKWPYk/Gpl93p/ohUnM8w4vUNu49tprK6u05F3m2K6HKIvNohHXR8Ipb2+ZE3lO9EWMz6uqyZOlB3me3jJd66yzzsJL1mFLy1umv7y9ZfLYyHND/FHnDCrWRXjLnJdM7YQ0OgFE2eh8+NQjAhJO+lHnOZM4XrJyDCxPlm7+envOK7lYMrxkeRFt/DrylsmWeXnL9LIkb40mHCZ1lkDe3jK8ZM3ZD1HWHC/OLpmAbv5XX311Ljd/rYsokYeXrByj6uavB68L5m6nFLqOPG/z589v5zJ8t0UC+h1pOpm77767xStUv6aHuF6WvvGNb1QPstcxAvKW3XTTTXbllVfmcp+97bbbKvM/4iVrzIRd/f39/Y2dylkxEOjq6rLQTa6Hr9Y1XLJkScsm0fcPOeQQe+mll5gGo2WK7X9Rguziiy+uTELaajeVHuKXXnppZUJK1kZs3yatXkF2mDZtmt15552Vl51Wr5PH77vVvPlelYBE2dFHH93WhNp6WZo3b15bv+9qidLYw1OWhp2jqqVmg+7t7W25G1MPj29+85v2wAMPIMhKbhlad0+rKOjNvNWkN/H3ve99LFbdKsCcvidRfeutt7blYZFI15yEl112WU6l4jKtElB4gWwhYdVK0n1WgkxtotUXrlbyDf07iLLQLZhg+fUD181C3ZjyeDWb9BD/8Ic/zEO8WXAFna8ux+eff97UndxsUuzRhg0bKiK72e9yfv4EJLJPO+20iuey2avrtyyvqTxtPMSbpZf/+YrNlKCSsGr2Puu811pTU22C1AQBdV+S0iFgpt7LONKWLVv6TzzxxP6XXnqp4QqtWLGif8GCBf1vvPFGw9/hxOIJvPbaaxVbyqaNplbs3+i1Oa89Avqd6a/RpN+wfsvN2L/Ra3NeewSa/Z3p3qp7bDP2b6+EcX0bT1kTApZT/SKgAH11e+ltzE1tMVIJ9ea2bNkye/zxx+2WW27hTXwkUCUd11u5PGWrV69uaEktnasuLm21bh/JLwL6TSpddNFFY057oi5LjbLUb5lBN37ZUaVx91nZaKyuTE1Lo/hOraPp2oB/NfK7RAT6+22f3EsXQ6B/LRS51hUjprgizX+VdZfrJqHJEDVcXzcJxS+R/CUg8ayHs2IGNS/dlClT9glofaaltjQyTyO5ZHO6ufy1pUom0azfnuKTNJt7droSiTFNY6IH/fXXX9/W4AC/KcRROtlJwf89PT12+umnD7nP6h68cePGir21AgMDblq3OaKsdXZBfjNGUeYMIW/Z2rVrh0wwq+WZFOMisZZ9ILjvsPWTgB4Amo9OI/F++ctf7ivk0qVL7dOf/jQP8H1E/N/Ri9H9999feWDr9+mSprfRIth4xxwR/7d6MXrwwQcrU59kl2PSfVaetDPOOIP7bJtmRJS1CTC0r8csykKzBeWFAAQgAAEIZAkQU5alwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZal98sUjwAABZhJREFUwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhAoiQCirCTwZAsBCEAAAhCAAASyBBBlWRrsQwACEIAABCAAgZIIIMpKAk+2EIAABCAAAQhAIEsAUZalwT4EIAABCEAAAhBok8Bjjz1mr7/+etNXQZQ1jYwvQAACEIAABCAAgZEJPPfcc/b+97/fVq5c2ZQ4Q5SNzJRPIAABCEAAAhCAQNME5s6da6+99lrle82IM0RZ06j5AgQgAAEIQAACEBidwAEHHGALFy5sSpwhykZnyqcQgAAEIAABCECgZQLNiLOu/v7+/pZz4ovBEejq6gquzBQYAhCAAAQgECOBWgn2thgrSZ1GJlDbAEY+k08gAAEIQAACEMiLwNatW2358uWVyy1atMhOPvnkYZdGlA1DwgEIQAACEIAABCCQD4FGxJjLCVHmSLCFAAQgAAEIQAACORFoRoy5LBFljgRbCEAAAhCAAAQgkAOBZcuWWW9vr43UTTlSFgT6j0SG4xCAAAQgAAEIQKAFAprNX6Mum02IsmaJcT4EIAABCEAAAhAogADzlBUAlUtCAAIQgAAEIACBZgkgypolxvkQgAAEIAABCECgAAKIsgKgckkIQAACEIAABCDQLAFEWbPEOB8CEIAABCAAAQgUQABRVgBULgkBCEAAAhCAAASaJYAoa5YY50MAAhCAAAQgAIECCCDKCoDKJSEAAQg0RGDPTvv5DUvt9p1/GDh973ZbNavbuhdvtN0NXYCTIACBmAgwT1lM1qQuEIBAQAT22u6NV9uRn3jGrtnxQ7tw0jsCKjtFhQAEiiCAp6wIqlwTAhCAAAQgAAEINEkAUdYkME6HAAQg0D4B5yX7ju2yu23+5HcOdFkO6b7UOUusu+u/2A1r1tgN5x9jXV1d1tU1yxbf3mu7dqvr83zrrhw7xs6/aavt2psp2d5d9vDti+3jlc+7rOvji23Vxp22J3MKuxCAgF8EEGV+2YPSQAACSRAYZ+NnXGPbf/FVm2hn22073rS+62bY+Lp1v88Wrdhmh1+11fr7/2h9v/hL673gL6z7yKX25F9day/3v2X/8fQVZsu/YFff96JVdNneF23NRTPtUxsPtev6/mj9OufvPmqb551lX14zeE7dvDgIAQiUSQBRViZ98oYABCAwJoET7Mq/vdzmTpJke7tNnHqq9UycaDOv+ap9uWeijbNxtv+kv7Bpx7xm6/7tWdtje233pr+3hauOsmuumm89E99upnOOPM9W3PkpW7fw723T7qxLbcwCcAIEINAhAoiyDoEmGwhAAAKdIfC6bXtgve2aeIQdNkGCzKVxtv/BR9gxu9bbA9tedwfZQgACHhF4m0dloSgQgAAEIDCMwOE2+eD9hx0d88Cu79gn3vOdOqedYMfVOcohCECgfAKIsvJtQAkgAAEI5E9g5m22Y92FNon+kPzZckUIFESAn2tBYLksBCAAgXIIHGBTZ820ib96xJ7c9adMEfbanodvso93nWOr3GS1mU/ZhQAEyieAKCvfBpQAAhBIksBgjFel7nvtjT1vDIycbJvFOBs//fO2cvZmW7jk+9ZbEWZ7bc/O++zbV3zXbPkVdg4T1bZNmQtAoAgCiLIiqHJNCEAAAg0QGHfELFv81X+3+ZP/3P78rH+2Z/IaFDnuQzb35nvtzmm/tsXdf2ZdXfvZu6evtYMu+ZHddXmPtRCh1kBtOAUCEGiXAMsstUuQ70MAAhCAAAQgAIEcCOApywEil4AABCAAAQhAAALtEkCUtUuQ70MAAhCAAAQgAIEcCCDKcoDIJSAAAQhAAAIQgEC7BBBl7RLk+xCAAAQgAAEIQCAHAv8fpWHRypdC7RwAAAAASUVORK5CYII="></p>
<p>Explain how this effect arises.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«light» superposes/interferes</p>
<p>pattern consists of «intensity» maxima and minima<br><em><strong>OR</strong></em><br>consisting of constructive and destructive «interference»</p>
<p>voltage peaks correspond to interference maxima</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s = \frac{{\lambda D}}{d} = \frac{{6.3 \times {{10}^{ - 7}} \times 5.0}}{{1.5 \times {{10}^{ - 3}}}} = ">
<mi>s</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>λ</mi>
<mi>D</mi>
</mrow>
<mi>d</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>6.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>5.0</mn>
</mrow>
<mrow>
<mn>1.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 2.1 x 10<sup>–3 </sup>«m» </p>
<p> </p>
<p><em>If no unit assume m.</em><br><em>Correct answer only.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct read-off from graph of 25 m s</p>
<p><em>v</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{x}{t} = \frac{{2.1 \times {{10}^{ - 3}}}}{{25 \times {{10}^{ - 3}}}} = ">
<mfrac>
<mi>x</mi>
<mi>t</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>25</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 8.4 x 10<sup>–2</sup> «m s<sup>–1</sup>»</p>
<p> </p>
<p><em>Allow ECF from (b)(i)</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>angular width of diffraction minimum = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.13}}{{5.0}}">
<mfrac>
<mrow>
<mn>0.13</mn>
</mrow>
<mrow>
<mn>5.0</mn>
</mrow>
</mfrac>
</math></span> «= 0.026 rad»</p>
<p>slit width = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{d} = \frac{{6.3 \times {{10}^{ - 7}}}}{{0.026}} = ">
<mfrac>
<mi>λ</mi>
<mi>d</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>6.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>0.026</mn>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 2.4 x 10<sup>–5</sup> «m»</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> for solution using 1.22 factor.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«beyond the first diffraction minimum» average voltage is smaller<br><br>«voltage minimum» spacing is «approximately» same<br><em><strong>OR</strong></em><br>rate of variation of voltage is unchanged</p>
<p> </p>
<p><em>OWTTE</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«reflection at barrier» leads to two waves travelling in opposite directions </p>
<p>mention of formation of standing wave</p>
<p>maximum corresponds to antinode/maximum displacement «of air molecules»<br><em><strong>OR</strong></em><br>complete cancellation at node position</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Yellow light from a sodium lamp of wavelength 590 nm is incident at normal incidence on a double slit. The resulting interference pattern is observed on a screen. The intensity of the pattern on the screen is shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The double slit is replaced by a diffraction grating that has 600 lines per millimetre. The resulting pattern on the screen is shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why zero intensity is observed at position A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The distance from the centre of the pattern to A is 4.1 x 10<sup>–2</sup> m. The distance from the screen to the slits is 7.0 m.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAnAAAACSCAYAAADFAPcDAAAZ5klEQVR4Ae3dT3CcxZ3G8WYrBVWhyvIZbPnADSLlFGIR+WpvkI/gBHlPG6fWVk5kqxabS0y2FpsD+IScqgAn5GwBl1RkFqdSm9qVCpMcqFoLuEs4cKMkU8lVW88rnklP6+3RaPzqVc/o21Xjmem33+5+P++45zf9/tEDm5ubm4GEAAIIIIAAAgggMDQC/zA0PaWjCCCAAAIIIIAAApUAARwfBAQQQAABBBBAYMgECOCGbIfRXQQQQAABBBBAgACOzwACCCCAAAIIIDBkAgRwQ7bD6C4CCCCAAAIIIEAAx2cAAQQQQAABBBAYMgECuCHbYXQXAQQQQAABBBAggOMzgAACCCCAAAIIDJkAAdyQ7bBR6O74+JFR2Ay2AQEEDqAA49cB3OmFbjIBXKE7hm4hgAACCCCAAAI5AQK4nAz5CCCAAAIIIIBAoQIEcIXuGLqFAAIIIIAAAgjkBAjgcjLkI4AAAggggAAChQoQwBW6Y+gWAggggAACCCCQEyCAy8mQjwACCCCAAAIIFCpAAFfojqFbCCCAAAIIIIBAToAALidDPgIIIIAAAgggUKgAAVyhO4ZuIYAAAggggAACOQECuJwM+QgggAACCCCAQKECBHCF7hi6hQACCCCAAAII5AQI4HIy5COAAAIIIIAAAoUKEMAVumPoFgIIIIAAAgggkBMggMvJkI8AAggggAACCBQqQABX6I6hWwgggAACCCCAQE6AAC4nQz4CCCCAAAIIIFCoAAFcoTuGbiGAAAIIIIAAAjkBAricDPkIIIAAAggggEChAgRwhe4YuoUAAggggAACCOQECOByMuQjgAACCCCAAAKFChDAFbpj6BYCCCCAAAIIIJATIIDLyZCPAAIIIIAAAggUKkAAV+iOoVsIIIAAAggggEBOgAAuJ0M+AggggAACCCBQqAABXKE7hm4hgAACCCCAAAI5AQK4nAz5CCCAAAIIIIBAoQIEcIXuGLqFAAIIIIAAAgjkBAjgcjLkI4AAAggggAAChQoQwBW6Y+gWAggggAACCCCQEyCAy8mQjwACCCCAAAIIFCpAAFfojqFbCCCAAAIIIIBAToAALidDPgIIIIAAAgggUKgAAVyhO4ZuIYAAAggggAACOQECuJwM+QgggAACCCCAQKECBHCF7hi6hQACCCCAAAII5AQI4HIy5COAAAIIIIAAAoUKEMAVumPoFgIIIIAAAgggkBMggMvJkI8AAggggAACCBQqQABX6I6hWwgggAACCCCAQE6AAC4nQz4CCLQmcP36fBgfP5J9XLhwvmdfLl58oWtdlV9bW+u5DgsRQACBYRYggBvmvUffERgRgQsX5sLa2t1tj+npE2FsbCxcuvRidkuvXHk53Ly5GK5efaVaf3n5wyp4m539cXYdFiCAAALDLvCtYd+Ag9j/u3c/D59/fjf87W9/rTb/e997Mhw6dKh6rWUff/xxePjhh8O3v/1weOKJJzrLDqIV2zy8ApqVW15eqgKz8fHx7IYoeJuZOR1mZ89WZVT27NmzQbNymoXrtW62UhYggAAChQsQwBW+g+Luffrpp+Gll34RPvroo3D8+PHw1VdfVYu//PLLcPnyS0HL33rrzfDYY49VQdtDDz1UlT158lS4fPlyOHLkaFzdvr3WTAsJgV4CGxsbYX7+9TAxMdkJzOrKK0DT49ixY12LNXOnpOBOs3txWlm5E2Zmnq5m9ZaWlqogUcsVBGqmzzN6ylM916//qpoFjOvgNQIIILDfAhxC3e890Gf7Cs7OnHkmnDr1j9VhonfeeS/84Q//XT30WrMNH3zwX+HDD2+HP/7xf8Jvf/u7oPxPPvmsCuZOnToZ7t2712drFENgfwUUvCmIm5vrDr7SXikYU0pn2XTYVWl9fb16rvtHbWimTj8odPhVwd709FNhcnKyyrt58/2g+hXQkRBAAIHSBAjgStsjmf5o5u3cuZ+Gn/zk3LYSOmz64IMPhi+++GLbMh1afe21a2Fq6qlw+fIvti0nA4ESBW7cWKhm3zQrdj+p14UMqtv16/Crgj7NuHnGTrN/eugwLgkBBBAoTYAArrQ9UtMfzb7p8fzzP69ZGqrDo7/85b9Xy3WotC4p/7333mUWrg6HvKIEFLxp9k2zY3uZ0sOuasszd25X79UXEgIIIFCaAAFcaXukpj+///2t8OyzZ2qWhHDr1gdVvpZrdk5lNSOXJp3/pvPmXD5dznsEShFYXFysAinPjt1Pv9JDq/dTF+sigAACJQkQwJW0NzJ9uX37wzA1NVW79NatW+Hcua3Dqjpc+swzzwbl1SUdRtVMHgmBkgV03pkOXaazYXV9Vjml9FCpZ80OHz5ctxp5CCCAwNALEMANwS5U0KXbgdQlzaidOnWqs0iBXm6W7fjxqfDZZwRwHSxeFCeg4E3B14kTW1eR7tRBzbDpsbq62lXU561NTEx05fMGAQQQGBUBArgh2JNff/117S1AFNgdOjTWtUxXqeo2I3VJM3QlzMDpjvskBOoEVlZWqux+Zt+8vg616rw5PZQ0G7ewsHURhG8n4rI8I4AAAqMiQABX+J68fft2ePTR+oBHs2npzJyCNJWvC9RUVsEgCYFSBXzoM3fumm71oR8A8a095uZ+Vt0rzn9OS7cCUQCo+7eREEAAgVEVeGBzc3NzVDduFLZLAdy1a69W93RLt+fatdeqrPTqVN0v7vnn/7X2vDl9+e33jXR36sO7774T9NB97EgIIIBAGwK6zZICf10Mph/CubTT+JVbj3wEmhZgBq5p0Rbr0yzbkSPbZ+d0xWmvc93qZuda7Ha2KQVtU1PHq+BNASgJAQQQaEtAp59sXTD2/aAfx9z4vC152hlUgABuULkC1rt3b6Pr/Dd36ejRo9nBR7cSKW1gigM33XRYM2+5q269jTwjgAACTQpozNHY88YbbxHINQlLXXsmQAC3Z7RUvJMAgdtOQixHAIG2BQjk2hanvUEF+GP2g8q1tF6vQ6G5LuhE8N1cxZerZy/zdaj06NEj3/yZr/p73O1l+9SNAAII9BJQIDc19V7wechvvPHr6s8Z9lqHZQi0KUAA16b2AG3pHLf8bUHGqnPd0sONCvpy55CpLgVO+53+8pe7QY8f/ejZ/e4K7SOAAAIIIDB0AgRwhe8ynVibS7otSN0FCcrrdRWVLnLY7/TJJ5+FN998I+hXrbYjd9XsfveT9hFA4GAKeOZN4+m5cz/tXJ3qq/8PpgpbXZIA58CVtDd22ZeTJ09V0/vxavorDLq5b3p/uLhMCa8VYOr2J7dv/ynoT3ydO/fPQbc/0aBJQgABBPZLQGOQxiKNSRqbNEZprOr1o3i/+kq7B1ugiABuZubpoIfTxMQT4cKF837b6vP16/PVjUL1J32U1A/1ZzcprSO3rsrp5qODJgVpY2OHgu5fpKSrS/Xr8MyZ+j98P2g7e7kegdxe6lI3Agj0K0Dg1q8U5UoRKCKASzFWVj4t5i7qupu7+rMXaX7+9ervPt5P3a++eq364/Xf/e5EOH78yfD44zoc+fP7qXJf1k0DOd28mIQAAgi0JaCjF8y4taVNO00IcA5cE4r7WIdm4W7f/ij8+c9/Co888kjtfeH2sXu7btqB3DAGobveWFZAAIFiBC5ffqmYvtARBPoR6HsGTof79DcG9WdE9NAhT/1dwjjpj0kr32VmZ5/bVkaHJuMydYcQ40OoucORqkMPJ62junTIM25ff9jadbjfPjzqdXs91x1CjeuTif4uo+pWfpwWFxe7zLytus2HyuvZf9txN32K2/DrJ5/8/tAHb94WnhFAAAEEEECgt0BfAZyCDAUp+qPR+juaeuiPTSu4UYCkpOBNAcrExESnjPJVZnl5qSrj4E33KHM9Wv9+g5eq8m/6MDk5WdW9vPxhVa8CrKWlpSrPh0LVp0GTtlGHPnVoVdtw6dKL1bbX1Sc3l9OzjOTo7dfzzMzpqp6Jicm6KkYyT24kBBBAAAEEEBhcoK8A7s6drRP6p6dPdFpyYKJATklBjYKQq1df6ZS5ceM3VaB35cqVb8rMV8GL8p1UT1M3nd0KKueqqvVa/VHdbk+vT59WwLTWCTzdj36etZ6CsNnZs1XgpXUUgOl9XVLA68BM5dSn5eXluqLkIYAAAggggAACfQv0FcCdOLEVuHkmzrNubkUzaMpTcJQmBX1erpk4BzQup6AqzfOy3T6n9fQKDDc21ndbfWcm0R6uIH3vfM1Gxmls7HD8ltcIIIAAAggggMBAAn0FcArCNFO2urpaneflc+F0OFApDejinjiIcsDk93Vl4rwSX+ucNaV0G9L3JfadPiGAAAIIIIDA6Aj0FcBpc3UIUIdHdf7SzZvvV+910v7WCfxbh1HrWBz0jI8fqxb7fVy2Li9eXsprB2ppwDos/S/FkX4ggAACCCCAwP0J9B3Axc3oUKXPXVMwo/c6v0tXXaZJh021TMGPgkAdTk0Dnn4uYkjXWVtbTZva8/c+B9DnBLrBlZUVv+QZAQQQQAABBBDYc4G+AjjNsuk2HToHzkmzbwqqfP6XTthXIOZbZaicbiOiAM8XNqiMUnwVqMqkwZnb0PP09HT1dmFhoZO90zqdgg2/UCCqCxZ0IYMt9KwLOAZJCmo9m9fLYJC6WQcBBBBAAAEERlegrwBOt8pQ8KXgzPdYW1h4uwrMfAWmnhWoaTbKZcSmmTrPXCkA8hWhLuOZuRyxZve26r3TqVdBY3rBQm79pvPVF1koCNU2KLi1gbZvN8lBr+rxrVZ2s/6wltX2khBAAAEEEEBgcIEHNjc3NwdfnTUl4HvgKTh1sNqkjAKepu6d1mRdg25jCX0YtO+shwACB1uA8etg7/+Str6vGbiSOryffdk6n+9I12FiHQLV4V0FbnsRvO3n9tI2AggggAACCJQpQAC3i/2iAC09TKxbqug8PR8a3kV1FEUAAQQQQAABBAYS4I/Z75JN57v5nLddrkpxBBBAAAEEEECgEQFm4BphpBIEEEAAAQQQQKA9AQK49qxpCQEEEEAAAQQQaESAAK4RRipBAAEEEEAAAQTaEyCAa8+alhBAAAEEEEAAgUYECOAaYaQSBBBAAAEEEECgPQECuPasaQkBBBBAAAEEEGhEgACuEUYqQQABBBBAAAEE2hMggGvPmpYQQAABBBBAAIFGBAjgGmGkEgQQQAABBBBAoD0BArj2rGkJAQQQQAABBBBoRIAArhFGKkEAAQQQQAABBNoTIIBrz5qWEEAAAQQQQACBRgQI4BphpBIEEEAAAQQQQKA9AQK49qxpCQEEEEAAAQQQaESAAK4RRipBAAEEEEAAAQTaEyCAa8+alhBAAAEEEEAAgUYECOAaYaQSBBBAAAEEEECgPQECuPasaQkBBBBAAAEEEGhEgACuEUYqQQABBBBAAAEE2hMggGvPmpYQQAABBBBAAIFGBAjgGmGkEgQQQAABBBBAoD0BArj2rGkJAQQQQAABBBBoRIAArhFGKkEAAQQQQAABBNoTIIBrz3rgltbW7g68brpik3WldfMeAQQQQAABBNoRIIBrx5lWEEAAAQQQQACBxgQI4BqjpCIEEEAAAQQQQKAdAQK4dpxpBQEEEEAAAQQQaEyAAK4xSipCAAEEEEAAAQTaESCAa8eZVhBAAAEEEEAAgcYECOAao6QiBBBAAAEEEECgHQECuHacaQUBBBBAAAEEEGhMgACuMUoqQgABBBBAAAEE2hEggGvHmVYQQAABBBBAAIHGBAjgGqOkIgQQQAABBBBAoB0BArh2nGkFAQQQQAABBBBoTIAArjFKKkIAAQQQQAABBNoRIIBrx5lWEEAAAQQQQACBxgQI4BqjpCIEEEAAAQQQQKAdgQc2Nzc322mKVhBAAAEEEEAAAQSaEGAGrglF6kAAAQQQQAABBFoUIIBrEZumEEAAAQQQQACBJgQI4JpQpA4EEEAAAQQQQKBFAQK4FrFpCgEEEEAAAQQQaEKAAK4JxSGt48qVl8P4+JGwsbHR6BasrNyp6r1+fb5nvRMTT4QLF873LNPEQrWhtpzSdtXPixdf8GKeEUAAAQT2SeDmzcUwO/tcz9bX1taqMvquGZaUfg810e9vNVEJdSAwTAIrK592dXd+/vUwPX2iK483CCCAAALtCywuLoadAjMFecvLSyGES+13sKAWmYEraGfQFQQQQAABBBBAoB8BArh+lEagjA6Talpah0z10GtNQ6dJhxN1iNHlNO0bl6ubBlbdKq9DsnFaXV0NMzNPd+rq5zClD+u6/Z0Ow6o9lZmefqrTjtrUL7Rc8iFU91vPKq82d/rll6uTfAQQKEdAY5bGKo8jeq4bf+LxRuPCjRsLnY3QOKJx0uOmlmusUIrXU91141Q6Lqk/Xj+uQ23udpzsdLKQF+q/Htpmf3/oOXXR9ms/xPsl/t5QHRqLVS7nqvJeR+Xl6hS3r/W1LP7+crn4We15H2udun6nnye1G39XpMtVT+47Nm57p89IXLb2tW7kSxp9gR/8YGrz6ad/uLm6ulpt7Pz865tHjz5aPdbX16u8F174t+r9wsLb1XuV1Tpa12XOn/+Xze985/EuMC1TXS+//B9V/p07/9ep23UpT/U899yPO+uqHtXnpGXKW1z8XZWlZ71Xv3JJZdS221E51ak8b2va57Td9H2uLfIRQGA4BDRu6eGk8ScdSzTeaJzweKPxK36v9fXe45rL9TNOeXzVs5LH0rhPbk956p+SxrG4zSpzCP6xlWz8XeHvE7tpM1RO3wPeXi3TftF6Tul47fz42b6uR8vcnr8LbB5/f8V16LX6mn4uXLfrURnVoYe/U/wZ8LZqWbwNbjve3+l2uZ1en5G0v+n7kGbwfvQE/EFZWvrfro3zfzp9CPUfoW7gSPPTD6Eq1Prxul5HZeOU9iMOnDxw+cPs9bxO/B/Vy/TsQdD/seJlfp32OW5XZdL3Xo9nBBAYPgGPR71++Gks1JiVltFY4C9ij4/x2NLPOKXyqjsd/zwueozz2OVAwdIKBuIvfueX/FxnZQcHwB7L44BO25Tmp+N13XZ7HX8v2NZteZ1cvperL9pX6T7wcj27rbiMPz9a5s+E++J1vX8d5MXbZZudPiOuK/fMIdTaecnRyrxz504YGxvbdqL+6dOnOxu6vLxcvT5xovtk/omJyTA+Pt7zkGSnkuRFWtfMzFZ7KysrSckQ1Ecll3GB6enp6qX753w/uw1Ng2tafafpcq/HMwIIjKaAxzqNCXqkh/G01R6DJicnuxB0gdONG7/p5KkujX9O/YxTWyfXh+CxyetqLFV9S0s6+f7vaWJi4u9vQghjY4e73g/Lm9RK7+Pk76F0jPf71CVed6fX/n6oM+/1/aWL17RcF07oc6LPS5rcr/hCN71eW7sbLlyYC7OzZ6vXWs+Hd3X4tO5z57p3+xnxeukzAVwqckDfr6+vV1ue/qdTpgaU+NyNfonSuvzebcX1uP74XDadR6BzDZTq1lG+/iNdv/6roPPt4vMJfI5E3AavEUDgYAgoCNMX6/z8fOd8NX2p+gva44nHpH5V+hmnXCY910vjmZZ5eb9tjkq53I9r74P7cem1P3t9f6ntGzf+MyiI1t0IfN5kfO6c++V+1u0Pfbb0XRUHkgrucsl13u9nhNuI5IQPWP7hw1u/+vzBijd/Y2M9jI8fi7MGeu263VZcif9z6BewX8fLe73WLzg9rl59pTqxVIO2f/1cuvRir1VZhgACIyoQ/9/XeLCw8HZ1Ar1+9HkM8pjUL4HHpl7jlC+E0A9Lzy71W/8ol9NM19ra6rZN9D6IZzq3Fdoho9f+3On7S+3qs6KH+qJATp8XBZw3b77f+T7SMu//uDsqqxm1dH/XXTTj9VxPuo6X9/vMDFy/UkNcTtPK+vD516c3xVPDeu9DlXGe8nWljT7I6TS/63CZ+L1f+3CD37t9t+V8PftQhqeWvUzr6Jer13V+7lmHKfSfQv9Bcr/4cuuSjwACoymg2ZCzZ/+pGgcVRHg8S8coHQHQVYi51M845UNtad0ag1X3QT06ILu67yGP7ceODT5J4O+UQb6/4n2t7w0Fcgq8HWz6sGz83aTvFl9p6v3s/e76fJje7+Nnl/W6XrbbzwgBnOVG+FmHEhTYaGbKQY1/NXiztVzllO9fkCp78eLF6hwB/5r1f0KVU1KZK1euuJqu57gu/SfVLxv3patgCJ18DW7+D63gUe/1Yc/9ktVyDYpeR/WqXf1H8H+8tK30fRzsaT0SAggMr4C/BHVYy0njlM5z0jinh8YUPTRueOzQuKFyc3M/82rbnj1+9RqnNKPjsdTjpPqkw3Iaa3rVv63BEcpQEC172fkWHLL3jdRlpiQjJZlpf9Qll9FyPfr9/krrUvsKxLyftFx5Ctb8naN+aZ8uLCx0+qNtUJqbm+tMPmg7nLSvvY113ymNfUZyVzeQP1oCuhJGV7zoihs9dKVVepWMtlhX1ehKLJfTOvFVWC7j5bpiylfp+AogX/mjfF+dpPJ6H6e6qz/dJ9efXiUWr+/XaZ/Vp/iKofjqH62TtuuriNRmeoWU2+AZAQSGR0BjkMY4jyN61jjgKwK9JfF4o3EhHqM0dimvLsXrqe66cUp1aSxyH9SfeCx1HenVi2pXj2FKdVa+Gljb6aQ8WdlEz/FylZOH3dJlcT3ev7FV+l1Q9/3lOvys8V91xH2KPwcqp/2mulxG5ePvCu9LL9c2qg69d7n0e0j17vQZcR9zzw9ogaNGnhFAAAEEEEAAAQTKF+AQavn7iB4igAACCCCAAAJdAgRwXRy8QQABBBBAAAEEyhcggCt/H9FDBBBAAAEEEECgS4AArouDNwgggAACCCCAQPkCBHDl7yN6iAACCCCAAAIIdAn8P0QN5HJJmORfAAAAAElFTkSuQmCC"></p>
<p>Calculate the width of each slit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the separation of the two slits.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain the differences between the pattern on the screen due to the grating and the pattern due to the double slit.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The yellow light is made from two very similar wavelengths that produce two lines in the spectrum of sodium. The wavelengths are 588.995 nm and 589.592 nm. These two lines can just be resolved in the second-order spectrum of this diffraction grating. Determine the beam width of the light incident on the diffraction grating.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the diagram shows the combined effect of «single slit» diffraction and «double slit» interference</p>
<p>recognition that there is a minimum of the single slit pattern</p>
<p><em><strong>OR</strong></em></p>
<p>a missing maximum of the double slit pattern at A</p>
<p>waves «from the single slit» are in antiphase/cancel/have a path difference of (<em>n</em> + <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>)<em>λ</em>/destructive interference at A</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>θ</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4.1 \times {{10}^{ - 2}}}}{{7.0}}">
<mfrac>
<mrow>
<mn>4.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>7.0</mn>
</mrow>
</mfrac>
</math></span> <em><strong>OR</strong> b</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{\theta }">
<mfrac>
<mi>λ</mi>
<mi>θ</mi>
</mfrac>
</math></span> «= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{7.0 \times 5.9 \times {{10}^{ - 7}}}}{{4.1 \times {{10}^{ - 2}}}}">
<mfrac>
<mrow>
<mn>7.0</mn>
<mo>×</mo>
<mn>5.9</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>»</p>
<p>1.0 × 10<sup>–4</sup> «m»</p>
<p><em>Award <strong>[0]</strong> for use of double slit formula (which gives the correct answer so do not award BCA) </em></p>
<p><em>Allow use of sin or tan for small angles</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <em>s</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\lambda D}}{d}">
<mfrac>
<mrow>
<mi>λ</mi>
<mi>D</mi>
</mrow>
<mi>d</mi>
</mfrac>
</math></span> with 3 fringes «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{590 \times {{10}^{ - 9}} \times 7.0}}{{4.1 \times {{10}^{ - 2}}}}">
<mfrac>
<mrow>
<mn>590</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>9</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>7.0</mn>
</mrow>
<mrow>
<mn>4.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>»</p>
<p>3.0 x 10<sup>–4</sup> «m»</p>
<p><em>Allow ECF.</em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>fringes are further apart because the separation of slits is «much» less</p>
<p>intensity does not change «significantly» across the pattern <em><strong>or</strong> </em>diffraction envelope is broader because slits are «much» narrower</p>
<p>the fringes are narrower/sharper because the region/area of constructive interference is smaller/there are more slits</p>
<p>intensity of peaks has increased because more light can pass through</p>
<p><em>Award <strong>[1 max]</strong> for stating one or more differences with no explanation</em></p>
<p><em>Award <strong>[2 max]</strong> for stating one difference with its explanation</em></p>
<p><em>Award <strong>[MP3]</strong> for a second difference with its explanation</em></p>
<p><em>Allow “peaks” for “fringes”</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Δ<em>λ</em> = 589.592 – 588.995</p>
<p><em><strong>OR</strong></em></p>
<p>Δ<em>λ</em> = 0.597 «nm»</p>
<p><em>N</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{{m\Delta \lambda }}">
<mfrac>
<mi>λ</mi>
<mrow>
<mi>m</mi>
<mi mathvariant="normal">Δ</mi>
<mi>λ</mi>
</mrow>
</mfrac>
</math></span> =» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{589}}{{2 \times 0.597}}">
<mfrac>
<mrow>
<mn>589</mn>
</mrow>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>0.597</mn>
</mrow>
</mfrac>
</math></span> «493»</p>
<p>beam width = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{493}}{{600}}">
<mfrac>
<mrow>
<mn>493</mn>
</mrow>
<mrow>
<mn>600</mn>
</mrow>
</mfrac>
</math></span> =» 8.2 x 10<sup>–4</sup> «m» <em><strong>or</strong> </em>0.82 «mm»</p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A vertical solid cylinder of uniform cross-sectional area <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> floats in water. The cylinder is partially submerged. When the cylinder floats at rest, a mark is aligned with the water surface. The cylinder is pushed vertically downwards so that the mark is a distance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> below the water surface.</p>
<p style="text-align: center;"><img 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" width="509" height="210"></p>
<p style="text-align: left;">At time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math> the cylinder is released. The resultant vertical force <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> on the cylinder is related to the displacement <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> of the mark by</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mo>-</mo><mi>ρ</mi><mi>A</mi><mi>g</mi><mi>x</mi></math></p>
<p style="text-align: left;">where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math> is the density of water.</p>
</div>
<div class="specification">
<p>The cylinder was initially pushed down a distance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>250</mn><mo> </mo><mi mathvariant="normal">m</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the cylinder performs simple harmonic motion when released.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The mass of the cylinder is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>118</mn><mo> </mo><mi>kg</mi></math> and the cross-sectional area of the cylinder is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>29</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></math>. The density of water is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>03</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math>. Show that the angular frequency of oscillation of the cylinder is about <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>4</mn><mo> </mo><mo> </mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the maximum kinetic energy <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>kmax</mi></msub></math> of the cylinder.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during <strong>one</strong> period of oscillation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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" width="610" height="371"></p>
<div class="marks">[2]</div>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">the </span><span class="fontstyle2">«</span><span class="fontstyle0">restoring</span><span class="fontstyle2">» </span><span class="fontstyle0">force/acceleration is proportional to displacement </span><span class="fontstyle3">✓ </span></p>
<p><em><span class="fontstyle4"><br>Allow use of symbols i.e. </span><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>∝</mo><mo>-</mo><mi>x</mi></math><span class="fontstyle4"> or </span><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>∝</mo><mo>-</mo><mi>x</mi></math></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">Evidence of equating <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><msup><mi>ω</mi><mn>2</mn></msup><mi>x</mi><mo>=</mo><mi>ρ</mi><mi>A</mi><mi>g</mi><mi>x</mi></math> «to obtain <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>ρ</mi><mi>A</mi><mi>g</mi></mrow><mi>m</mi></mfrac><mo>=</mo><msup><mi>ω</mi><mn>2</mn></msup></math>» ✓</span></p>
<p> </p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><msqrt><mfrac><mrow><mn>1</mn><mo>.</mo><mn>03</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>×</mo><mn>2</mn><mo>.</mo><mn>29</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></mrow><mn>118</mn></mfrac></msqrt></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>43</mn><mo>«</mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</span></p>
<p> </p>
<p><em><span class="fontstyle0">Answer to at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">3</mn></math> s.f.</span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi mathvariant="normal">K</mi></msub></math> </span><span class="fontstyle1">is a maximum when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn></math> hence</span><span class="fontstyle0">» <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mrow><mi mathvariant="normal">K</mi><mo>,</mo><mo> </mo><mi>max</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>118</mn><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>4</mn><mn>2</mn></msup><mfenced><mrow><mn>0</mn><mo>.</mo><msup><mn>250</mn><mn>2</mn></msup><mo>-</mo><msup><mn>0</mn><mn>2</mn></msup></mrow></mfenced></math> </span><span class="fontstyle3">✓</span></p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>71</mn><mo>.</mo><mn>4</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math> <span class="fontstyle3">✓</span></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">energy never negative </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">correct shape with two maxima </span><span class="fontstyle2">✓</span></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAgEAAAE4CAYAAADCeyCZAAAgAElEQVR4Ae19iXdUZba9/8Z7v9XTe7a+sdvu1m59+vR1K4o4KwK22ip2q20LKGFKIAOBhEFmlCkBZAphDmSEhDDPYQjzPEMYMjKD4vmt/WmFSmWoqnu/ut+9t3bWqlWpqjvus885+55vuk/4RwSIABEgAkSACMQlAvfJ93eFL+cwaGiol+QBA+S7b+8Qd3KPHCAHyIEoOXD3u29lw4b1xC1K3Jrk+SC5QxFgB8go9/3+7ncyfvw4uf/++6WstJQkjhK/JiTmvuQPORCXHIAIyM/Pj8t71xYDKQKce/IPNtrly5fk448/lnfeflv6909iNYBBnIGMHCAHouQAHqYqKyuJW5S4BeeiIA0grATYATLKfWfPniWFBfnyeY8esmjhQildsZxEjhLDJkTmvuQPOUAOkAPRcyBIBVAEOESgy5cuSs8vvpCG+jolAmpqqiUlJVnu3L4VvQEdumYmXDMVI+JO3MkBciCmHKAIcJZgKF9Nnz5dyleWydUrDUoEwMC5uXNl9apyigCKGnKAHCAHouAAOljHNElGcS2evA6KAGdFAJ7+e/fqJRADwSKgvq5WUlJS5PatmyS0352O90eOkwNaOMCOgRryF0WABhCjcOjiokLZ+OOQlmARAFGQn79MDuzfr8U5PKlIo8CR9+csb4k38XYjBygCNPCSIkADiFEkLyT7gDMFi4DAd3x31h7Em3iTA97lAEWABttRBGgAMQoREBxwKALMYR9sB/5PO5AD3uQAREBJSUnjgxXtaMGOoSLg5s0bAmBDwcQTbGu/hW4bzefv796VWzdvxOU4eYoAC4S1KLii4SS3pV3IAe9w4MqVhmb5ivaLwn7BIgDJHxPYHDjQvF26rrZG/v7JJ3Lq5EnbgNdUX5ZtW7eoznE3rl+TTz/9u2yvqLB9XK8ZniIgCqIy+cedf3jNn3m99GdPciBUBPz2N7+RrVu3NAs4165ekawpUwRj3O3eaEbGYPnbX/+qnv7RGz47K0uOHT1q+7h2r8vp/SkCGDSc5hzPR875jQPB/az8dm+O3E9bIuDmjety9swZwdM6FrmpOn9OTWij/q86LxAG586ekaNHDsulixfUk33gopHcz5w+pX47e/aM3LlzWyX5Kw310qNHdzVd7oWq843HxbkC+9bW1sjxY0fVCxWIwPeh77gOnP/I4cNy+tRJ1awQ2Ka2plpQccD+x44eafY7iFN9+ZL67cTxY2rinsC+uF/cz8ULVeoarl+7qu6tuvqyHD16RM6cOS24D5wb1RMM7wu9TuyP7wPHbOmdIoABuSVe8DvyghyIjAOI49u3x18VWSs/WhMBSIR9+vSRzp06qWSICsAzzzyjEi6SZ/vnnpPPP/9c3njjDfnTH/8o//fUU7Jl86bGRJ+SPEDat28vr77yijz//POSmZGhxETekiWCasN//dd/SlpammC2vGefbSdrVq9W+27auEFefvlleeXll+XFF16Q59u3l8OHDjZLpt/euS1jx46RZ9u1a9y222efqcSLxIzV+bp07izvvvuOvNChg/zh97+XQYPSVdIGcTBNL75/6cUX5aWXXlLb7t27R52nuKhInnv2WXXtT/7v/8r6dWtl86aN8uKLL6preu211+TtP/9Zfv/II0poYArgD7t2bRzjj/PjnhcvWtTsuoONRxEQmaMHY8b/iRk5QA4EOIBYywWEbPKhJRGwds0aNY0tEiyesgE4noof/t3v5OCBA+op+aFf/1pU0q2vU0/B7/3lL5KUmKi2zcqaIq+9+qqqBOBpHU/iEA0L5s8XJO9+/fpK164fCJ7+kQgfeeRhtZIeKgvPPP20Wl0PnQXx+xeffy4pycnNOiuuXr1KHv3DH+TgwQOqmgBhgqQ/bOhQtS2m5X3ooYdk184dcuvWTVmat0QefvhhdU2oUDz9pz/JooULVOKG4Bk+fJh06dJFrl69Ikvz8uTnP/uZmtv/0qWLqmLwwgsdZNzYMaraUH35sqpk/OLnP1e/7d+3T355//2NWFVs2yoP/PKXgmpEgKwtvVME2CQv+wm0ya+WOMfvyDk/cYAiQAOfQ0XAbx56SN5880356U9+ItsrtjUGmVAR8MjDDwuemAOEGjlihHz44Ycq4XZ6800ZOXKEHDl8qPGFJ3M8LUMUYNW8QJ+AYBGwa+dO+Z/HHlOJNXBcnPfkieNNmhrwW2K/fmrmveBzTJ2arUQEiAER8M47bzfuBzHzu9/+VnZXVsqK5cvl+efby6GDBxqvb9WqcnnqySdV1QEiAJWD8+fOqvvbt3ePoCJw7uwPn3H+hQsXqMQP8YHKwhuvvy5ZUyar7XGv7737rnzfwiiLwH3hnSJAA4EpBBp9MJhb/J/cigcOUARo4HmoCPj1r36lkiHK8JjGFgkOZAoVAUjWmzZubAxAo0eNUiIA7eDt2j2jmgcgBgIvVAaQHFEJaE0ElJevVEm8ob7tuaC///6uvPvuu/Loo39oPD7Og0QMoREQAd26fdZ4fUePHFGVDIiAadOmyX/8+7832bdjxzfU/ujfABHwxz/+nyr14943btwg7Z55pkmnyKLCAvW0DxGAbSZNnCAdOjyv+hagmSB/2dLGc7fmjBQBGghMERCWZ63xj9+Tf17nAPJTRdDDqtfvx8j1h4oAVAJKS1fI5k2bBIJg3Zo1KshEKgJQxn+zY0eZOGGCKp3jM1579uyW3ZW7lKhoTQTs2tW8EoBpdCdOnNBshb1+fftKYr++Tc6BEQa47nAioKSkWDo8/7zqPxC4PiTz9evWCToBhoqAw4cPyROPP646CQaMlDNnttz/r//aWLVAnwk0P+TOnSv/9uCDgk6EgW1be6cIYBBujRv8ntwgB8gBRzgQKgICQwSRSIdkZkq7du1UsoxUBOCis7OmyLPPPit7dleqpIqSPZLumNGjlQjAsrlv//ktlUDRyz7QJwAJGOcbO2aMOid63CckJMhfP/xQNSMEA7KqfKWgXwI67GE/jFxAdaBH9+5hRQBGEqD0P2XyZKmvq1PnGjVypOqEiGQeKgIw0uHtt/8s/ZOSVJ8CCBN0Wgz0CQhc1/vvvaeaEdAUEaigBH5r6Z0igE7eEi/4HXlBDpADjnEgVAR06NBB8ESOC0ASfvXVV2TGN9+ohI3Eh7I6ht69/tprTYZmYKx/n9691X5I7Cj9v/DCC9K5c2d56aUXpVu3blJX+8OQuWVLl8rvf/+IfPbZPwTDBPE7nsJxzp07tstrr70qb77ZUY08QJkefQJCAUGzwujRo1SHw86dO6mOiDgX2vEhYAalp6vOjYH9Tp44oRI3EjgStOoX0L69qlp07NhRXn7pJVmzelXjb126dG4y7O/UyRPy7jvvqO1R6ej6wQfy4AMPNFYCcB7c1//7539WCwEFztvWO0UAHb0tfvA38oMcCM+BcM3HxDAMhsEiAGBh7DtK5AHgaqqr5UJVlXoSR8e4O7dvqf+RbDGNcGA7LJEbPJEQkvSpUyelsnKXHD9+rEk5H8dAif3QwYPq+3Pnzqrhg8HH2rdvr+zft1fNRRD4PvQdyR7XgXMcOnRQjSYIbAOhEmivx3e4Hlx/YKleCAH03sewQJwreJx/oLKA42Nf3BtW/8MxcQzsh5EFTz/9tOrcFzgn+gmgrwRGOQS+a+udIiAMOdneHxGP2uIYfyPH/MwBxOji4mL6iZ1YGSoC/EwYq/cGgYB5EDIGD5b9+/epJgh0Qhw5cqSqOlRVnZfylWVqHgEMUYykKQDXQhHAAG2Vk9yP3CEH7qr4y3kCbPoCRUBkAGLs//vvv6fmIkBzAPotXGn4YeGKyl071cRDgcmKInVOioDIsI8UT25HPMmB+OIAKgEUATZtThEQOYBoUmhoqJfr1681edoHEdEP4s6PUyNHGogoAiLHPlJMuR0xJQfihwOIvUVB89XQ9hZsTxFgATQ77S9B+1IEmMOewYLYkwP+4AD6bNGWNmxJEWADvKCEboWEFAHmsLdiL+5De5ED5IDvOEARYI7UFAHmsPedI9sUpMSDXCQH4pQDFAHmDE8RYA57BjxiTw54nwMYibV3z242B9h5CKAIMOcIFAHmsGcCIPbkgPc5wNEBGmxIEaABRIsqjCLAHPZMAMSeHPA+BygCNNiQIkADiBQBLMdZ5AATkTn/I/bex54iQIMNKQI0gGgxAbASYA57JgBiTw54nwPoE7Bzxw4+hFjMQcoHKALMOQJFgDnsmQCIPTngDw5EOk077d2KvSkCWgHGjrKKcF+KAHPYMyAQe3KAHCAH7gZJAJH7CIizTkER4Cze5DfxJgf8x4Eb16+zOSDCB88W+R8kAygC7ABpYV+KAP8FpBadzAI3eBxygxwIzwF0DCwpKaEIsBNjKALCEy1WzkgRYA77WNmUx6VNyQHnOMDRARqwpgjQAKJFFUYRYA57BmpiTw54nwMUARpsSBGgAUSKAJbjLHKAicic/xF772MPEVBQkM/4Yyf+xJsIuNJQL0OGDJGEhIRmrwH9+8v5c+ccIxQrAd4PQkwktCE5YJYDN65fcyxm+9LW8SYCjh45LL/61a9kSGamZGdlNXnlzJkt9XXOrU1NEWA2ePjSoe08EXBfJhNyIP44EG8iYOnSPPmfxx6TmurLxo1NEUARQCFCDpAD5IBRDsSbCEhKTJT2zz0n3965TRFA1W+cA0adn/an/T3OAcwWiOou/ciGkIonEfDdt3fkw65d5dl27WTY0KFNXqNGjpSq8871BwBpWQmwQVyPBy8GLdqeHLDPAY4OsI9hkAbw/4yBFy9ckMcff1w6vvGGfPLxx01eKSkpUl9X66iipAjQQGCKAUc5y8RFzrqJAxQBGvgYpAJ8P2Pg9opt8m8PPii7KytdETgpAjQQmCLAFVx2U2LgtcSPX1EEaLB1PImAefNy5dFHH5XamhpXBE6KAA0EpghwBZeZeMllExxAn4DtFRX0ATtxMJ5EwMC0NOncuZMq+6P0H/y6fu2qgFBIzFCXThCaIoCB0wme8RzkGTlADrTKgXgRAbdu3pB333lHHnzgAfnNQw81e6FPALbp1auXVF++1KoICF27OvRzq0C3oNQoAuiY0fCF25Iv5AA5oJ0D8SICMCTw6NEjcuDA/hZfFy9UKRHQrVs3NWtg3pLFcvLkCSksKJBFCxdIdna2oE/BV+PHybatWwUjDYoKC2Ts2LGSM2eO2nf+/PmC2asOHtgvq8rLmwgJbB/6QiWiR/fuTbbTbuAWxIdfz4EKTgBjO+LMr/jwvswmEHAywE+nqo3xYPM7t28xhtqJ8/EiAiJxBlQCPv30U0lLS5MhQzLl5o3r8tqrr8riRQtl+LBh0rt3L1m3do107dpVKiq2SUbGYNm+vUI+eP992bRpoxIDw4YNk86dOsmxo0caiQkBgiGJmJY4+NW3Tx95q0uXxu0iuUZucy+QI5DW1dYoUZc1ZYqkpaYqfJOTByh7rV69Si5fuqgEGnG7hxuxcA6L27duyqWLF2T1qlUqBqQkJyuOgqtTs7Pl0MEDqlmSosCaTYBbUVERYyhFgDUChQZDiIBXXn5ZnnrySVmzerUi1j8+/VSqL1+WFcuXqyQPYYDhhWfPnJbs7CxJTUmW59u3l/KVKwWKtN0zz8jo0aNU/4Lg41+7ekWwbkHwC/MSdO/WjQSOksB4mtq3d4+MGztWEFQXzJ+vqi+YBRL4osJy5vQpVY0ZOXKEpKenS+mKFeq3YJvwfz1+Qxyb4wh/X15SImmpKTJyxJeKi2dOn1bcBEfR5Hhg/z6ZlztXidevv/5a9u7ZoyoFxLM5nq1hAhGQn88FhFrDJ6LvWQm4RziIADQHbNywXrp37y61NdXy2Wf/kJrqaiUCcufOVdUBiIBvpk+TjMGD1ZMmhEJZaalS+395913BC4konAHYJ+Ae9uGwwu8op54+dVK+/HK4ZGZmKCEWyX4QbvPnzRP0+0Azza1bN8PaJpLjcpvo7BcPeOFBYFX5SklKShTECwjWSO779KlTqlIAYXvyxPFmDxGRHCMet6EI0OCDFAH3QETpDoocCTw/f5mUlq6Q8ePHS0N9vRqGgqd9JBA46uFDh6TbZ58JpiEeM2aMrFixXCUmVA2wb1FhYVjnpwi4h324AHbr5k2Zl5sr/fsnyRGL04RiBMismTNlUHq647NDhrs//h45F9yKFZ7uU1NSZMY338iNG9fD+n/ofUDkHjl8SAYPGiR5S5awGSuCCiFEQHExmwNCuRTVZ4oAc8GHIiAy7FGRyczIkNzcubbXfECg3btnt2pG2LJ5s2PDQaNyygiCH48XGXecwAmc2rp1i/Tp00c1S9k9JyqS4PrQIZlyuY2RSnbP45f9a2qqoxZcfrl3LfdBEWAumFAEhMcepdHExETZtm2rVkdHh0J0/iwsyI+4ZKvF4ZjgtdrRtE1Q7sfKpAMHpmldhhzCYvOmjaqycPzYUV9hZtpmPH9I3KUICAHEwSBNEdA29vv27ZWePb+QEyeOxyQIYjjnhK+/ljmzZ6tOnQwObduD+DTFB6N+Zs2cIV999VXM+HP40EFJSUlWnQghDGiDpjYgHhrwoAjQAKJF4UAR0Dr2B/bvl359+8a87R4duaZNnSqzZs2KWSBnoGrdzl7FBgJgxoxv1DA//B/L+zh16qRg2CtGxMTyPF48NoQR5mXx4rW75popAswFKIqAlrHHpE5oX62qOu+Ic0MIZGVNkfnzctk0YFHQuiagOXD96IyWkzNHsrOybPdRiRQ3DC/EHCPoOBjpPvGwHUcHtBxDo7I9RYAGEC0GHoqA5thfqDovCQk95cTxY44GOwwjHDd2jBQXFrKzoEU+RxV4PHyO/GXL5Mvhwx2vHEEApKamyPlzZx31DTfblSKgeQyN2l4UARpAtBjQKAKaYg88MOTS1FLPmMQlIyNDNm/exCBrkdNRByCPnWfL5k1qCB/6k5i41x3bK9QEZfX1dUbOb+Ke2zonRUDTGNoWVq3+RhGgAUSLgYwi4B72KMmPGjVSyleWGZ0o5cKFKjUXwYnjsemM2KojWuQQj3ePQ7HG4uSJE5KY2E9NEBbrc7V2fLSBlxQXybhxYwXzmrS2Xbx8Dzy2bdsW9zjYsjdFgHNBJNRQFAH3sF8wf55MnzbVFW3y+/ftVetHRDLrY6hN+fmeTf2EBbgwYMAA1Uvf9H1hWCL6IyxetMioYDaNA8+vydcoAjQBaeFJjiLgB+x3bN+uZvFDu7xbHLsgP18NH7wT457fbrlfXkfrcQBJd8zo0YIFqdwyTA+zX6anDxT4Dm3Xuu2ITQTYUAREAJKFBB8J+SgC7srlS5dUP4BzZ8+4Kph9e+eOKrmuWF7iquuKhFfcRq9PY8nwiRMnODYSIFL7nT59Svr3768WI4p0Hz9uB0Hkx/ty7J4oAvQGjGgMF+8iILDEMhZsigY3p7ZFCbh/UqJatMipc/I85vyxJewxSgWT9WCGyZZ+N/0dqhPoH4A+NaavxcT50TGwtLQ0Lu9dG94UAeaCTryLgOXLS2TypEmu6AfQmkPtrtzluqaK1q6V3+v1ZTRPYTrgvS6epAdNFahSlJWuiMtEyNEBGjhPEaABRIvNBfEsAs6eOaM6Wrn1CSuQUNEGjGmFly1dGpdBNoBDvL3D7lh+et68XNfPG4GKVfKAAYIJheLNThQBGvIXRYAGECkCogo+3357RzIzM6WioiKq/UwFuGtXr6gge+zoEU9crymc/HRezNmfmpoqsL0X7gurGI4cMSLuhg1CBBQUFHjCRq7lEUUARYDT5CwpLlZDnL777lvPOO++vXvVcsZY5tVpvHg+Z30U4+/R8x429wr2qFxMnDhR1mAEg8WHEq/ca+h1crllm/5BEWATQBsOF4/NAZcuXlBLA9d6cA3waVOzpay01DXDxEKDIT/r8eW8JYvV6oB4yvQSprU1NWrRLfiYl66b16qHt5ZxpAgwZ4B4EwEIquPHj5MNLh0NEM6JMK0wFja6eKGKQdaG+A2Hs8nfz507K8nJyeLViaLWrV0jkyZOcH0/BpM25rlDch5FQAggDga3eBMBFdu2yYgRX3p6ONOmjRvlq/HjXT2igUHOmk8HJgXasmWzZ0Ue7iEzI0N27dzh2XuIhr9oBjl44EBc3Gs0uES1LUWAtYARFcitCIt4EgFquFVampw6ecLTDhtvQVYHz71yjG1btyiRivkrvHLNLV0nJt5KTUkRU4sctXRNsfqOowM05C+KAA0gtpLkwxE/nkTAgvnzJTd3ri/a0xFksbZ7PATZcBz2y+8QqWmpqXLm9ClPC4CAPWbPmiWY+jrw2a/vFAEa8hdFgAYQKQLaDDYXqs6rAIs2db8Eo5kzZ0ghhyb5xp6LFi6Q3Lk5vrkfDG3s3buXeLEDbjQxgiJAQ/6iCNAAIkVAq8ETTjpp0kRx69TA0QSc4G0xX3mvhASpq61t9d6Dt+f/5vwsHPbo6IkqwNUr3pgTINz9BH5ft26tmk0QPhj4zm/v6BOwefMm396fI/aiCDAXnOKhOeDggf2SmZnhy0lMEGSnZmf5oonDkWBjUSzH8tqQILOzpsia1at9l0jQfyUtLVWOHT3qu3sL5oSfRU7wfcbsf4oAioBYkQtBaMSXX8qhgwd9GYTQgQxrzJ8+5Y925FjxwM3HRYIcNCjdlyIVuB86eECGDR3q6RE5buaPL66NIoAiIFZEXr9urXz99Vdy97vvfCkCgNu+vXvUWvN8GjHnR1b5C5sNHzZU2dDqMbyw38iRI2X37krf+mC8rqCojXsUAeaCl5+bA9DbGs0AZ8/4e1ETtEmi5IpmD21O6cKyuR/vDfNWfPXVeN9PrHP50iXVSRDTIfvNjhByJSUlvrsvR+1EEUAREAvCYXrdWTNnxIVzomNZYr9+4vXx5bHggVuPiTUghg7JlJMnjscFR2fM+EZWrizz3b1CBOTHwVDImPoRRQBFgG6CNdTXSVJSku+HJwXjhhEQFRXbfBdkg+/RT/+vW7tWpkyeFDf2wvDchISevpvbgiJAQ/6iCNAAosXyrV+bA5YsXhQXE5UEJ0XMNZ+QkMBqgEVfCMYy1v9jeGdSUqLE20I7ixcvkuLiIl8JH4oADfmLIkADiBYDnx9FACYnGZiW5pl12HUmHDR/lK9c6asgqxMftxxrVXm5LFwwP+7shA50Pb/4QhB33GILu9eBPjlc0MtmDqMIsAmgRQEA8vtRBOTMmS3FRf562og0UKEzZELPnoL25kj34XbO+t+VKw3SPykpbid5KioslPnz5pGfNuK273yWIsDZIBRMIL+JAEwPPDAtNa7HJEMEFRUVMsi6NMguW7ZUluYtiVv7oHzevXt3uXn9WtxiEByD+f/dIAkgch8BcVYQ+E0EzJkzx5czr0XrF5/36MG+AS4UAbW1NWpyJ8yrH61N/bQ9pvCeMmWyL2a6RHPAoUP+nIzMMc4FyQCKAIcDl59EwPnz5yQpMTGuqwABp8XCQnNz/LMYTeC+vP6+ZMkSWbo0L64FAGyIakDfvn190TeAHQM1PLhSBGgA0aJ48IsIgBqfmp0tWI/d64lCx/VjuuTu3br5dipaHRg5fQx0WE0eMIA2+TFWbdy4wRdDJCkCNOQvigANIMa5CDh/7qwMGjRI7ty+TRHwIxdUD/SFC4iHRd/QKRIgUrFMcElxMe0RZI/evXpJXW2NpzGhCNCQvygCNIAY5FjRBC8/VAIQYKdPmyqbNm7wdDCJxm6RbIvghGoARwqY86+AnaovX5KUlBTB6I3Ad3y/K5W7dsnkSd6eMAnxZ/XqVbSrxRyk/IAiwFyQ8oMIwLSrqampvp9/3UrSWF5SLDk5cxig7AQoDfvOn5crq1aV0w4tYNkrIcEXfQOs+Cf3+TH3UQRQBFh1BjztTp48SdavX8cA20KAxVPKZ599xifQFrCxyrlo97t86aKkDxwot2/dIkdbsMOe3ZUyftw4YtMCNtFyzbPbUwRQBFgl79mzZ9SQK4gBq8fw+37lK8tk2tSpxMdAkIUIW7hggSxfzlXmWvMzYNSvbx9PVwO4cJfNHEYRYBNAG8HNy80BCB5oT9yyeRMTXBscUFO1chZBIxypvnxZ0lJTBaM1WkuC/B59A3bKhAlfexIjPICsLPPf6oiO8pIigCLACuGqzp9TawRQhYfnD9qjc3PnejLIWuGGG/aBSF2wYL6sLCsl7m2I1ICtvLrqJ0QAlxIOH4MCdm7xnSLAJoAROFiLwHt47QAE2G+mT2cVIELb3751U3r37uW7ZVxb47Ubvse8AFjHgSMCIotvqAZgOWw32C6aa6AIiMy+bWJKEaABxAiTQaghvNoccO7sGUlPH8gyaxR2LysrFSzlGsoBfo6N/y1atJB9AaLgJ5Jp7969PTdvAK67oKCAfhWFrZvFHIqA2AShZkC3YCQvigBUAWZ8M13Wr+OIgEhsHNgGfQMwOQvWsg98x/fY+F59Xa2kpnJegGj5tW3rVpk0cYKn+Il4dPbMaU9dc7R2ifn2FAGxCUSRGM6LIuBCVZVaijWS++M2TblVXFwkuXPZNyDWvMjLWyLLuEZA1IkRQjUxMdHTIwVizS1fHp8ioGmgdtLIXhMBUN05OTmydu2aqAOMk7i69Vw3rl+TxH79OH99C1UxXTZDFaBf375cyMoixlj/IytrCv3bIn66eOzocSgCKAIiJdwP068mM8DaCBCYRXD+/HkMsjYwbI2vEKmFBfmyeBH7XrSGUbjvUQ3o16+foGNluG3d8DtsfuLEcU9cqxvwavEaKAIoAlokRkiQhrPNmjVT1nCeblsBB9WfPn36cKRACL8i4WC4ba5dvSJ9+/aRG1wjwBZHMRf/nNmzbR0jnK10/c7RARryF0WABhAtBjQvNQegCsClWPVwBaMECvLzPRFkdQVrJ45TVFQo+cuWEVeL8Shgo0An1isN9a7HkiJAQ0yiCNAAokWn85IIWLhgvqCUHQgUfLfOG9gdw7E4hsAEqiAAACAASURBVN06hqH8UxWW3r3Zqc1iLArFc/Wqcpk5c4br/Z0iQIMPUQRoANGi43lFBGDNcXRo4/SreriCphXMaV9cVOT6IBuaHNz6uXTFCpk7N4d4WoxFoXZFJ9Y+vXu5XqhCBKxbt5Z2t2N3igA9gT3UiSL57AURgIS1aOECKSrkhByR2DTSbRrq6wTLuKL0Guk+3K5lX71+/ZpazppzMLSMj1XeQFjNmjnT9fyEELB6j9zvbpAEELmPgOh1onB4ekEEoLMVOrLdunmDjmZHbYfsG6gGrFi+nLiGYBPOb0J/x2yM06dPI442cQzF9dq1q5KWliqIAaG/8bOzuSKmeAfJAIoAzU4UznBuFwFIVEsWL2ZfgBjxoqb6h1XuWA2wHlCxLkMf9gWIWZJGZ8vFixbG7PjhYmQkv3MRM+v+o/ClCLAJoI0E4XYRgN7BCQk9WQWwYeNwQWxuTo6g7BpuO/7esp+uW7uWszDGkJ+oAqDZyq1NLWgK4ORlLftGxDGDIsAmgDYc0O0iIH/ZUsFCLBGTyQYW8XqOy5cuSnLyAPYNsMAdVFBQBUD/injljxP3jemuMQmTE+eK9hwcHaAhf1EEaADRQgAD2d0sAqD8ExP7yU32BYhp8EMQmz1rFhdksuBD69auUUtaR5s4uH10MQ9xakD//q6sCFIERGfLFrlPEaABRAsBzO0ioKS4SBYsmB/TBNgiIS1i6eVjqemYk5OFbZuR++KdO7clKTFR6upqyVEHfKawsEANa3Wbn0EEFLi0SuE2rFq9HoqAyANPqyBadEK3VgJQZu3VK8GVyl+3DdxwPHTAnDcvV9au4cJMkdpj69Yt8vXXX1EAWIw9keIc2A5zhSQnJ7tyuuuLF6rIAzs8oAigCAg4euAdU9ouW7aUjmXHsaLc98KFKhmYlsYJmSLADU9/ffr0dm1ntYAf+e09b8kSKSzgfCF+s2uQBuA8AU4b142VAMwHkNCzp+tnCnPaVrE+H6oBOXPmCKZrjfW5vH78LVs2y9TsbOIUgWDSaWtUA1JTUlxZDdB5n3F3rCAVwHkCHHYqN4oAzAy4NC+PAdZhLiDwXLxwQYYMGSIY+x53gSgKvD//vIfUc0SA4xz5/u5dWbo0T0pXuGeCK4jnqvPnHMfCV/5JEcDmgAChVRUgIYFJKIqEFMBOxzsC2uzZHCnQFpabNm2UGTO+YdA3xNG62lrpn5Tkmv5CP3QMZBNFWz4T9jeKAIqAAEmwoM3ChQsYYA0FWNjh0sULaqpWziLY3C8hktAXoMEDS9wGfMpv77ABqgF5Sxa7Ik5wiGBzP4macxQBGkC0mDTc1ByAFQJ79OjOYWoWbRm147VyHgRZjBTATHi6jumX42zauEEmTZxIXFrhjlN2rq2pVkIVKw06dc7WzkMRoCF/UQRoANGiU7pJBCxbmif5y5YZd+rWnD2evr9QdV6NFOC8Afd8E8G+e/fu7LBqMdbo9h/MJorlsHUfN9rjQTSvpWC2ZweKgHuBJloC2t3eLSIAyebvn3zCvgAuCbAIbHNmz5bly0vsObdL7seun2D/VavKBess6DgWj2E/5jXU18vgQYPUrKem8aRYtmlPigCbANoItG4RAfNzc13V49d0UHHD+bGmwJAhmXLzBpdwRhWgR/fuXNLWRqyJBaeLCgslL28JhZnL7BK1rSkC4lsEYI2Anj17cpIaFzqyWmGwlCsMosPqksWLmGxcxlGsMtqvX18O13SZXSgCPGQQN1QCsHjNmjWrGWBdyJuammrp26dPXD8B37p5U3p+8QVnB3QhP5FsyleWycwZM4zFD1SJyleuNHb+qBOuG+3ISkD8VgKwVjg6W2FkgC/I7EYHs3lN6KyJ6Vrj1T6YuIpTWJuLUeF4h0rioPR0QfNVuG1j8TtHB2jgBkWABhAtBnrTlYDRo0dJxbZtRpw3FgHBj8dsqK+T9PSBcuVKQ9zZCUPQ/vGPT9lh1WJ8ccofsKRzVtYUI/ykCNCQvygCNIBo0UlNigAsX5uUlMgqgEXbORVgcR5M5TxtavzNlY8y85rVbKpykmtWznX79i0ZOHCgnD510nEhQBGgIX9RBGgA0WIiMSkChmRmyL59ex13WitBJt73wXTOgwcPkvPnzsaNvdDprG/fPqwCWIwtTvvMju3bZdy4cYLhrU6eG+c7F0d+ERNsKQLiTwQcO3pUBg9KF6jomJDKI4HLS/e+Yf16yc7KcjzImsJo2LChbKrykB9hrD76Bhw6eJAxxUN2U/5NERBfIgDKGQuAnD1zhs7qIWfFWgIZgwfLiRPHfW+3UydPqBkT2WHVXGyyIv6OHzsqw4YNixuhagUjV+5DEWDO0Uw0B6Aj4LixY+moHhIAgcCxf98+GTZ0qK8rOBCpgwYNkmNHj/he7ATs6pd32A5rO2zcsN4x26nmgLN8oLHFIYqA+BEBeLJKSOgp9XW1jjmpLXJ6MFHH8n4R8MaOGSPbtm7xrf3Qtjx82DBfC51YcsT0sc+eOa1Gs9y8cd0RjrJjoIb8RRGgAUSLycrpSgCWCV7MmdccCU6xCsanTp2U9IEDfTmdMEQqOgNSpJqLSTp4mzNnthQU5DviZxQBGrhCEaABRA+IgLramriffU5HgHPDMWZ8M10KCwscCbJO3u+C+fNlwfx5vrsvJzF0w7kC0wlfungh5rakCNCQvygCNIDochHwQ1vdBEfb6twQjPx6DQiy/fsnGZulLRa4BkQqqmOxOD6P6WycW79urZpACLEnlthDBJSXc9pgWxhTBDjrHMHGcqo54PChg5I8oL9wyU1ztg62u47/165ZLdlZU3zRdo5EMX78ONngYIcyHTbgMVr3J4xmGTJkiKAzK3FqHSdXYEMRYM5ATogAJP7Efn0FHXZcQTiLVRNee1Oe3rlzWwXZfXv3eN6u+/fvU0MCKVKb2tjrnD98+JBaDhuCwOv34uvrpwgw53hOiIAlixcLVgqMdVnO107iUuFy9MgRGTx4sDjVEzsWNr5966YkJvbjvBUu5Zhdm0+bNk0KC2Lbf+VbLoBmT2RRBPhXBFy8UCVJSUmCNmS7zsz9zfGkLeynT5smS/OWeFbkoSNg7ty5nr3+tmzD3+5KQ0O99OvbVy5UnY9JDEKfgHXr1sbk2HFjP4oAc8E9lpUADLfC1Kvbtmymg/j0KQtBCku5YiEoLzb3YMGZ5AEDBH4QNwHXx1xszYaYPAgTlMWiuYejAzTkL4oADSBadOxYigB0HBs9ahRXCbRom9YCmhu/315RIZmZGZ5abAftxJkZGbJ7104KAJ9zFA8k48aNlQ3r12m3NUWAhvxFEaABRItOHCsRcPnSRendu5fU1lRrdzo3JsF4v6YfhoBOlOUlxZ6xd3FRoUzNzvbF6IZ4518k94/mAIxQ0j13AEWAhvxFEaABRBeJAKju4cOHcU4AizaJJKC5cRuMs8fCUCbWdI8WDywQhHZi9lUxF3uitZmO7VevKpfx48ZpbRaAAD554oRnxK8OHLUfgyLAnCPGohJQUlwsEydMYDNAnIkABIadO7arZgE3jxa4dfOGGg64u7KSgTvOOIqEjWaBdWvXsCOom2xPEeAfEYB55fv37y94KtSuFt1EWl5Lq/adOWOGYI0IlEndxgEkgdmzZnI0QBzzF7EpsV8/OcWnd/f4J0WAP0QAqgpYWGbPnt3uIVccBztTCVg9aQ9Mk1073dfhbtfOHWqZYDdXKkzZLZ7OiwmuBg8eJNeuXtESq6piNPwwbmxCEeB9EYB+AFMmT5aiwkK5G+O5uuPGMTwsYNAJq1evXoJ5Itxir6rz52RA//5yjmu/u8YmJrmROzdHMMeF3WGD7BioIX9RBGgA0WLC0NUnoCB/mepwg9nXTDo2z22OS6HYb9q0UYYOHSI3rl8zzgk88WVkZMj2im3GryUUJ342w1kk/1EjR8rKsjJb/QMoAjTYjyJAA4gGRcDuyl0ycGAa12C3aAM/JwEszZuVNcX205YdjDAfwKSJE2XRwgW2gr2da+C+5mJcW9g31NdJcnKy7NltvZMoRYAG21IEaADRYgKyWwk4cfyYDBjQX06fPsUnLIs2aCtIef03BMivvhoveXlLjHQURDPVkiWLlQiwW/b1ui14/S3HWTQP9e7d2/KMl+B4eXk545+d+EcR0DI5nXBaOyIA7b5paamylx0BGQDaCAA3blxXqw2uKi939EkcIwFQ6v1y+HA1tbET/sRzmItldrDfu2ePqghgkjMrx0FnWCv7cZ8f+UIRYM5xrIoAOEt6erps27bV0cBOpzHHFTvYg2epqamyYf16R/gCAbBmzWolPurr6xig2xBpduzqp323bN4sqSkpnOXUBFcoAswFdisiAD2+09MHyqaNGxhcTTiMR8+JKaSxWM+mjRtjKgRQnl29apUMycxkQPcoV0yJC6wtMDAtTaKtCKDZydQ1++K8FAHeEQEnjh9XcwFs314R00DuC2IzADcLjOiIhfHZmFUSyVq3ndHuX1xUJEOHDJH6OlYAdOMbD8fDYljoLBjpqpjg8dq1a7RzOR6wbrxHigB9IgBlUCyQsXt3ZUS99SOtBOC4W7dsUX0ADuzfRwHABG856GHI4NdffSVZU6YIeu43BgKbmOK406ZOlcmTJnFpYJtY6rKJV49zYP9+1eG5omJb2FgHEZCfn6+Nx17FzNZ1UwToEwFZUybLiy+8IJ06dZIXOnQIS85IRADWi8+dO1e+HD5M0BnQlrEZnIjf93dVYF28aJFkDB4U8RNXa7yDQMUCLljKeOnSPK3CorVz8nt9McutWKLZc+jQoZKbO1fammGSIiA8F2bM+EbWr1vb+lLjFAHhQYzEUTZv3iSPPPywVO7aKegMtWJ5ifzqv/+7zYpAWyIA7VyY+nXwoEGSv2xZm44QyfVxGz129guOSN6HDh2U3gkJkr9sqaUe/OAv1ilIS02Vw4cPhX1q8wt2vA9nfAm9/hcvWtjmglMUAeFtger0rFkzJS0tTTZu2NB83hCKgPAgRuL0A9NS5R+fftrY1oog2759e5k+bWqrT58tiYBvv72jOv1hNi1MsoKlYXGsSK6B2+ixZTzhiEoTRMCg9HSZl5sb0fK+WAQGExFlZmRIYUG+JQERTxjzXu355Zkzp2X8uLEycuQI2bJlc5N4iNh45MhhxscwVV7ghOrKnDmzla+vWlXemKuCNIDcR7JaJ+v7770nkyZNakLGpKRESR+Ypkh78OABwex+wa/NmzbJe3/5i+zYXiEF+fkqqL733l+kb58+krdkiaoEBG/P/5viRzz04YGe2cOGDZOuXbtKjx49ZPasWbJx4wbF18rKXYJpiPE08XmPHtL1gw9k5IgRsm7tWsFvtAMxiDUHdu3aKWjC6tu3j7zzzjuSMXiwEq87dmwn/6LwQfhr6YoVgtz01w8/FPh98B9FQBg11ZZIev2112Re7twmImDkiC+lT+/eSgSUlZXK0ry8Jq9583IF+y1ZvFjmzJ4tM2bMkLk5OU22Cd2Hn5tiSDz04oFACx5iSeIFC+Y3chFlf3wXWKqYuOvFnXhGjmdOTo7i6OzZs9SMlMQucuyAFR4wsZbH/zz2mCBHBf9RBNgQAW927ChYGStYKKAzH9bODv4u+P+WmgOCf+f/1iszxI7YkQP+5wDK3OfPnW01xpIDTTmwc8d2NcwcyR/Tzqs5FoJUAEWADRHwyccfy5gxY5qQEWXVIZkZTb4LJmWoCMA465MnjsvBA/vZzmrDFsEY8/+mQYB4EA8/cQAdAwsLC1qNsX66V6v3Aox279olqSnJMm7cWDly+NC9/gCIs0F/FAE2Es+oUSPlrbe6NPa8xBjsh3/3O1Wuas14wSKgvq5W/v7JJ/LSiy/KG2+8Li+/9JJq62ptX37PYE4OkAPxzgGODgjvA+hgjvx07OiRpsk/kO8oAsKDGImjYTUsDBEcP26cbN26RQ2bevpPf2pz3HRABKCkNWbMaEGTAnpwQhCM+PJL+fNbbzWKikiugdvosSVxJI7kgDc4QBEQ3k6YKbTNqZUpAsKDGGlAqNi2Vb744nN56623JCkxUTDNb1v7BkTA9WvXpFOnN2XZ0qWN26NZ4LHHHhO04bR1DP6mz37EkliSA97iAETA8uXLGSMDT/VW3ikC9JIeigtTqIKc4QJKQARgwYxH//AHwUpagX1qa2vkmaefloUL5jd+F/iN73ptRjyJJzngXQ7cvnWTMdJK8g/sQxFgjvwBEYDFMh584AGp3LWrkcz4DVMQY7w2A5Q5GxF7Yk8OkAO+5gBFgDmCB0TAuXNn5T/+499bFAE5c+ZQBAQUK9/JBXKAHPA4BwJLJd+5fVswr39wBdiI2KAIMC8CMA0rOhFuWL++0cEx3/MTTzyh1g0wQgyPOxoxM8drYk/sneIAOlWrWe88Eq+WLc2Trl0/UHEezRhDMjNlhek+DRQB5hw2UAnAcMKP/vY3tbxrwHn2798nTz31pJw9c6ZRGAR+47s5mxF7Yk8OuIcDXhsdMGXKZOnSuXNjTEcfstD+Y/iMNT0CPIPQuXrlSos9/LHtlYaGZscI7BvRO0WAOUIHRAAMVVxcJL/9zW8kZ85sKV+5Up5v316tqQ0CRGRIjyhh3os5vhF7Yu83DnhJBJSUFMt//ed/yr/84hfyyssvS031ZbVOx8KFC9XCXR9+2FWtH9Ph+eflFz//ubzzztuyYcN66fjGG+pz++eek+PHjqp8gPuePWum/O8TT8jPf/YzeerJJ2XRwoXWxABFgLnAECwCoAhLiovl/fffl86dOsnEiRPk2tUrFAAUN+QAOUAOhHBgz57d8vHHH8nHH32kOlCr//H5448Es7euXbPGdZgh3g8dOkRefeUVQWfwa1evqgQ/NTtbzQ3Trt0zauXZvXt2y+7KSnni8cfl0UcflXVr18ipkyekY8c35NO//12tRYPh5Ej8GzesV3kCi31h25VlpdHfN0WAO0RAQKHjyR8qL/CZ7+bsQ+yJPTngTg5sr9gmw4YOUS8IgZ/99KeSkpysPo/4crgcPXLElTE0uDngxvXrzUTA5KCVaHt07y4pKSmN9zFixAglIDC9PFYAnD5tWuNv4OnECROkT5/eTb6LiL8UAeZIHlwJiMhYIWqY+5izHbEn9uSAOzgwdWq2PPTrX4sX5gsIJwKCR4N98fnnMmb06MakPnr0qEYR8EKHDvLP//RPzV5dunSRWzdvNO4TEUcpAswRmSLAHPYROQdFV3TBhHgRL4c5gMppakqKdO/e3RPY6xIB6CeApZTr6+oaX9WXLwsmmYs6tlEEmEtEFAHmsI/aURwObrw+coMcCM8BPPU++2w7+WZ609K4W7GDCOj05puqybel5oBIKwGZGRmqc2FtTbVK+pil9qOP/iZYvj7qe6cICE+0qEGNMGFQBJjDPlY25XFpU3LAOQ5cqDovP/3JT6TMSoe4COO0TnuWlZbKv/7Lvwja+3HtEATTpk5VHQPbt39O5ubkNCbxhJ49ZdzYe8vTjx0zWl5/7TW1qBwmHHqrSxclgNA34s03O0q7Z55RHQijvl6KAOcIG2ocigBz2Ifagp9pC3LAexzYsnmT/PL++6Xq/PnG5OlmO2JOmBUrlgsmDbrSUC/o4Hj61Em5c+e24F6wGm3g+vfv2ysnjh9r/IzhgVikLjBsHFWQNatXqfVlSlcsF+STwL5RvVMEmCM+RYA57KNyEgNPDLw+coMcCM+B7Ows+b+nnrKW/OjXP+BGERCeaLFyRooAc9jHyqY8Lm1KDjjDAQyl/uijj+T111+nCLAjaCgCnCFsS4GBIsAc9i3Zg9/RHuSAdziAcni7du2atJvTfhbsRxFgATQ7qitoX4oAc9gzWBB7csDbHEAl4PChg1JbY2FYXFAcjnseUASYcwSKAHPYx73jMwiyhOwTDgQ6ytGnLcZTigCLwGlwIIoAc9gzYBB7csD7HIAA2F5RQUFnJx9RBJhzBIoAc9gzARB7csD7HECTQH5+PkUARYA3yUwR4E27MXnQbuSAOzhAEaDBDqwEaADRogqjCDCHPYM4sScHvM8BigANNqQI0AAiRQDLcRY5wERkzv+IvfexR5+AI4cPM/7YiT8UAeYcgZUAc9gzARB7coAcIAfuBkkAkfsIiLNOQRHgLN7kN/EmB8gBciCEA0EygCLATknFwr4UASFktIAhHZoYkgPxzQEsxEMO2OAARYAN8GwmLYoAc9gzaBB7csD7HEDHwMLCQooAO7mIIsCcI1AEmMOeCYDYkwPe5wBHB2iwIUWABhAtqjCKAHPYMwEQe3LA+xygCNBgQ4oADSBSBLAcZ5EDTETm/I/Yex97iICysjLGHzvxhyLAnCOwEmAOeyYAYk8O+IMDN65fowigCPAmmSkCvGk3Jg/ajRwgB3zDAVYCzJGZIsAc9r5xYDtPANyXT5DkADlAEWAuEVEEmMOeIoDYkwPe5wCXEtZgQ4oADSBaVNMUAeawZwIg9uSA9znA0QEabEgRoAFEigCW1CxygInInP8Re+9jTxGgwYYUARpAtJgAWAkwhz0TALEnB7zPAYoADTakCNAAIkUAKwEWOcBEZM7/iL33sUefgP379zH+2Ik/FAHmHIGVAHPYMwEQe3KAHCAHuJSwUQVJEcAgxCBEDpAD5IBRDrASYI6AFAHmsDfqdHZKd9zXqHAnb9znszXV1eSEnbhAEWCO1BQB5rBnMCf25ID3OYCOgcVFRRQBFAHeJDNFgDftxuRBu5ED7uAARwdosAMrARpAtKjCKALMYc8gTuzJAe9zgCJAgw0pAjSASBHAcpxFDjARmfM/Yu997FVzQHEx44+d+EMRYM4RWAkwhz0TALEnB/zBgdu3blIEUAR4k8wUAd60G5MH7UYOkAO+4QArAebITBFgDnvfOLCdJwDuyydIcoAcoAgwl4goAsxhTxFA7MkB73MA0wbv2LGDidyOmKMIMOcIFAHmsGcCIPbkgPc5wNEBGmxIEaABRIsqjCLAHPZMAMSeHPA+BygCNNiQIkADiBQBLMdZ5AATkTn/I/bex54iQIMNKQI0gGgxAbASYA57JgBiTw54nwPoE7Bnz24+hFjMQcoHKALMOQJFgDnsmQCIPTlADpADXErYqIKkCGAQYhAiB8gBcsAoB1gJMEdAigBz2Bt1OjulO+5rVLiTN+7zWcRR2sWGXSgCbIBnMyBTBJjDnkGD2JMD3ucAOwZqsCFFgAYQLYoBigBz2DMBEHtywPscoAjQYEOKAA0gUgSwHGeRA0xE5vyP2Hsfe4oADTakCNAAosUEwEqAOeyZAIg9OeB9DkAEFHMpYXsPYRQB5hyBIsAc9kwAxJ4c8AcHEEdpSxu2pAiwAZ7FCkCAsBQB5rAP2IDvtAE5QA7ENQcoAsw5AEWAOezj2ultildiR966iQOYNdBN1+O5a6EIMOfQFAHmsPecozJxM9CTA804AAFQUVHR7Hv6dxSxlSIgCrA0OyFFgDnsGSSIPTngfQ5wdIAGG1IEaADRojigCDCHPRMAsScHvM8BigANNqQI0AAiRQDLcRY5wERkzv+IvfexpwjQYEOKAA0gWkwArASYw54JgNiTA97nAPoE7Nyxgw8hFnOQ8gGKAHOOQBFgDnsmAGJPDpAD5ACXEjaqICkCGIQYhMgBcoAcMMoBVgLMEZAiwBz2Rp3OTumO+xoV7uSN+3y2ob6OnLATFygCzJGaIsAc9gzmxJ4c8D4Hflg7oIgigCLAm2SmCPCm3Zg8aDdywB0c4OgADXZgJUADiBZVGEWAOewZxIk9OeB9DlAEaLAhRYAGECkCWI6zyAEmInP+R+y9jz1EQGFhIeOPnfhDEWDOEVgJMIc9EwCxJwf8wYHammqKAIoAb5KZIsCbdmPyoN3IAXLANxxgJcAcmSkCzGHvGwe28wTAffkESQ6QAxQB5hIRRYA57CkCiD054H0OYNrgyspdTOR2xBxFgDlHoAgwhz0TALEnB7zPAY4O0GBDigANIFpUYRQB5rBnAiD25ID3OUARoMGGFAEaQKQIYDnOIgeYiMz5H7H3PvYUARpsSBGgAUSLCYCVAHPYMwEQe3LA+xxAn4DtFRV8CLGYg5QPUASYcwSKAHPYMwEQe3LAHxyAEKAtbdiSIsAGeHbU1/d3hSLAHPYMGsSeHCAHyIG7QRJA5D4C4qxTUAQ4izf5TbzJAf9x4Pr1a6wE2HkgDZIBFAF2gLSwL0WA/wISkwxtSg44xwF0DFy+fDlFgIX808hTigDnCNsI+o8Gowgwh32oLfiZtiAHvMcBjg7QYDOKAA0gWlRhFAHmsGfAJ/bkgPc5QBGgwYYUARpApAhgOc4iB5iIzPkfsfc+9hQBGmxIEaABRIsJgJUAc9gzARB7csAfHGior+NDiMUcpHyAIsCcI1AEmMOeCYDYkwPkADnAIYJGFSRFAIMQgxA5QA6QA0Y5wEqAOQJSBJjD3qjT2SndcV+jwp28cZfPYrbAgwf2kxN24gJFgDlSUwSYw57BnNiTA97nADsGarAhRYAGEC2qMIoAc9gzARB7csD7HKAI0GBDigANIFIEsBxnkQNMROb8j9h7H3uKAA02pAjQAKLFBMBKgDnsmQCIPTngfQ6gT0AFlxK29xBGEWDOESgCzGHPBEDsyQFygBzgEEF7CspiBSBAPIoABqEAF/hOLpAD5IARDrASYI54FAHmsDfibDZFI6+ZfCEHmnPgu2/vGH2Y87xNKAKak8opo1IEmMPeKRvzPLQxORA7DqBjYElJMUWAnQcMioDYETSc81MEmMM+nG34O21DDrifAxwdoMFGFAEaQLSowigCzGHPAE/syQHvc4AiQIMNKQI0gEgRwHKcRQ4wEZnzP2LvfewhAoqKihh/7MQfigBzjsBKgDnsmQCIPTngDw7UVF+mCKAI8CaZKQK8aTcmD9qNHCAHfMMBVgLMkZkiwBz2vnFgO08A3JdPkOQAOUARYC4RIzezGgAAA3tJREFUUQSYw54igNiTA97nAKYNPnToIBO5HTFHEWDOESgCzGHPBEDsyQHvc4CjAzTYkCJAA4gWVRhFgDnsmQCIPTngfQ5QBGiwIUWABhApAliOs8gBJiJz/kfsvY89RYAGG1IEaADRYgJgJcAc9kwAxJ4c8D4H0Cdgy5bNfAixmIOUD1AEmHMEigBz2DMBEHtygBwgB7iUsFEFSRHAIMQgRA6QA+SAUQ6wEmCOgBQB5rA36nR2Snfc16hwJ2/c57M3rl8jJ+zEBYoAc6SmCDCHPYM5sScHvM8BdAwsKyujCKAI8CaZKQK8aTcmD9qNHHAHBzg6QIMdWAnQAKJFFUYRYA57BnFiTw54nwMUARpsSBGgAUSKAJbjLHKAicic/xF772MPEVBYWMj4Yyf+UASYcwRWAsxhzwRA7MkBf3CgtqaaIoAiwJtkpgjwpt2YPGg3coAc8A0HWAkwR2aKAHPY+8aB7TwBcF8+QZID5ABFgLlERBFgDnuKAGJPDnifA5g2+OiRI0zkdsQcRYA5R6AIMIc9EwCxJwe8zwGODtBgQ4oADSBaVGEUAeawZwIg9uSA9zlAEaDBhhQBGkCkCGA5ziIHmIjM+R+x9z72FAEabEgRoAFEiwmAlQBz2DMBEHtywPscUEsJb+ZSwra4TBFgzhEoAsxhb8tpLIo+npP2Jgf0cwDVAOJqA1eKABvg2UwGFAHmsGfQIPbkADlADtwNkgAi9xEQZ52CIsBZvMlv4k0O+I8Dd27fYiXAzgNpkAygCLADpIV9KQL8F5CYZGhTcsA5DqApYMWKFRQBFvJPI08pApwjbCPoPxqMIsAc9qG24GfaghzwHgc4OkCDzSgCNIBoUYVRBJjDngGf2JMD3ucARYAGG1IEaACRIoDlOIscYCIy53/E3vvYUwRosCFFgAYQLSYAVgLMYc8EQOzJAe9zAPMEXLp0kQ8hFnOQ8gGKAHOOQBFgDnsmAGJPDpAD5ACHCBpVkBQBDEIMQuQAOUAOGOUAKwHmCEgRYA57o05np3THfY0Kd/LGXT6L5oDDhw+RE3biAkWAOVJTBJjDnsGc2JMD3ucAOwZqsCFFgAYQLaqwa1evyOBBg6hiLeLHIG6Ou8Se2LuBAxABZaWljKF2YmgTERD0gf8SASJABIgAESAC8YPAffFzq7xTIkAEiAARIAJEIBiB/w81yZFfXQFe1QAAAABJRU5ErkJggg=="></p>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was well answered with candidates gaining credit for answers in words or symbols.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Again, very well answered.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A straightforward calculation with the most common mistake being missing the squared on the omega.</p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates answered with a graph that was only positive so scored the first mark.</p>
<div class="question_part_label">c(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>There is a proposal to power a space satellite X as it orbits the Earth. In this model, X is connected by an electronically-conducting cable to another smaller satellite Y.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Satellite Y orbits closer to the centre of Earth than satellite X. Outline why</p>
</div>
<div class="specification">
<p>The cable acts as a spring. Satellite Y has a mass <em>m</em> of 3.5 x 10<sup>2</sup> kg. Under certain circumstances, satellite Y will perform simple harmonic motion (SHM) with a period <em>T</em> of 5.2 s.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Satellite X orbits 6600 km from the centre of the Earth.</p>
<p>Mass of the Earth = 6.0 x 10<sup>24</sup> kg</p>
<p>Show that the orbital speed of satellite X is about 8 km s<sup>–1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the orbital times for X and Y are different.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>satellite Y requires a propulsion system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The cable between the satellites cuts the magnetic field lines of the Earth at right angles.</p>
<p><img 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"></p>
<p>Explain why satellite X becomes positively charged.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Satellite X must release ions into the space between the satellites. Explain why the current in the cable will become zero unless there is a method for transferring charge from X to Y.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The magnetic field strength of the Earth is 31 μT at the orbital radius of the satellites. The cable is 15 km in length. Calculate the emf induced in the cable.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the value of <em>k</em> in the following expression.</p>
<p><em>T</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi \sqrt {\frac{m}{k}} ">
<mn>2</mn>
<mi>π</mi>
<msqrt>
<mfrac>
<mi>m</mi>
<mi>k</mi>
</mfrac>
</msqrt>
</math></span></p>
<p>Give an appropriate unit for your answer. Ignore the mass of the cable and any oscillation of satellite X.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the energy changes in the satellite Y-cable system during one cycle of the oscillation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \sqrt {\frac{{G{M_E}}}{r}} ">
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>G</mi>
<mrow>
<msub>
<mi>M</mi>
<mi>E</mi>
</msub>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</msqrt>
</math></span>» = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{6.67 \times {{10}^{ - 11}} \times 6.0 \times {{10}^{24}}}}{{6600 \times {{10}^3}}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>6.67</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>11</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>6.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>24</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>6600</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span></p>
<p>7800 «m s<sup>–1</sup>»</p>
<p><em>Full substitution required</em></p>
<p><em>Must see 2+ significant figures.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Y has smaller orbit/orbital speed is greater so time period is less</p>
<p><em>Allow answer from appropriate equation</em></p>
<p><em>Allow converse argument for X</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>to stop Y from getting ahead</p>
<p>to remain stationary with respect to X</p>
<p>otherwise will add tension to cable/damage satellite/pull X out of its orbit</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>cable is a conductor and contains electrons</p>
<p>electrons/charges experience a force when moving in a magnetic field</p>
<p>use of a suitable hand rule to show that satellite Y becomes negative «so X becomes positive»</p>
<p><em><strong>Alternative 2</strong></em></p>
<p>cable is a conductor</p>
<p>so current will flow by induction flow when it moves through a B field</p>
<p>use of a suitable hand rule to show current to right so «X becomes positive»</p>
<p><em>Marks should be awarded from either one alternative or the other.</em></p>
<p><em>Do not allow discussion of positive charges moving towards X</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>electrons would build up at satellite Y/positive charge at X</p>
<p>preventing further charge flow</p>
<p>by electrostatic repulsion</p>
<p>unless a complete circuit exists</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<em>ε</em> = <em>Blv =</em>» 31 x 10<sup>–6</sup> x 7990 x 15000</p>
<p>3600 «V»</p>
<p><em>Allow 3700 «V» from v = 8000 m s<sup>–1</sup>.</em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <em>k</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4{\pi ^2}m}}{{{T^2}}} = ">
<mfrac>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>m</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4 \times {\pi ^2} \times 350}}{{{{5.2}^2}}}">
<mfrac>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>350</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mn>5.2</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>510</p>
<p>N m<sup>–1</sup> <em><strong>or</strong> </em>kg s<sup>–2</sup></p>
<p><em>Allow MP1 and MP2 for a bald correct answer</em></p>
<p><em>Allow 500</em></p>
<p><em>Allow N/m etc.</em></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>E</em><sub>p</sub> in the cable/system transfers to <em>E</em><sub>k</sub> of Y</p>
<p>and back again twice in each cycle</p>
<p><em>Exclusive use of gravitational potential energy negates MP1</em></p>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A painting is protected behind a transparent glass sheet of refractive index <em>n</em><sub>glass</sub>. A coating of thickness <em>w</em> is added to the glass sheet to reduce reflection. The refractive index of the coating <em>n</em><sub>coating</sub> is such that <em>n</em><sub>glass</sub> > <em>n</em><sub>coating</sub> > 1.</p>
<p>The diagram illustrates rays <strong>normally</strong> incident on the coating. Incident angles on the diagram are drawn away from the normal for clarity.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the phase change when a ray is reflected at B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain the condition for <em>w</em> that eliminates reflection for a particular light wavelength in air <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mtext>air</mtext></msub></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the Rayleigh criterion for resolution.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The painting contains a pattern of red dots with a spacing of 3 mm. Assume the wavelength of red light is 700 nm. The average diameter of the pupil of a human eye is 4 mm. Calculate the maximum possible distance at which these red dots are distinguished.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>«change is» </mtext><mi>π</mi><mo>/</mo><mn>180</mn><mo>°</mo></math> <strong>✓</strong></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«to eliminate reflection» destructive interference is required <strong>✓</strong></p>
<p>phase change is the same at both boundaries / no relative phase change due to reflections <strong>✓</strong></p>
<p>therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>w</mi><msub><mi>n</mi><mtext>coating</mtext></msub><mo>=</mo><mfenced><mrow><mi>m</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced><msub><mi>λ</mi><mtext>air</mtext></msub></math></p>
<p><strong><em>OR</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mfrac><msub><mi>λ</mi><mtext>coating</mtext></msub><mn>4</mn></mfrac></math></p>
<p> <strong><em>OR</em></strong></p>
<p><strong><em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mfrac><msub><mi>λ</mi><mtext>air</mtext></msub><mrow><mn>4</mn><msub><mi>n</mi><mtext>coating</mtext></msub></mrow></mfrac></math> ✓<br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>central maximum of one diffraction pattern lies over the central/first minimum of the other diffraction pattern<strong> ✓</strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mo>«</mo><mn>1</mn><mo>.</mo><mn>22</mn><mfrac><mi>λ</mi><mi>b</mi></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>22</mn><mfrac><mrow><mn>700</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>9</mn></mrow></msup></mrow><mrow><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfrac><mo>=</mo><mo>»</mo><mn>2</mn><mo>.</mo><mn>14</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup><mo>«</mo><mtext>rad</mtext><mo>»</mo></math> ✓</strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mn>14</mn><mo>«</mo><mn>0</mn><mo>.</mo><mn>05</mn><mo> </mo><mo> </mo><mtext>m</mtext><mo>»</mo></math> ✓</strong> </p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>On a guitar, the strings played vibrate between two fixed points. The frequency of vibration is modified by changing the string length using a finger. The different strings have different wave speeds. When a string is plucked, a standing wave forms between the bridge and the finger.</p>
<p> <img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The string is displaced 0.4 cm at point P to sound the guitar. Point P on the string vibrates with simple harmonic motion (shm) in its first harmonic with a frequency of 195 Hz. The sounding length of the string is 62 cm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how a standing wave is produced on the string.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the speed of the wave on the string is about 240 m s<sup>−1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a graph to show how the acceleration of point P varies with its displacement from the rest position.</p>
<p> <img src="data:image/png;base64,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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in m s<sup>−1</sup>, the maximum velocity of vibration of point P when it is vibrating with a frequency of 195 Hz.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in terms of <em>g</em>, the maximum acceleration of P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the displacement needed to double the energy of the string.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.v.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The string is made to vibrate in its third harmonic. State the distance between consecutive nodes. </p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«travelling» wave moves along the length of the string and reflects «at fixed end» <strong>✓</strong></p>
<p>superposition/interference of incident and reflected waves <strong>✓</strong></p>
<p>the superposition of the reflections is reinforced only for certain wavelengths <strong>✓</strong> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mn>2</mn><mi>l</mi><mo>=</mo><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>62</mn><mo>=</mo><mo>«</mo><mn>1</mn><mo>.</mo><mn>24</mn><mo> </mo><mtext>m</mtext><mo>»</mo></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>f</mi><mi>λ</mi><mo>=</mo><mn>195</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>24</mn><mo>=</mo><mn>242</mn><mo> </mo><mo>«</mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</p>
<p><em>Answer must be to 3 or more sf or working shown for<strong> MP2.</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>straight line through origin with negative gradient <strong>✓</strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>max velocity occurs at x = 0 <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>«</mo><mo>(</mo><mn>2</mn><mi>π</mi><mo>)</mo><mo>(</mo><mn>195</mn><mo>)</mo><msqrt><mn>0</mn><mo>.</mo><msup><mn>004</mn><mn>2</mn></msup></msqrt><mo>»</mo><mo>=</mo><mn>4</mn><mo>.</mo><mn>9</mn><mo> </mo><mo>«</mo><msup><mtext>m s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mfenced><mrow><msub><mn>2</mn><mi mathvariant="normal">π</mi></msub><mo> </mo><mn>195</mn></mrow></mfenced><mn>2</mn></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>004</mn><mo>=</mo><mn>6005</mn><mo> </mo><mo>«</mo><msup><mtext>m s</mtext><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>600</mn><mo> </mo><mtext>g</mtext></math> <strong>✓</strong></p>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>∝</mo><msup><mi>A</mi><mn>2</mn></msup><mtext mathvariant="bold-italic"> OR </mtext><msup><msub><mi>x</mi><mtext>o</mtext></msub><mn>2</mn></msup></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn><msqrt><mn>2</mn></msqrt><mo>=</mo><mn>0</mn><mo>.</mo><mn>57</mn><mo> </mo><mo>«</mo><mtext>cm</mtext><mo>»</mo><mo> </mo><mo>≅</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>6</mn><mo> </mo><mo>«</mo><mtext>cm</mtext><mo>»</mo></math> <strong>✓</strong></p>
<div class="question_part_label">b.v.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>62</mn><mn>3</mn></mfrac><mo>=</mo><mn>21</mn><mo> </mo><mo>«</mo><mtext>cm</mtext><mo>»</mo></math> <strong>✓</strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.v.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Monochromatic light of wavelength <em>λ</em> is normally incident on a diffraction grating. The diagram shows adjacent slits of the diffraction grating labelled V, W and X. Light waves are diffracted through an angle <em>θ</em> to form a <strong>second-order</strong> diffraction maximum. Points Z and Y are labelled.</p>
<p style="text-align: center;"> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASYAAADzCAYAAAArQLvyAAAbPklEQVR4Ae2dzwvmxnnH838E4zohbGMMDRSzaRNKzBKcpgRiSiC+xof42Fy8N++puTU0h/jSHL2H5hTjhRjiUwO+e/E/sM0/sP4L3vJ53Wd3Xu1IGml+PSN9B4T0SqOZ0XdGn3lm9Ejv1y4KUkAKSAFnCnzNWXlUnEQFXnrp64kxFU0KjKeAwDRenV1LLDANWnEqdpICAlOSTP4iCUz+6kQlKqeAwFROy6YpCUxN5VZmjRUQmBoLXio7gamUkkrHowICk8daSSiTwJQgkqIMq4DANGjVCUyDVpyKnaSAwJQkk79IApO/OlGJyikgMJXTsmlKAlNTuZVZYwUEpsaCl8pOYCqlpNLxqIDA5LFWEsokMCWIpCjDKiAwDVp1AtOgFadiJykgMCXJ5C+SwOSvTlSicgoITOW0bJqSwNRUbmXWWAGBqbHgpbITmEopqXQ8KiAweayVhDIJTAkiKcqwCghMg1adwDRoxanYSQoITEky+YskMPmrE5WonAICUzktm6YkMDWVW5k1VkBgaix4qewEplJKKh2PCghMHmsloUwCU4JIijKsAgLToFUnMA1acSp2kgICU5JM/iIJTP7qRCUqp4DAVE7LpikJTE3lVmaNFRCYGgteKjuBqZSSSsejAgKTx1pJKJPAlCCSogyrgMA0aNUJTINWnIqdpIDAlCSTv0gCk786UYnKKSAwldOyaUoCU1O5lVljBQSmxoKXyk5gKqWk0vGogMDksVYSyiQwJYikKMMqIDANWnUC06AVp2InKSAwJcnkL5LA5K9OVKJyCghM5bRsmpLA1FRuZdZYAYGpseClshOYSimpdDwqIDB5rJWEMglMCSIpyrAKCEyDVp3ANGjFqdhJCghMSTL5iyQw+asTlaicAgJTOS2bpiQwNZVbmTVWQGBqLHip7ASmUkoqHY8KCEweayWhTAJTgkiKMqwCAtOwVaeCS4HjKiAwHbdudWVSYFgFBKZhq04FlwLHVUBgGrBuHzx4//Kzn/3r5Ve/+rfLl19+OeAVqMhSYFmBRTDR6D/77DMtjjT49a///cLEty3ASUEKHE2BRTB98cUX156Z3nltef31v7+89dZPV+OtpaPjy1p/97t3n0HJ4JS63tJ4U9MM43lJPyxT6nas7LR/rNNpSE0zjDdNY+l3eF7q9lJ602OpaYbxpmnM/Q7PSd2OpbUIptgJsX2ffPKn683ym9/8R+yw9hVUgJvl1Vf/9hmc7t174/ob7TWsKyj05XIdKdBRKrRXIBtM3AzWi3PD/PWv/9v+Kk6WIxozxAZSBLa5gdBfgCrXGEzXcikqpVQFssHEjRCabJrzSJW+fDxupHfe+cUVUAxB1EnkacxIQBZTnoZ7z84CEw0/HFYYoLhBFPopQL3QQVAfrAWofXVBp8ui0F6BLDBZ4zcg2Vq9zLaKfPvtn18h8pe//M8LJ/74x/98YZkGtF4LAtSaQsvHBaZlfWoezQKTVRxrbpTwt3rp9Gp7+vTp5Xvf+4cXAHT//nuX11579fLkyZMXEksBk51EXVA3WLcM9WTRmjLLa2vPy7F0tIYCWWAKC7TlRgnP0/ZXCjx69PEV7sCI8PDhh9ffrGNhj948qDBAYdUKUDFln+9jng69FNorIDC113w2R6AEcIAUlpJBKnbCHjBZOlNAMck7emAYzJAXXbA+Hz/+PPuSBO9sCXcnIDDtlq7OidxU3FyxeaUwxxwwhen84Q//fXX3wOWD7REDUEKPDz743bX4zNmx5AaBKVfB/ecLTPu1q3KmvXKyZC2RcSkw2UWMCijm37Au0c0CgCqhj/zyTNH2a4GpveazOVrPb0MShnRzocSNF0sbQL355g+vVtTvf/9f7r3JAThWZhhsSBzu27NdS+M9ZTnbOQKTkxq3J3M2BAFO3HDsj4XaNw0T4wxlPHuTYy2hgw3hTCd0m8LKjqWu8apneKvQRwGBqY/uL+QKkEIQ2RDl3Xd/+UJcdtQGk2XqGVA2ZEOL6TKnm13X2tquey2ejtdRQGCqo+umVO0Gm7oGzO0n8VZgsgvBgsChFgvKizc5ViXzS2FYc7MI4y5t4yYQ+7LA0jk6Vk4BgamclrtSsnmlucluLKmYk2VrMNnFefEmZ4iLBuGkN2U0veaGwHYda2vgyxybQh8FBKY+umfn2gtMVvApoOxLB3a89trml0Ir0yA/nXPaUxa5CuxRrdw5AlM5LZum1BtMdrFTZ81W3uQxMJWylrg29OXaFPooIDD10T07Vy9gsgvpASgeFtgkt83HYTXlBj2Ry1Uw/3yBKV/DLil4A5OJYIDiUTvDoZre5Lx2wvwbWjARXgJKXAdzS7zsrNBPAYGpn/ZZOXsFU3hRc97kDPdaz0mF5Vrb1sT3mkL1j3cDkz3WZa5AYbsCI4DJrioE1N27r18tHMrv9XE81p5ncJquR153AxOPeXO9c49cMWvXNhKY7Fp++9v/fAYlyu/xGnjaiK+WQl8FuoGJJygsCvsU8HhTr10JN70BifXLL790/d6Rp6dfWHeaX1qryfrHm4AJZzcgZI2SJyhMWpbwN6kvkc8cRgQTSn7/+/94+eY3X3n2knD4Ph7g6h2Akhwre9fC5VIdTECJIZtZR8wp8ZsbK3SO6y/FWCUYEUx8kI75m6mFNHXW7AkoferEx31QHUyxuSTzOdHE9/5GMBqYgBFQWvpaZm9AGTj314rOLKVAdTBhHU3fA7OhXKmLOGM6o4GJl2IZtqUEA5S9MNzKm5ynhF6fFKbodqQ41cEUm0sCVDjEKexXYCQwARrKu3WIZs6aAKrFu2tyE9jfHkuf2RxMNuc0taJKX9jR0xsJTEAlxxJpASisMsCk4EOB6mDiXSasI4AUPp3TE7m8BjAKmJi3weIJJ7xpB5R/brH336YKkYY5a/L5X7ZLBby9c+BZqhxK5ysFqoMphBHzTTbxXeq9prNW5AhgAiRYIakA2dI2DFBb0l9qK8BT3t5LCrU9Vh1MbS/nPLmNAKYtE957v6U0BVRomaW2BtLAAlPwo4DA5KcuNpXEO5hswjvFCsGqDn3dNgnx/5GZIwqdNbcAivNSrbo9ZdM52xUQmLZr5uIM72DCgzp1zgbnW8AEoHLDVkAB0OkcWG4ZdH6+AgJTvoZdUvAMJuCQerNvmVfaIjRlAI6UA0DOuSow6c2i4EsBgclXfSSXxjOYUiek984rJYt0uVyBBHjQi3UIKIZ7gCvctyVtxa2ngMBUT9uqKXsFEzd5yhCuxLzSFoEp1xRQWybnt+SluPkKCEz5GnZJwSuYUsUoOa+UmifxABRAwlJ65ZWX9SWBLeI1jCswNRS7ZFYjg6nWvNIWfRnGYdkBqBavu2wpm+I2+OyJRK6jwMhg4k0Ayj+38H5lqwCgzIICUEtfP2hVJuUjMA3bBkYGk1fRp86aXst5hnJpKDdoLQtM9SpOgKqnbWrKAlOqUs7iCUz1K8ReVcH9gc/tbvEmr1+6Y+cgMA1av17AxA17dD+grd7kgzYpV8XOAhNPNLhBYsvRG2vvWvQApi0e3r31KpG/AFVCxbQ0ssCEqRuDEk85FI6vAG/kn/EfRXgxGWdNOuapN/nxa73NFWaBiSLyiDWEE5WlsXibyuuZC0A6+6dCYt7kPevkSHlngwnzNgQTVpTCsRWg46EDou4VXnwfL+VTL9JtWYFsMJG8vYOE9aRQXwE8ltEa3XtYp+TLonCrAHUROmsK3Lf6bPm1CCaERty15aOP/ni5c+db1/mGtbg6vq7nkkb8T19ooaa8MLulQazFpWwari+rJEAt65NydBFMmKT0zCnLd77zd0nxUtJSnHnN8akJwfSjH72ZUs/F4jCvpIcbaXICKObiqDPatKY50nQj1iKYUpPh/SJuFjXYVMX2x6OzwGIxON2798b1N9pzI9QMdpPVzOOoaQMlAMUiQK3XcjaYuBmsF+eGkf/Suui5MdCYzsAmWRle0SOjfy1AUc+kT14K+xUQoNK0ywYTN4L13qw1KZomfI1YU0CV7CSoVz5Vq1BGAToWOhM69VqdSZmS9kklC0w0/HBYYYBSr9qnMi1X6gWQWEeRCygbPuamY+XT+rkC086k9nD8ec6+t7LAZI3fgGRregKFuAJ8JC32vSH7eNrDhx/enMhvdH3y5MnNfvathVKAoj7p1RXqKTAF1Nk7gSww0Vht4UaxbdZnF3auCdsH+Kf/RMynZgHW9O+x799/7/rXRtP0UsBk51AX9rVGOpMtFq3NiVhaWtdVoFRnUreU9VPPAlNYvC03SnjeGbcBEBaSBawh9ItZU/zfGnCahj16M0yg02D4jRW0BihNeE9Vb/f77IASmNq1tWc5YR2xWGC4xm8DlFlT9vvRo48t6rP1HjDZyVsAtQYvS1PrOgrkWLt1StQmVYGpjc43uWAZYQlZwCIyC4r9tg2wYvNRnJcDJssXQNlQLfSvwV8Jy8rcESy+1v0U2NKZ9CtluZwFpnJaJqdk80w2oQ18bBtImTUVbk8TLwGmME0D1Le/fecKPdJnyEePreBHgbMASmDq1OaAERYRkAqtJ36blcS/iZj1NC1maTBZ+nfvvv4MTOTx6ad/tkNaO1Jgztp1VMSsoghMWfLtPxlryIZwvJgbBsBkgGIdC7XAhBMladuCBcWwjhtBwacCZu2Gw3GfJU0vlcCUrlXRmFhLWEoM26bwYR+LWU6xjGuBCQDhWgCg8E6e+tcIULHa8LFvCqiR60pg6tSm7IlbOIyzojB8A0o212T7w3UtMIV5hNsACh8o5p0Al+aeQnV8bR+hMxGYOrYpoMRwbhoeP/78OpSam18ifg0w4dtEr7sUzu5fs6SNt2MjA0pg8taaEstTGkwM25ijSDX/BajEinIQbURrV2By0HD2FKEkmIARUAJOWwOA2uJNvjV9xS+nwEidicBUrt6bplQSTIAl98Vr4CZANW0CuzMbAVAC0+7q7XtiKTDRSEmLdYkwBdQeK6xEOZTGugLUudfORGBarz+XMUqBqeYnTaaPr10KqUJd5xW9AaobmPDj4eayVzHUPrYpUAJMWDM8/p9OePM0kPRjLw9TSp4m4pWeGgSoVKX6xvNk7XYDE97OMR+evlUzTu65YKIRLnkKAx7q5+nTpzeiUG/4WO3pUAAUFhr58qLwFIg3GelHVwV6dybdwGTezV3VHzjzXDCtTXgDHgAU+lml+FelSDqyf03K9R0pTi9ANQETvS4g4mZiMc/mJQfCI1VujWvJAZNNeK991sSGdPbKDFbUliHc2nULUGsK+Tne2tqtDiagxJDAXq+gJ+Y3NxbzTAr7FMgBE8Op1H/wtSGddSZ7hnBrVwgg7fvxrEs9IVzLV8e3K9CqM6kOpthckvXENRr5dqnHPGMvmGhYsQnvORVsSEd+tS1cgCRAzdWEr/17AIXVxXkpoTqYsI7CeQoKZb1vSgEVJ67AXjAtTXjHc7pc62/pSwdz5+3dPwXU2pBzbz46L1+BLdYubS+1U6wOJhr0tKcFVCXnKvLlHS+FPWBam/CeU8GexM0dr7V/+vg6tbetVR6lO6/AtDOZDsexlmizLCl/nNocTDbnNLWi5i9ZR2IK7AHTm2/+cNd3vHuBya5bgDIl/K+ngDJrF2vJwMR67Y2A6mDif9KwjgBS+HRuakX5l9xXCfeAae8V9AaTlRtA4f9EI2cCn15YwacCYWfygx/80w2UaLtrQ7rqYAphxHwTQKJg9gjap6z+S3VGMIW1ApQAFIsAFSrjaxtATa0l2i4LnctcqA6muYy1P0+BlmDKK2ndswWouvrmps68oIEotsYCjgWBKabKAPsEpttKYs6CHpghApP89NQK/RWgTmJAsn3U13SinFILTP3rblcJBKa4bHv8a+IpaW+uAmvWksEpNqQTmHLV73S+wLQs/BRQsV55OQUdzVXA3FNwD2DbFurGljnLVmDKVb/T+Wtg4jGtbsbLVQN5k3dqpBnZCkwZ4vU8dQ1Melp1WztT/xpB+1Yfb78EJm81klieJTDxpANnSoUXFQBIvMDMpCuWFEMKBX8KCEz+6iSpRHNgYszOTacbbllGdGLOA62YfJVey3q1PiowtVa8UH5zYMIKYFFIU0CAStOpdSyBqbXihfKLgYleHwtg7klHoawPmQyayVnTT9UKTH7qYlNJYmBiXmnOk3ZT4iePLED1bwACU/862FWCKZjs5dZdiemkqAIACtjbE05ZolGZquwUmKrIWj/REEzcMJrwrqc5Q2S97lJP31jKWWDiZuAGiS3yE4nJXW5fCCYmu1M+vlUu93OmJEC1q/csMGHqxqDEY1iFNgrYhLc6gjZ6kwua0xnQMeMTJe3La58FJorDGDyEk54Kla+kpRTRXx3BkkL1jgEkAEX7Zy1AldM6G0z0HiGYsKIU2ihgT4/a5KZc5hQQoOaU2b8/G0xkbb1G7PMF+4umM+cUYPjw1ls/vXzjG39z+fTTP89F0/7GCgAoeZOXEX0RTDztwSJaWz766I+XO3e+dfWhWYur4+t6LmnE97dDCzX1jyvLNBelkqIA940AlaLUfJxFMPHpDKyglIU/HEiJpzhpes7pNP1+Mh96V/CpgAGKOqM+1/4ZxOdV9CnVIpj6FEm5LilAZxG6ady798bVAZAemhtBwacCNh9ozpo+S+mnVAKTn7pILglzGXh62392MfSjRwZYAlSyjF0iClBpsgtMaToNEUuAGqKaroUEUHQmWFDqTF6sN4HpRU2G34MlZU9K5V/juzrVmcTrR2CK6+J+L0/m1oL8a9YU8nNcgLqtC4HpVo/mvx49+vj6+H/un4nZD4Smx1PAZBdjgGIOCgvK5qbsuNZ+FJC1+1VdCEwO2iR/nX7//nvRkrAfV4xp2AImO9ceXwMo5jfopRV8KmCdCfV8xuG4wOSgXX7wwe8ur732arQk7Of4NOwBk6UhQJkS/tcGqLNZuwKTg7b59OnTK5gePvzwpjT8ngNWDpgsEwBlH5jjZWCeFCn4VOBsnYnA5KQdvvvuLy9vv/3zm9IwhOMVlFgoAaYwXfnXhGr43T4LoAQmJ23QJrmfPHlyLdHjx59fJ71Zx0JpMFkeApQp4Xt9dGtXYHLU/rCQbD4JS2lqQYVFrQUmy4P3uuRNbmr4Xh+xMxGYHLU5oMQTOgJrXAnmQm0wWb7yrzEl/K+PBCiByVl7A0ghoOaK1wpMlj+A4rvi9j4eT4sUfCpwBGtXYHLWthjCzbkIhEVtDSbL2x5fk/8Z/WtMhxHWI1u7ApOzFsbkN2DChWAp9AKTlUmAMiX8r0e0dgUm/+0qWsLeYLJCASi+oskQj6EeN4GCTwVG6kwEJp9taLVUXsBkBT2Lf41d78jrEQAlMA3awryByWQUoEwJ/2vP1q7A5L/9REvoFUxWWAB1pMfXdl1HXHvsTASmQVuadzCFsgpQoRp+tz0BSmDy204WSzYSmOxCABQvC9sH+bkRFPwp4MHaFZj8tYukEo0IJruwkf1r7BrOsu5l7QpMg7awkcFkkgtQpoT/dWtrV2Dy3yaiJTwCmOzCABRe5PYxNJ4WKfhUoFVnIjD5rP/VUh0JTHaxI/jXWFnPvt4DKN7h47yUIDClqOQwzhHBZDILUKaE//UWa5eHHljFKQ89BCb/dR8t4ZHBZBfs6fG1lUnruAJrnQlzVLRZFl5dWgsC05pCTo+fAUwmvQBlSvhfzwEKa8nAxJph3VIQmJbUcXzsTGCyajBA0cj5uuZa47bztG6vAIDir88Zut2798YNlGi7a0M6gal9nRXJ8YxgCoXr5V8TlkHb6wrQmUytJdouC53LXBCY5pRxvv/sYLLqEaBMCZ9rJscNRLE1fx8WCwJTTJUB9glMt5UEoOiB6Z0ZQtBTK/RXgDqJAcn2MaRj2DcNAtNUkUF+C0zxitrjXxNPSXtzFVizlgxOsSGdwJSrfqfzBaZl4QWoZX1aHMVyBTosbNtC3dgyZ9kKTC1qqEIeAlOaqHOPr9POVqxeCghMvZTPzFdg2iagALVNr96xBabeNbAzf4Fpn3AGKCZdeXGYIYWCPwUEJn91klQigSlJptlI5qwJoJgDEaBmpepyQGDqInt+pgJTvoakIECV0bF0KgJTaUUbpScwlRUaQOHshx8Un//FL0qhnwICUz/ts3IWmLLkWzxZ3uSL8jQ5KDA1kbl8JgJTeU2nKQpQU0Xa/RaY2mldNCeBqaici4kxMc4EORPlet1lUapiBwWmYlK2TUhgaqs3uQlQ7TQXmNpprZwOogCA4iuMWFAPHrwffQn1IJfa7TIEpm7SK+PRFTBnTaxXnDX5rVBGAYGpjI5K5cQKCFDlK19gKq+pUjypAgCKoR1DPIZ68ibf3xAEpv3a6UwpEFVA3uRRWTbtFJg2yaXIUiBdAQEqXatpTIFpqoh+S4EKCshZc5uoAtM2vRRbCmQpIEClyScwpemkWFKgqAIAipeFeWmYl4cZ9ik8V0Bgeq6FtqRAcwXkTR6XXGCK66K9UqCpAgLUrdwC060e+iUFuioAoPAixxfqzN7kAlPXZqjMpUBcgbN7kwtM8XahvVLAhQJnBZTA5KL5qRBSYFmBszlrCkzL7UFHpYArBc4CKIHJVbNTYaRAmgIGKPyg+LomflFHCgLTkWpT13JKBY7oTS4wnbIp66KPqMCRACUwHbGF6ppOrQCAYnjHMG/UP08QmE7dhHXxR1ZgZG9ygenILVPXJgUG/XcXgUlNVwqcRIGRnDUFppM0Sl2mFDAFRgCUwGS1pbUUOJkCBih7YZg5KS9BYPJSEyqHFOikgDlrAiie5nkAlMDUqTEoWyngTQFPgBKYvLUOlUcKdFYAQPG5X/yg+Pxvj9ddBKbOjUDZSwHPCvTyJheYPLcKlU0KOFGgNaAEJicVr2JIgREUaOVNLjCN0BpURingTIE9gPrkkz8lP/ETmJxVuIojBUZSAEC9884vrn+e8ODB+xd8o+YCk+ksTK6vBYFpTSEdlwJSYFUBc9Z86aWvR//dhTkqjrEAsrUgMK0ppONSQAokKzAHKCwlAxNrhnVLQWBaUkfHpIAU2KUAgOJbUHiT/+Qn/3IDJcDE/qUhncC0S3adJAWkQIoCwGdqLZnltDSkE5hS1FUcKSAFdinA5LiBKLbGwzwWBKaYKtonBaRAEQV4KTgGJNvHkC72JE9gKiK/EpECUmCqwJq1ZHACXtMgME0V0W8pIAWKKMDkN9BhYdsWc7QEXDFricwFpiJVoESkgBQoqYDAVFJNpSUFpEARBQSmIjIqESkgBUoqIDCVVFNpSQEpUEQBgamIjEpECkiBkgoITCXVVFpSQAoUUUBgKiKjEpECUqCkAv8HbFK55dno8n4AAAAASUVORK5CYII="></p>
</div>
<div class="specification">
<p>State the effect on the graph of the variation of sin <em>θ</em> with <em>n</em> of:</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the phase difference between the waves at V and Y.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State, in terms of <em>λ</em>, the path length between points X and Z.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The separation of adjacent slits is <em>d</em>. Show that for the second-order diffraction maximum <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>λ</mi><mo>=</mo><mi>d</mi><mi>sin</mi><mo> </mo><mi>θ</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Monochromatic light of wavelength 633 nm is normally incident on a diffraction grating. The diffraction maxima incident on a screen are detected and their angle <em>θ</em> to the central beam is determined. The graph shows the variation of sin<em>θ</em> with the order <em>n</em> of the maximum. The central order corresponds to <em>n</em> = 0.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" 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"></p>
<p>Determine a mean value for the number of slits per millimetre of the grating.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>using a light source with a smaller wavelength.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>increasing the distance between the diffraction grating and the screen.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>0 <em><strong>OR</strong> </em>2<em>π</em> <em><strong>OR</strong> </em>360° <strong>✓</strong></p>
<p> </p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>4<em>λ</em> <strong>✓</strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mi>θ</mi><mo>«</mo><mo>=</mo><mfrac><mtext>XZ</mtext><mtext>VX</mtext></mfrac><mo>»</mo><mo>=</mo><mfrac><mrow><mn>4</mn><mi>λ</mi></mrow><mrow><mn>2</mn><mi>d</mi></mrow></mfrac></math><strong>✓</strong></p>
<p><em><br>Do <strong>not</strong> award <strong>ECF</strong> from(a)(ii).</em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>identifies gradient with <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>λ</mi><mi>d</mi></mfrac></math> <em><strong>OR</strong> </em>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi><mo>=</mo><mi>n</mi><mi>λ</mi></math><strong> ✓</strong></p>
<p>gradient = 0.08 <em><strong>OR</strong> </em>correct replacement in equation with coordinates of a point <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfrac><mrow><mn>633</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>9</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><mn>080</mn></mrow></mfrac><mo>=</mo><mo>«</mo><mn>7</mn><mo>.</mo><mn>91</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mtext>m</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>26</mn><mo>×</mo><msup><mn>10</mn><mn>2</mn></msup><mo> </mo><mtext mathvariant="bold-italic">OR</mtext><mo> </mo><mn>1</mn><mo>.</mo><mn>27</mn><mo>×</mo><mn>102</mn><mo>«</mo><msup><mtext>mm</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>
<p><em><br>Allow <strong>ECF</strong> from <strong>MP3</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>gradient smaller <strong>✓</strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>no change <strong>✓</strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.</p>
</div>
<div class="specification">
<p>The beam is incident normally on a double slit. The distance between the slits is 0.300 mm. A screen is at a distance <em>D </em>from the slits. The diffraction angle <em>θ </em>is labelled.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_17.53.34.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/03.a"></p>
</div>
<div class="specification">
<p>The graph of variation of intensity with diffraction angle for this experiment is shown.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-13_om_12.36.49.png" alt="M18/4/PHYSI/HP2/ENG/TZ1/03.b"></p>
</div>
<div class="specification">
<p>A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.</p>
</div>
<div class="specification">
<p>The beam is incident normally on a double slit. The distance between the slits is 0.300 mm. A screen is at a distance <em>D </em>from the slits. The diffraction angle <em>θ </em>is labelled.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_17.53.34.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/03.a"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the beam has to be coherent in order for the fringes to be visible.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The wavelength of the beam as observed on Earth is 633.0 nm. The separation between a dark and a bright fringe on the screen is 4.50 mm. Calculate <em>D</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the angular separation between the central peak and the missing peak in the double-slit interference intensity pattern. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce, in mm, the width of one slit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The wavelength of the light in the beam when emitted by the galaxy was 621.4 nm.</p>
<p>Explain, without further calculation, what can be deduced about the relative motion of the galaxy and the Earth.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>superposition of light from each slit / interference of light from both slits</p>
<p>with path/phase difference of any half-odd multiple of wavelength/any odd multiple of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> (in words or symbols)</p>
<p>producing destructive interference</p>
<p> </p>
<p><em>Ignore any reference to crests and troughs.</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>light waves (from slits) must have constant phase difference / no phase difference / be in phase</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of solving for <em>D </em>«<em>D</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{sd}}{\lambda }">
<mo>=</mo>
<mfrac>
<mrow>
<mi>s</mi>
<mi>d</mi>
</mrow>
<mi>λ</mi>
</mfrac>
</math></span>» ✔</p>
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4.50 \times {{10}^{ - 3}} \times 0.300 \times {{10}^{ - 3}}}}{{633.0 \times {{10}^{ - 9}}}} \times 2">
<mfrac>
<mrow>
<mn>4.50</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>0.300</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>633.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>9</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>×</mo>
<mn>2</mn>
</math></span>» = 4.27 «m» ✔</p>
<p> </p>
<p><em>Award <strong>[1]</strong> max for 2.13 m.</em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>sin <em>θ</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4 \times 633.0 \times {{10}^{ - 9}}}}{{0.300 \times {{10}^{ - 3}}}}">
<mfrac>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mn>633.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>9</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>0.300</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>sin <em>θ</em> = 0.0084401…</p>
<p>final answer to three sig figs (<em>eg </em>0.00844 or 8.44 × 10<sup>–3</sup>)</p>
<p> </p>
<p><em>Allow ECF from (a)(iii).</em></p>
<p><em>Award </em><strong><em>[1] </em></strong><em>for 0.121 rad (can award MP3 in addition for proper sig fig)</em></p>
<p><em>Accept calculation in degrees leading to 0.481 degrees.</em></p>
<p><em>Award MP3 for any answer expressed to 3sf.</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of diffraction formula <strong>«</strong><em>b</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{\theta }">
<mfrac>
<mi>λ</mi>
<mi>θ</mi>
</mfrac>
</math></span><strong>»</strong></p>
<p><strong><em>OR</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{633.0 \times {{10}^{ - 9}}}}{{0.00844}}">
<mfrac>
<mrow>
<mn>633.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>9</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>0.00844</mn>
</mrow>
</mfrac>
</math></span></p>
<p><strong>«</strong>=<strong>»</strong> 7.5<strong>«</strong>00<strong>»</strong> × 10<sup>–2</sup><strong> «</strong>mm<strong>»</strong></p>
<p> </p>
<p><em>Allow ECF from (b)(i).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wavelength increases (so frequency decreases) / light is redshifted</p>
<p>galaxy is moving away from Earth</p>
<p> </p>
<p><em>Allow ECF for MP2 (ie wavelength decreases so moving towards).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>An elastic climbing rope is tested by fixing one end of the rope to the top of a crane. The other end of the rope is connected to a block which is initially at position A. The block is released from rest. The mass of the rope is negligible.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_17.44.22.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/01"></p>
<p>The unextended length of the rope is 60.0 m. From position A to position B, the block falls freely.</p>
</div>
<div class="specification">
<p>In another test, the block hangs in equilibrium at the end of the same elastic rope. The elastic constant of the rope is 400 Nm<sup>–1</sup>. The block is pulled 3.50 m vertically below the equilibrium position and is then released from rest.</p>
</div>
<div class="specification">
<p>An elastic climbing rope is tested by fixing one end of the rope to the top of a crane. The other end of the rope is connected to a block which is initially at position A. The block is released from rest. The mass of the rope is negligible.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_17.44.22.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/01"></p>
<p>The unextended length of the rope is 60.0 m. From position A to position B, the block falls freely.</p>
</div>
<div class="specification">
<p>At position C the speed of the block reaches zero. The time taken for the block to fall between B and C is 0.759 s. The mass of the block is 80.0 kg.</p>
</div>
<div class="specification">
<p>For the rope and block, describe the energy changes that take place</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At position B the rope starts to extend. Calculate the speed of the block at position B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the magnitude of the average resultant force acting on the block between B and C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the magnitude of the average force exerted by the rope on the block between B and C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>between A and B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>between B and C.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the time taken for the block to return to the equilibrium position for the first time. </p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed of the block as it passes the equilibrium position. </p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>use of conservation of energy</p>
<p><strong><em>OR</em></strong></p>
<p><em>v</em><sup>2</sup> = <em>u</em><sup>2</sup> + 2<em>as</em></p>
<p> </p>
<p><em>v</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2 \times 60.0 \times 9.81} ">
<msqrt>
<mn>2</mn>
<mo>×</mo>
<mn>60.0</mn>
<mo>×</mo>
<mn>9.81</mn>
</msqrt>
</math></span><strong>»</strong> = 34.3 <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of impulse <em>F</em><sub>ave</sub> × Δ<em>t</em> = Δ<em>p</em></p>
<p><strong><em>OR</em></strong></p>
<p>use of <em>F</em> = <em>ma</em> with average acceleration</p>
<p><strong><em>OR</em></strong></p>
<p><em>F</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{80.0 \times 34.3}}{{0.759}}">
<mfrac>
<mrow>
<mn>80.0</mn>
<mo>×</mo>
<mn>34.3</mn>
</mrow>
<mrow>
<mn>0.759</mn>
</mrow>
</mfrac>
</math></span></p>
<p> </p>
<p>3620<strong>«</strong>N<strong>»</strong></p>
<p> </p>
<p><em>Allow ECF from (a).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>upwards</p>
<p>clearly longer than weight</p>
<p> </p>
<p><em>For second marking point allow ECF from (b)(i) providing line is upwards.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>3620 + 80.0 × 9.81</p>
<p>4400 <strong>«</strong>N<strong>»</strong></p>
<p> </p>
<p><em>Allow ECF from (b)(i).</em></p>
<p><strong><em>[</em></strong><strong><em>2 marks]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(loss in) gravitational potential energy (of block) into kinetic energy (of block)</p>
<p> </p>
<p><em>Must</em><em> see names of energy (gravitational potential energy and kinetic energy) – Allow for reasonable variations of terminology (eg energy of motion for KE).</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(loss in) gravitational potential and kinetic energy of block into elastic potential energy of rope</p>
<p> </p>
<p><em>See note for 1(c)(i) for naming convention.</em></p>
<p><em>Must see either the block or the rope (or both) mentioned in connection with the appropriate energies.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>k can be determined using EPE = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>kx</em><sup>2</sup></p>
<p>correct statement or equation showing</p>
<p>GPE at A = EPE at C</p>
<p><strong><em>OR</em></strong></p>
<p>(GPE + KE) at B = EPE at C</p>
<p> </p>
<p><em>Candidate must clearly indicate the energy associated with either position A or B for MP2.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>T</em> = 2<em>π</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{80.0}}{{400}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>80.0</mn>
</mrow>
<mrow>
<mn>400</mn>
</mrow>
</mfrac>
</msqrt>
</math></span> = 2.81 <strong>«</strong>s<strong>»</strong></p>
<p>time = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{T}{4}">
<mfrac>
<mi>T</mi>
<mn>4</mn>
</mfrac>
</math></span> = 0.702 <strong>«</strong>s<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[0] </em></strong><em>for kinematic solutions that assume a constant acceleration.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p><em>ω</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{{2.81}}">
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mn>2.81</mn>
</mrow>
</mfrac>
</math></span> = 2.24 <strong>«</strong>rad s<sup>–1</sup><strong>»</strong></p>
<p><em>v </em>= 2.24 × 3.50 = 7.84 <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>kx</em><sup>2</sup> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>mv</em><sup>2</sup> <strong><em>OR</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>400 × 3.5<sup>2</sup> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>80<em>v</em><sup>2</sup></p>
<p><em>v = </em>7.84 <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[0] </em></strong><em>for kinematic solutions that assume a constant acceleration.</em></p>
<p><em>Allow ECF for T from (e)(i).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The ball is now displaced through a small distance <em>x </em>from the bottom of the bowl and is then released from rest.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-14_om_06.19.20.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/01.d"></p>
<p>The magnitude of the force on the ball towards the equilibrium position is given by</p>
<p style="text-align: left;"><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\frac{{mgx}}{R}">
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
<mi>x</mi>
</mrow>
<mi>R</mi>
</mfrac>
</math></span></p>
<p>where <em>R </em>is the radius of the bowl.</p>
</div>
<div class="specification">
<p>A small ball of mass <em>m </em>is moving in a horizontal circle on the inside surface of a frictionless hemispherical bowl.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_12.45.38.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a"></p>
<p>The normal reaction force <em>N </em>makes an angle <em>θ</em> to the horizontal.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the direction of the resultant force on the ball.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, construct an arrow of the correct length to represent the weight of the ball.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the magnitude of the net force <em>F </em>on the ball is given by the following equation.</p>
<p> <span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="F = \frac{{mg}}{{\tan \theta }}">
<mi>F</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</math></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The radius of the bowl is 8.0 m and <em>θ</em> = 22°. Determine the speed of the ball.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the ball will perform simple harmonic oscillations about the equilibrium position.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the period of oscillation of the ball is about 6 s.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The amplitude of oscillation is 0.12 m. On the axes, draw a graph to show the variation with time <em>t </em>of the velocity <strong><em>v </em></strong>of the ball during one period.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.</p>
<p> <img src="images/Schermafbeelding_2018-08-12_om_13.41.19.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.d"></p>
<p>The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>towards the centre <strong>«</strong>of the circle<strong>» </strong>/ horizontally to the right</p>
<p> </p>
<p><em>Do not accept towards the centre of the bowl</em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>downward vertical arrow of any length</p>
<p>arrow of correct length</p>
<p> </p>
<p><em>Judge the length of the vertical arrow by eye. The construction lines are not required. A label is not required</em></p>
<p><em>eg</em>: <img src="images/Schermafbeelding_2018-08-12_om_13.22.33.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a.ii"></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p><em>F</em> = <em>N</em> cos <em>θ</em></p>
<p><em>mg</em> = <em>N</em> sin <em>θ</em></p>
<p>dividing/substituting to get result</p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>right angle triangle drawn with <em>F</em>, <em>N </em>and <em>W/mg </em>labelled</p>
<p>angle correctly labelled and arrows on forces in correct directions</p>
<p>correct use of trigonometry leading to the required relationship</p>
<p> </p>
<p><img src="images/Schermafbeelding_2018-08-12_om_13.28.39.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a.ii"></p>
<p><em>tan θ</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\text{O}}}{A} = \frac{{mg}}{F}">
<mfrac>
<mrow>
<mtext>O</mtext>
</mrow>
<mi>A</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mi>F</mi>
</mfrac>
</math></span></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{mg}}{{\tan \theta }}">
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</math></span> = <em>m</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v^2}}}{r}">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span></p>
<p><em>r</em> = <em>R</em> cos <em>θ</em></p>
<p><em>v</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{gR{{\cos }^2}\theta }}{{\sin \theta }}} /\sqrt {\frac{{gR\cos \theta }}{{\tan \theta }}} /\sqrt {\frac{{9.81 \times 8.0\cos 22}}{{\tan 22}}} ">
<msqrt>
<mfrac>
<mrow>
<mi>g</mi>
<mi>R</mi>
<mrow>
<msup>
<mrow>
<mi>cos</mi>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mi>θ</mi>
</mrow>
<mrow>
<mi>sin</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</msqrt>
<mrow>
<mo>/</mo>
</mrow>
<msqrt>
<mfrac>
<mrow>
<mi>g</mi>
<mi>R</mi>
<mi>cos</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</msqrt>
<mrow>
<mo>/</mo>
</mrow>
<msqrt>
<mfrac>
<mrow>
<mn>9.81</mn>
<mo>×</mo>
<mn>8.0</mn>
<mi>cos</mi>
<mo></mo>
<mn>22</mn>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mn>22</mn>
</mrow>
</mfrac>
</msqrt>
</math></span></p>
<p><em>v</em> = 13.4/13 <strong>«</strong><em>ms <sup>–</sup></em><em><sup>1</sup></em><strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[4] </em></strong><em>for a bald correct answer </em></p>
<p><em>Award </em><strong><em>[3] </em></strong><em>for an answer of 13.9/14 </em><strong>«</strong><em>ms <sup>–</sup></em><em><sup>1</sup></em><strong>»</strong><em>. MP2 omitted</em></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>there is no force to balance the weight/N is horizontal</p>
<p>so no / it is not possible</p>
<p> </p>
<p><em>Must see correct justification to award MP2</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the <strong>«</strong>restoring<strong>» </strong>force/acceleration is proportional to displacement</p>
<p> </p>
<p><em>Direction is not required</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>ω</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{g}{R}} ">
<msqrt>
<mfrac>
<mi>g</mi>
<mi>R</mi>
</mfrac>
</msqrt>
</math></span><strong>»</strong> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{9.81}}{{8.0}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>9.81</mn>
</mrow>
<mrow>
<mn>8.0</mn>
</mrow>
</mfrac>
</msqrt>
</math></span> <strong>«</strong>= 1.107 s<sup>–1</sup><strong>»</strong></p>
<p><em>T</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{\omega }">
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mi>ω</mi>
</mfrac>
</math></span> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{{1.107}}">
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mn>1.107</mn>
</mrow>
</mfrac>
</math></span> =<strong>»</strong> 5.7 <strong>«</strong>s<strong>»</strong></p>
<p> </p>
<p><em>Allow use of </em>or <em>g = 9.8 or 10</em></p>
<p><em>Award </em><strong><em>[0] </em></strong><em>for a substitution into T = 2π</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{I}{g}} ">
<msqrt>
<mfrac>
<mi>I</mi>
<mi>g</mi>
</mfrac>
</msqrt>
</math></span></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>sine graph</p>
<p>correct amplitude <strong>«</strong>0.13 m s<sup>–1</sup><strong>»</strong></p>
<p>correct period and only 1 period shown</p>
<p> </p>
<p><em>Accept ± sine for shape of the graph. Accept 5.7 s or 6.0 s for the correct period.</em></p>
<p><em>Amplitude should be correct to ±</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> <em>square for MP2</em></p>
<p><em>eg: v /</em>m s<sup>–1 </sup> <img src="images/Schermafbeelding_2018-08-14_om_06.59.06.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/01.d.iii"></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>speed before collision <em>v</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2gR} "> <msqrt> <mn>2</mn> <mi>g</mi> <mi>R</mi> </msqrt> </math></span> =<strong>»</strong> 12.5 <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p><strong>«</strong>from conservation of momentum<strong>» </strong>common speed after collision is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></span> initial speed <strong>«</strong><em>v<sub>c</sub></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12.5}}{2}"> <mfrac> <mrow> <mn>12.5</mn> </mrow> <mn>2</mn> </mfrac> </math></span> = 6.25 ms<sup>–1</sup><strong>»</strong></p>
<p><em>h = </em><strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v_c}^2}}{{2g}} = \frac{{{{6.25}^2}}}{{2 \times 9.81}}"> <mfrac> <mrow> <msup> <mrow> <msub> <mi>v</mi> <mi>c</mi> </msub> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>g</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <msup> <mrow> <mn>6.25</mn> </mrow> <mn>2</mn> </msup> </mrow> </mrow> <mrow> <mn>2</mn> <mo>×</mo> <mn>9.81</mn> </mrow> </mfrac> </math></span><strong>»</strong> 2.0 <strong>«</strong>m<strong>»</strong></p>
<p> </p>
<p><em>Allow 12.5 from incorrect use of kinematics equations</em></p>
<p><em>Award </em><strong><em>[3] </em></strong><em>for a bald correct answer</em></p>
<p><em>Award </em><strong><em>[0] </em></strong><em>for mg(8) = 2mgh leading to h = 4 m if done in one step.</em></p>
<p><em>Allow ECF from MP1</em></p>
<p><em>Allow ECF from MP2</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Monochromatic light from two identical lamps arrives on a screen.</p>
<p> <img src="images/Schermafbeelding_2018-08-14_om_07.02.59.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/05.a_01"></p>
<p>The intensity of light on the screen from each lamp separately is <em>I</em><sub>0</sub>.</p>
<p>On the axes, sketch a graph to show the variation with distance <em>x </em>on the screen of the intensity <em>I </em>of light on the screen.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Monochromatic light from a single source is incident on two thin, parallel slits.</p>
<p><img src="images/Schermafbeelding_2018-08-14_om_07.10.48.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/05.b_01"></p>
<p>The following data are available.</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\begin{array}{*{20}{l}} {{\text{Slit separation}}}&{ = 0.12{\text{ mm}}} \\ {{\text{Wavelength}}}&{ = 680{\text{ nm}}} \\ {{\text{Distance to screen}}}&{ = 3.5{\text{ m}}} \end{array}">
<mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>Slit separation</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>0.12</mn>
<mrow>
<mtext> mm</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>Wavelength</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>680</mn>
<mrow>
<mtext> nm</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>Distance to screen</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>3.5</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</math></span></p>
<p>The intensity <em>I </em>of light at the screen from each slit separately is <em>I</em><sub>0</sub>. Sketch, on the axes, a graph to show the variation with distance <em>x </em>on the screen of the intensity of light on the screen for this arrangement.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The slit separation is increased. Outline <strong>one </strong>change observed on the screen.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>horizontal straight line through <em>I</em> = 2</p>
<p> </p>
<p><img src="images/Schermafbeelding_2018-08-14_om_07.07.00.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/05.a"></p>
<p><em>Accept a curve that falls from I = 2 as distance increases from centre but not if it falls to zero.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>standard two slit pattern<strong>»</strong></p>
<p>general shape with a maximum at <em>x </em>= 0</p>
<p>maxima at 4<em>I</em><sub>0</sub></p>
<p>maxima separated by <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{D\lambda }}{s}">
<mfrac>
<mrow>
<mi>D</mi>
<mi>λ</mi>
</mrow>
<mi>s</mi>
</mfrac>
</math></span> =<strong>»</strong> 2.0 cm</p>
<p> </p>
<p><em>Accept single slit modulated pattern provided central maximum is at 4. ie height of peaks decrease as they go away from central maximum. Peaks must be of the same width</em></p>
<p><em><img src="images/Schermafbeelding_2018-08-14_om_07.15.48.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/05.b/M"></em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>fringe width/separation decreases</p>
<p><strong><em>OR</em></strong></p>
<p>more maxima seen</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Two equal positive fixed point charges <em>Q</em> = +44 μC and point P are at the vertices of an equilateral triangle of side 0.48 m.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Point P is now moved closer to the charges.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">A point charge <em>q</em> = −2.0 μC and mass 0.25 kg is placed at P. When <em>x</em> is small compared to <em>d</em>, the magnitude of the net force on <em>q</em> is <em>F</em> ≈ 115<em>x</em>.</p>
</div>
<div class="specification">
<p>An uncharged parallel plate capacitor C is connected to a cell of emf 12 V, a resistor R and another resistor of resistance 20 MΩ.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASoAAADoCAYAAABYbakkAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABFwSURBVHhe7d0NcJT1gcfxnzsMIksjMihcwIjNRY5gmRjB8uIgYJFMeLk0eBwKZHIWLG9G0I4cYZpjUg2mVVJiKRx0MBNkjloT0+jltLkA1xGc42W7vpA2lyKQC5kgXIxhg8rgcvtsnuBCNpCNSfhn9/uZ2cmz/10CzD755vk/z7PP3nTJRwBgMIf9FQCMRagAGI9QATAeoQJgPEIFwHiECoDxCBUA4xEq9BCvPK58JcWsVEn9RXvMckH1rl1alzRSMTHD/bdRizeqxFXv+xNBNO3TulG+580pUHXQJ/j+puoCzYkZqTkFVcG/B3odQoUe4ItU1S6tWvBzVdojLax4bVV6yiadTn5VB0/UqqayQhuG7FVGyjJtcjXazwsQNV7pax6S3OXaf+xLezDQlzq2v1xujVXqpLtYwcMEryNCZm31dJi3Xq6dP9Xjv/hME1NH2oOtGnS46HVVDpqv5csnaqi1Ng4YqZQ1z2qR85C2FbnV1PLEAP0UO2m6EnRYxftPtt1i8nykt3cflnPREqXG9bMH0dsRKnSji6ovfV4pu27RM88vVMLgPvZ4q8Ga8sJ7qnE/o8TAh/pHafDNUvPpRp23hwI54mbpmUW3y737Xbk9ganyqunwW9pWebtSp9+rKHsUvR+hQjdyaMDoJ1XxRqamDO1rj12f9/iH2tsgDRod40tZMIOUOH2anJWvq+iw74mXNchVvkfNCYuVPjn4n0TvRKjQjXyhihujuAGhrGaNcr/9e7n1kFbNitfV22AtHIqavEBrEs6ouPzjb6aHTR+rvPiMElInKJY1O6xE8Mvpm5aUrLx8pKnNLWmdCvZVy2M/Gz3B2rleqMy8U0rO36C0a+1jctylSalj1Vy8R64ma/rnm/a59qhYSXrikbv5DRxmeD01WqtL/qKamtpvbpUVyr//Q2WlPaftwY48oRu0HhncLK3erJdSYq6zcvZTXOoSLdIelbt80z9vrfbsfkdK/aGmRXd8monegVAFc90jT+haF1R/aJtWpTyv2n/4tQqeHqcB9iPXFHWvpqfKP/1rPLZHO8qG6cm5CexED0OEqj3XOfKErtKkqoIMTZ2b1xKp9Q+3nKbQIYM1OX2x4orf1Ksl/yF3wt9rVsJA+zGEE0LVnvNNOvuV5BwyUP3tIXS1C6or+alSst6WknO1I6RItXDETlBq3DvKe+W4kp+Yxk70MMXLGoynSiW5L2tn8zimEt3p4sf67foiNfsWm8tWavyIqw5oJGyUK/DdNsE44pT6zD/K6UzS/GnDWaHDVARfM9066rdKD2SU2Pev5HzkGW1Y/rjmJA5l5b+KFRHroAPQU/gZDDzqd+KgCtPv843dp9RZM/UDIgUYgZ/DQI5oTVm/WfnJp7UzY5F+UlLT9r1kAHocobqaI0YpL23W6vjPVbb2ZZXWXbAfQEdZU0OgKxGqYAbcryU5KxTfXKS12WWqY7MKuKEIVVAODUhMU87qcWouy1F2KVNA4Ebik5IRsusd9eOoILoaW1QAjEeoABiPUAEwHqECYDxjd6ZH6rk4vWEnNDvT0dOMDlWkrey95f9MqNDTmPoBMB6hAmA8QgXAeIQKgPG+9c50a8dpd4nEnem9xfV2piOydPfPapeEqjv+kZF45Ki3/J+v9++MxNcukvXE683UD4DxCBUA4xEqAMYjVACMZ/TO9EjEznT0Nj3xehsbKpiLUCFQT7zeTP0AGI9QATAeoQJgPEIFwHiECoDxCBUA4xEqdDlOTUBXI1QAjEeoABiPUAEwHqECYDxCBcB4hAqA8QgVAOMRKgDGI1QAjEeoABiPUAEwHqECYDxCBcB4hAoh4+oI6GmECoDxCBUA4xEqAMYjVACMR6gAGI9QATAeoQJgPEIFwHiECoDxCBUA4xEqAMYjVACMR6gAGI9QATAeoQJgPEIFwHiECoDxCBUA4xEqAMYjVACMR6gAGI9QATAeoQJgPEIFwHiECoDxCBUA4xEqAMYjVACMR6gAGI9QATAeoQJgPEIFwHiECkDX89aoZOkDihn1tErqLtiDrZpUVbBUo2JmK2tfnbz26LUQKrQrJma4vdR1uuN7wkCOGM3JylSyirQ2u0x1l2vklcdVoKez9uqu1Vl6bkp0hyJEqNA5nmrtK96oxaOG++Nj3UYt3qjifdXy2E9BZHNEJytrw1ypLEfZpTUtW06eI9qeuVmV8SuUs+R+DfA/8/oIFULmra9Q1qOztKysjx4rrVRNTa1qThxW4ZijWpe2QKsKjhIr+PRV9JxntSHZ16q1L6u07lO5tucorzJeq3PSlDgghPxc+pbuvHOYvYRwE/S1/frkpTd/PO7SnTM2XTpy7mt7sNWZS3szJ/n+3OOXXv2fL+yxK7G+hJ/rvaZfn3rz0o//bpj/eXfeec+lGRsPXjpnP9ZRbFEhJN5je7Sj7HMlzJ+hhDa/EQdr8lP52py/SGO+w6oV7k6dOqXMzEz/8gcffOD/GkzrFNBp3UlYq1eeHtfhKV8r1iaE4Esd218ut8YqddJdQVcex9BEzU5JUuLQvvYIwtXjjz+m114r9C9nZDylL774wr/chrdeB995X83Wsvv3etvd6B8OBaFCCC7q3GdnfV9v08Dv9GkZQkRqaGjQ8eOf2PfkX66trbXvBWpSVWGO1pZJjzy1VI84Dykvs1AuT0dOSvgGoQIQskGDBmnmzNn2PWn8+ImKi4uz77VqPRXhbSk5U9nPPqdsawpYuVmZ24+EdMCFUCEE/RR9t7UyfqbGcxdbhhCxNm7cqPz8X/lvW7dutUcDXD4VYam2rE9WtKP1KOCtqszL0XZXx6eAhAoh6KM7Ro9Vgg6reP/Jds4oblL1vrf0lqu+Q2cco/e65ZZblJKS4r9ZW1hXagw4FWGlprTus2w9ETTEKSChQkgcsdP0hO83onv3u3K3Wcmst0Y8pzlpO/RX39YXK1ekuqC6kn/RgrxKxa/O1JLEgfZ4i8tHAUOYAt5knaNgL3eKdUaydcIfwk97r611wuf69OX63fAV+tWadD0cF+U/U71i+4tamfeRJmW/ql+mjw56CJr1BZ3BLz2EzDH0Ya0v+Df9/MHT+sXD8S1voYmfqpVHR+uFwl3tRgroLLao0K7ueG1ZX9AZbFEBMB6hAmA8QgXAeIQKgPEIFQDjdTpU1dXVWrZsmX/5wIED/q8AeoeSkhLNmzfP/zNsXa7FdJ0+PeGhhyZf8e5pt/vDIKfRozfj9ITwZIVpwoTv2/da3lD8+uuv2/fM1OlQWSscwl93hArhp7t/+XQ6VNaV/VovmtUbiozQsUUVnqwL3CUlzbg8I8rJeVELFy70L5vqW52Zbu2bmj9/nqqqqv3vpEZ4IVThy7rwnct1RP37OzVx4kR71Fy8hQbtIlQwBacnADAeoQJgPEIFwHiECoDxCBWALuetK9HSUcMVk5Qf/LronkPKSxrZ/uNXIVQAupzjmtdFD/zghzQltvnE7bYIFYBuEPDRWNte03/WXbDHrc/6K1RmOx/80B5CBaB7tH40loq0NrtMddYMz1utN9Zbn/W3QjlL7u/wtfUJFYBu0zoFVFmOskur9b+lv1auu+NTvlaECkCnWG+hs66iYt3av9STNQVcrjUJn6ssY6omZRRJi57Wjzo45WtFqAB0ivU+X+uNzdbNWrbePxiUI06Prl+heGvZOVcbVkxUlP+BjiNUAEIWLErWVRmCc2jAmAc1w7pc3aSpGh9tf7x7CAgVgJBZF8lcuDDNvifNnDlbw4YNs+91PUIFoFNycnJUUbHXv7xlyxb/1+5CqAB0WlxcnL3UvQgVAOMRKgDdr0+iVrtrVfObFA21h0JBqNCu7rgSJ1f3RGcQKgDGI1QAjEeoABiPUAEwHqECYDxCBcB4hAqA8QgVAOMRKgDGI1QAjEeoABiPUAEwHqECYDxCBcB4hAqA8QgVAOMRKgDGI1QAjEeoABiPUAEwHqECYDxCBcB4hAqA8QgVAOMRKgDGI1QAjEeoABiPUAEwHqECYDxCBcB4hAqA8QgVAOMRKgDGI1QAjEeoABiPUAEwHqECYDxCBcB4hAqA8QgVAOMRKgDGI1QAjEeoABiPUAEwHqECYDxCBcB4hAqA8QgVAOMRKgDGI1QAjEeoABiPUAEwHqECYDxCBcB4hAqA8W665GMvd0pMzHDV1NTa93AjWK9BpGLdu/F6ogGEKgxE6mvAumeGnngdmPoBMB6hAmA8QgXAeIQKgPG6ZGc6brxI3ZkOM3T3+vetQ4Ubj6N+CHdM/QAYj1ABMB6hAmA8QgXAeOxMDwORfPSLnemRgVABMB5TPwDGI1QAjEeoIoS3/pB2rpvt35/lv436kfJKXKr32k/QBdW7dmld0sjLzxm1eKNKXPW6/JSrXXQpL6H1+2VpX1PbZ3qrCzTH//1mKM/lsUeB0BCqSOA5pE3pC5VzeqaKDn6imppKVWwYpnczHlP6pkPy56PpgF5ZkK0j9+eqorJGNScOakv0XmWkPKvC6i/93+aamveo3NVg32n1pY7tL5fbvncFT7X2FW/U4lF26Py32VpXUCZX/QX7SUALQhX2vGo6/Ja2VY7Qk8sXatzQvr6xKMWlZOifF92uym1v6XDTRTW59qi4eazmpycpboBvtXBEa/KiuUrQR3rv6JmWb9Wee0Yr3nlGH534vyu3vrwntb+4WvHxI+yBFt76CmU9Oktpq/ZqSOabOnii1hfPT3SwZL60e7VSHpirrH117W/JIeIQqrDnUNSUbP255l2tThxgj1n6KWqw07cl1KDG8x799U//rWZnrEYMsULWwnH3GE0d1KD9h46pyR4LasRszU+9Xe7i93UsoC7eY++ruHqq5s+71x7x8Vap8MnlKqi8R+mF/6qfLRqnof61sK+GJi7Qz3bkKtn5JxUsy1VpHVtWaEGoIpX3lD7ce0Ia9F3FDPZtUZ1tlm4eqKj+AauEw6nbYpxqPt2o8/ZQcNGaMH2anO5y7T/WOk08qz8W/EbVqT/QhEF97DHf1t0fdynX7fu7EuZq0eToNiugIzpJz655yBfQd7TjD8fZqoIfoYpIXnnc72q329eLVTOV0OcLNZ4Oss3k6K+Bd9xs37kWh25NnKZU52EV7z/ZEpemj1VeLKVO/55u9T/H4tX5xgb5MqVBU8fo7qBrX18NGRErXx7lfu/P+tQeRWQjVJHIc0TbMzfrZHKutqaN7JqVICpW4ybdbE//fFtO1j4vTdP0xEH2EzrKof5RA2Xl0TlkoPq3DCLCEapI4zmqglUrlKcV2vXSHEX714BbNHBIlP/hK3jPq/HTr+w713O7Rj/4Pcl9WEc//VSu8j2+zalpSowKXMX66I7RY5XgW/rqbFM708mLOlvziRp821RxcX+jwL1qiFyEKoJ46w8of9U/Kat2jgoLlirROrrnZ+9Y/6pRTecD94Y367Oa5g5u2fRT7KTpvgi5dehAhT3tu1dX588RO01PJEeruXiPXEHOu5Ia9ZdDvjlp/AqtfzSOFRR+rAcRwStP1U49OXWeXvJH6jlN8Z+m0Kq//va+78vZfEwnTn9zpM17/EPtbej4lo0jdoJSE85o56o12tnetM8Ro5SXdio/9SO9mFuqak9gGOt1KH+Nlh2ZpvxX0gNCikjHmhABvHWl+knKWv1Bc5W/4+pIWRyK8u8M/y/l5v5OVVY8PFUqLSiS25mkJx65u2MriuMuTUod6190tpn2WZrlys/XPm+cUl4o0htp55SbVqhqf6s8cm1ar5LblmpvWbZSYhtVsmqrXBf9fxARjlCFPY/cv92iMutQW3ORMsZ/N+BMcOtmv7UlaqKe2pWr1NrnNT0+RjHxDyvjyBi9sGut5kRfHbb2tE7/RgSd9vl9/e9Ku9f3/WNiFD/dF89PGnTOH6rPVHP0gHau+6EeGOH7d42YqIx91z4pApGDy7wAMB5bVACMR6gAGI9QATAeoQJgPEIFwHiECoDhpP8HurI7PU2ADAgAAAAASUVORK5CYII="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the magnitude of the resultant electric field at P is 3 MN C<sup>−1</sup></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the direction of the resultant electric field at P.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why <em>q</em> will perform simple harmonic oscillations when it is released.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the period of oscillations of <em>q</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At <em>t</em> = 0, the switch is connected to X. On the axes, draw a sketch graph to show the variation with time of the voltage <em>V</em><sub>R</sub> across R.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The switch is then connected to Y and C discharges through the 20 MΩ resistor. The voltage <em>V</em><sub>c</sub> drops to 50 % of its initial value in 5.0 s. Determine the capacitance of C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«electric field at P from one charge is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>k</mi><mi>Q</mi></mrow><msup><mi>r</mi><mn>2</mn></msup></mfrac><mo>=</mo></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mn>44</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>48</mn><mn>2</mn></msup></mrow></mfrac></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>7168</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> «NC<sup>−1</sup>» ✓</p>
<p><br>« net field is » <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>7168</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo>×</mo><mi>cos</mi><mo> </mo><mn>30</mn><mo>°</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>97</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> «NC<sup>−1</sup>» ✓</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>directed vertically up «on plane of the page» ✓</p>
<p> </p>
<p><em>Allow an arrow pointing up on the diagram.</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>force «on <em>q</em>» is proportional to the displacement ✓</p>
<p>and opposite to the displacement / directed towards equilibrium ✓</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mi>a</mi><mo>=</mo><mfrac><mi>F</mi><mi>m</mi></mfrac><mo>=</mo><mo>»</mo><msup><mi>ω</mi><mn>2</mn></msup><mi>x</mi><mo>=</mo><mfrac><mrow><mn>115</mn><mi>x</mi></mrow><mrow><mn>0</mn><mo>.</mo><mn>25</mn></mrow></mfrac></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mi>ω</mi></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>29</mn><mo> </mo><mo>«</mo><mtext>s</mtext><mo>»</mo></math> ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow <strong>ECF</strong> for <strong>MP2</strong>.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>decreasing from 12 ✓</p>
<p>correct shape as shown ✓</p>
<p><img src="data:image/png;base64,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"></p>
<p> </p>
<p><em>Do not penalize if the graph does not touch the t axis.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><msup><mi>e</mi><mrow><mo>-</mo><mfrac><mrow><mn>5</mn><mo>.</mo><mn>0</mn></mrow><mrow><mn>20</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo> </mo><mi>C</mi></mrow></mfrac></mrow></msup></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup></math> «F» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the position of the principal lines in the visible spectrum of atomic hydrogen and some of the corresponding energy levels of the hydrogen atom.</p>
<p><img 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"></p>
</div>
<div class="specification">
<p>A low-pressure hydrogen discharge lamp contains a small amount of deuterium gas in addition to the hydrogen gas. The deuterium spectrum contains a red line with a wavelength very close to that of the hydrogen red line. The wavelengths for the principal lines in the visible spectra of deuterium and hydrogen are given in the table.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">Light from the discharge lamp is normally incident on a diffraction grating.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the energy of a photon of blue light (435nm) emitted in the hydrogen spectrum.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a)(i).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain your answer to (a)(ii).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The light illuminates a width of 3.5 mm of the grating. The deuterium and hydrogen red lines can just be resolved in the second-order spectrum of the diffraction grating. Show that the grating spacing of the diffraction grating is about 2 × 10<sup>–6 </sup>m.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the angle between the first-order line of the red light in the hydrogen spectrum and the second-order line of the violet light in the hydrogen spectrum.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The light source is changed so that white light is incident on the diffraction grating. Outline the appearance of the diffraction pattern formed with white light.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>identifies λ = 435 nm ✔</p>
<p><em>E</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{hc}}{\lambda }">
<mfrac>
<mrow>
<mi>h</mi>
<mi>c</mi>
</mrow>
<mi>λ</mi>
</mfrac>
</math></span> =» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{4.35 \times {{10}^{ - 7}}}}">
<mfrac>
<mrow>
<mn>6.63</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>34</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4.35</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> ✔</p>
<p>4.6 ×10<sup>−19</sup> «J» ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>–0.605 <em><strong>OR</strong> </em>–0.870 <em><strong>OR</strong></em> –1.36 to –5.44 <em><strong>AND</strong></em> arrow pointing downwards ✔</p>
<p><em>Arrow <strong>MUST</strong> match calculation in (a)(i)</em></p>
<p><em>Allow ECF from (a)(i)</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Difference in energy levels is equal to the energy of the photon ✔</p>
<p>Downward arrow as energy is lost by hydrogen/energy is given out in the photon/the electron falls from a higher energy level to a lower one ✔</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{{2\Delta \lambda }} = \frac{{656.20}}{{0.181 \times 2}} = 1813">
<mfrac>
<mi>λ</mi>
<mrow>
<mn>2</mn>
<mi mathvariant="normal">Δ</mi>
<mi>λ</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>656.20</mn>
</mrow>
<mrow>
<mn>0.181</mn>
<mo>×</mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>1813</mn>
</math></span> «lines» ✔</p>
<p>so spacing is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3.5 \times {{10}^{ - 3}}}}{{1813}}">
<mfrac>
<mrow>
<mn>3.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1813</mn>
</mrow>
</mfrac>
</math></span> «= 1.9 × 10<sup>−6</sup> m» ✔</p>
<p> </p>
<p><em>Allow use of either wavelength or the mean value</em></p>
<p><em>Must see at least 2 SF for a bald correct answer</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>2 × 4.1 × 10<sup>−7</sup> = 1.9 × 10<sup>−6</sup> sin <em>θ</em><sub>v</sub> seen</p>
<p><em><strong>OR</strong></em></p>
<p>6.6 × 10<sup>−7</sup> = 1.9 × 10<sup>−6</sup> sin <em>θ</em><sub>r</sub> seen ✔</p>
<p> </p>
<p><em>θ</em><sub>v</sub> = 24 − 26 «°»</p>
<p><em><strong>OR</strong></em></p>
<p><em>θ</em><sub>r</sub> = 19 − 20 «°» ✔</p>
<p> </p>
<p>Δ<em>θ</em> = 5 − 6 «°» ✔</p>
<p> </p>
<p><em>For MP3 answer must follow from answers in MP2</em></p>
<p><em>For MP3 do not allow ECF from incorrect angles</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>centre of pattern is white ✔</p>
<p>coloured fringes are formed ✔</p>
<p>blue/violet edge of order is closer to centre of pattern</p>
<p><em><strong>OR</strong></em></p>
<p>red edge of order is furthest from centre of pattern ✔</p>
<p>the greater the order the wider the pattern ✔</p>
<p>there are gaps between «first and second order» spectra ✔</p>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Two loudspeakers A and B are initially equidistant from a microphone M. The frequency and intensity emitted by A and B are the same. A and B emit sound in phase. A is fixed in position.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOMAAADjCAYAAAB3jqNMAAARFklEQVR4nO3df1CUd34H8HfsTeagHFM3l9EbQLHApHg6mFWSsngHxi0eh6dkpWdyYIIK08QkNdGLrYKX3gSSKYYoTeJpQYUTkugp4ORS2tzmJJ6wNZzErbnQ+MgJ6hPDNSwtsTyOM8f2D126/MyuPLvP93me92uGf3Z39vnO7Lz5fJ4fn+e5y+v1ekEGcgNSbRGy/6ENkQWHcLosE9FaL4kCMkPrBZDKhnvR3tSHv968AQmNJ9E5OKz1iihADKOhDGPw1JuolGxYsT4PuUnvoKpRAuOoDwyjoXjQ6WwFHMtg/bN5sD08H+ebXOhmGnWBYTSSwY/xfiOw2r4A0fg6EtLtWOh2or37htYrowAwjIZxA1JjDd5CJpZbLQCAGQlpyE35CJV1/45BjVdHX41hNIrhXrQ3fYRIxzJYo2//rDPmwvbw/RjigRxd+JrWCyB1DHe70OwewpB7Paz1Y9+9gvc7n0Fm5je1WBoFiJXREL7AqbpDOJ/yAlp+fwkXe/z/OlBTALy1+5eQWByFxjAaweDHeL/xJrLWP4SEcb+oBVZ7JiJ5IEd4DKPuDWOw8yROIAs/fCh2gh90BqKXrMSG5E/Q3NbLc44CYxj1blhC0+53EFe8EkuiJ/k5oxYiZ+18nK94E6d4IEdYd/HaVCIxsDISCYJh1Bmn04mnNm2CLMtaL4VUxjDqiCzLeKKoGDabDevy8+FyubReEqmI+4w6oSgKNhQWYmNxMex2OyRJwt8UF+OHax/B44WPQ1EU9Pf3AwB6e3vxv9evY3VursarpmAwjDqxq6ICAPD8tm0jr/kC2nHmQ8yJnwtbejoAIDY2Dt/61myGUWd4OZwOOJ1OdJ49i4O1taNev3DhAvr6+vBh51lYLBaNVkdqYWUUnCzLyEhfig/aTiMmJmbkdY/HgzyHA7urqpCSkqLhCkktPIAjuMuXLwMAurq6Rr2+s7QUG4uKGEQDYRgFl5aWhg/aTuNAdTV2VVRAURQ01N8ay8gvKNB4daQmtqk6oSgKXn/tNXSePYtr166hsbl53H6ioigAgIiICC2WSNPEyqgTEREReH7bNsxfsAAPr1kz4QGbxuPH8eOtW3lBgE4xjDqzatUq/Ncf/jDhe/kFBcjKykJG+lI4nc4wr4ymi2HUmbi4OLS3tU36/urc3HH7mKQPDKPOWCwWXO7phcfjmfQzMTExI+ckNxQWsm3VCYZRhx7J/9HIpW+T8e1jbiwuZtuqEwyjDiUnJ+OT3/0uoM/a7XZ80HYaTY2NKC0pYdsqMJ7aMAlFUVBXW4ejR97G/upqJCUlab0kGoNhNBmXy4WS7dux+dlneSG5YBhGE5JlGS+Vl2PmzJnYsnUrLzIXBPcZTSgmJgavVFYiOTkZeQ4H3G631ksisDKantvtxnObN2NjURGvddUYw0jweDzYWVoKAHixrIxtq0bYphIsFgve2LsXNpsNeQ4H762jEVZGGmXsvXU4ARI+rIw0SlJSEt5tacHVq1c4ARJmDCONExERgbLycmRlZWFdfj4vpQsTtqk0JUmS8JPSUlgXL8bTzzzDtjWEWBlpSklJSZwACRNWRgqY0+nEE0XF2FdTDbvdrvVyDIdhpKDIsowfb9mChMRElJSWsm1VEdtUCopvcDk2Ng452dmQJEnrJRkGKyPdMU6AqIthpGnxnwBh2zo9bFNpWvwnQHKyszkBMg2sjKQaToBMD8NIquIEyJ1jm0qqGjsBwrY1cKyMFDK+tpUTIIFhZaSQSUlJ4QRIEBhGCqmxEyAcXJ4c21QKG9/gcvb3v88JkAmwMlLY+AaXAU6ATISVkTTBCZDxGEbSjG8ChIPLt7BNJc34P7qOEyCsjCQIToAwjCQQs0+AsE0lYfgmQHyDy2a7lI6VkYRkxgkQhpGEZbYJELapJCyzTYCwMpIu+LetjjVrDHlwh2Ek3VAUBeVlZRgYGMCOkhLExMRovSRVsU0l3TD6BAgrI+mSER9dx8pIuuT/6DqjTICwMpLuGWUChGEkQzDCBAjbVDIE/wmQDYWFupwAYWUkw3E6nXiprEx3EyAMIxmSHidA2KaSIY2dANFD28rKSIbnG1wWfQKElZEMLy0tDccaG9He3o6nNm2Cx+OZ8vNutxuPrl2LxPh5eCgzEyeam8OyToaRTCHQCRDfBel/v2MHLvZcwv7qarz33nvhCaSXyGTOnTvnXZaR4a0/fNg7NDQ06r2SHTu87e3to17r7+/3LsvIGPc9f7xwyJs7N96bMDfeu7DkpPd/JtrYH//TW7tq/tSfuY2VkUwnJSUFxxob0dXVNe4ZIG83vIlFixaN+rzFYsHlnt5Jvi0SCcmJQONJdA4Oj3t3uNuF5qG5uC/yq9fFMJIpWSyWURMg/oI9DRL50ArkoBXvd47dF72B7rZOLHiyANYAvodhJFNbnZuL/dXV0/uSex/AXzmAE86PMej/+nAv2t+5F8sfmBXQ1zCMZHpJSUnT/IZ7sdieCZzvQZ9fpzrc7cIvk78Da/SfBPQtDCPRtM3AN6zLsFpyor37xu3XbrWof2FfgOiAv4WIAAClJSVIffCBcac9FEUBADTU108+Nxm9AMsdfWhu68Uw8P8tqjXwO9oxjES3tbe1YeUPfoB/3r9/JICKoqCutg6bt2zBgZqaKQ7uWGC129Dd5EL3MDDc3YEzS7+HJdGBR4xhJLptY1ERurq6kJqaipzsbJSWlCAnOxtXr14B4IUtPX2Ke7fOQPRIq/rf6G67hAdXLkRUENtnGIluc6xZg4GBAXR0dODvtm9H5rJl2FFSAuBW1dyydevUX+BrVX/zK5w+Ow+2hK8HtX2GkUzPtx8YERGBN/buRcG6dfjNqVN4oqgYra2tSE1NxcHa2gDuaH6rVb3yi3q4FqciIch0MYxkai6Xa9xJ/7S0NJSVlwMAysrLsTo3N8ALAW61qtm930B6+tygw8URKjIl34GZo0fexv7q6gnPNSbGz8PFnkthW9PXwrYlIkH4bl6VkJiId1taRqpeYvy8cZ8d+1oow8nKSKYi8m0dWRnJFBRFweuvvYbOs2fxQdtpIZ/TwQM4ZHiSJGFDYSEA4GBtrZBBBFgZyeBONDejas8e7CgtFa4tHYthJEPyf3zc4YYGYauhP7apZDiSJCEnOxuxsXF4pbJSF0EEWBnJYBrq63GgpgblL7+MtLQ0rZcTFIaRDMHj8WBnaSkA4FhjYwCXromHbSrpntvtRp7DAZvNhjf27tVlEAFWRtI5X1u6u6oKKSkpWi9nWhhG0iX/B9votS0di20q6Y5v0iIrKwtl5eWGCCLAykg6EsikhZ4xjKQL/m2p/6SFkbBNJeE5nU5kpC8daUuNGESAlZEEpodJCzWxMpKQZFnWxaSFmlgZSTgnmpux9dnnhBwADiWGkYThP2lhhrZ0LLapJAS9TlqoiZWRNOcbANbjpIWaGEbSjP+khV4GgEOJbSppYuykhdmDCLAykgaMNGmhJoaRwsZ3SRug3wHgUGKbSmHhP2mh5wHgUGJlpJAy+qSFmhhGChkzTFqoiW0qhYTT6Rw1AMwgfjVWRlKV/6QFzx0Gh5WRVGPGSQs1sTKSKkR+1JpeMIw0LWaftFAT21S6Y5y0UBcrI90RTlqoj2GkoHg8HrxaWamrR63pBdtUCphv0iI5OZltaQiwMlJAOGkRegwjTckIj1rTC7apNCmXy2WIR63pBSsjjcNJC20wjDQKJy20wzaVRnDSQlusjDRq0oJtqXZYGU1u7KQFg6gdVkYT46SFWBhGE/JNWnRfvMhJC4GwTTUZ/0kLDgCLhZXRRDhpITaGUYc8Hg8ABHxFjP8AMCctxMU2VYeOHjmKzs7OgD7rdruRk53NSQsdYGXUofPn/wPL7cu/8nOctNCXu7xer1frRVBwEuPn4WLPpUnf95+0eLGsjBd46wTbVJ2RJAmpDz4w6ftjH7XGIOoH21Sd+eKLL2BdvHjC93xHS9mW6hPDqCMejwe7X30VC769YML3v/Pd7yJrxQpe4K1TbFN1QpIk5DkcSE1NRWvrSbjd7nGfsVgsDKKeeUl4zU1N3mUZGd729nav1+v1njt3zrssI8Pb39+v8cpITTyaKjjffuDYk/UN9fVob2/HG3v3arg6UhPbVMFlrViBWbNmoaura9Tr+QUFAG6FkoyBlVEHZFlGRvrScRMWHo8HeQ4HnnzqKSxatAgAOI+oYwyjTjidThyorsbB2tqRgzQulwsl27cjNi4Oc+bMwcDAAP7tX1oAAHPi5+LXra1aLpmCxDDqyK6KCgDA89u2Yd/P9k159zaPx8MT/jrDMOqIoijYUFiIvr4+JM+fj1cqK3kqw0AYRgFJkoTY2NgJgybLMlpPnhw5gEPGwTAKxP8ubf77hmQOPLUhCEmSRt2lLaggDn+KutXfRmL8vPF/2aWoa5VwPUTrJvXw2lRBfHjmDDYWF0/vLm0pL6ClqRBJI/9ib+LzjoP4yeOP4cxLR/B67hz+9xUYfxtB5BcUhOB2iXdjdmoefuS4G+8d+jW6h1X+elIVw2gSkQvjMYu/ttD48xjaTXzecQxH+x/FwadtiNZ6OTQl7jOGkSzL+G1HB1bn5oZmA+6fIvvPfzr+9eTHsOLLG1gy++7QbJdUwcoYJi6XC+vy8/GnUVGh20jKC2j5/SVc7PH9dePcr3bjURzD1r+tQ+d17jSKjGEMMUVRsO9n+1CyfTv2V4f7mRYzEJX0PTy29n6g6xiafusJ47YpWAxjCPme8HT16hW829Ki0UTF3ZgVn4BIDbZMweE+Y4iI84Snm+jr6cZQZCaWW3nhuMgYxhBpPXlSgCc8DeO69K/4+ZFPcF/xZiyJZiMkMl6bagTDn6LuYQdedA+Nfy85Hzs3ObAix4rZzKLQGEYiQfB/JZEgGMZpcLvdkCRJ62WQQTCMd6ihvh7Pbd6s9TLIQHg0NUiyLOOl8nIAwLHGRt5nhlTDyhgE3yVtWVlZfMITqY6VMQCKoqCutm7Ku7ERTRfDGIALFy7gyy8H8W5LC+9LQyHD84xEguA+I5EgGEYiQTCMfpxOJzwezvyRNngAB7eeS7GztBQAYLVaNV4NmZXpK6Pb7UaewwGbzcZzh6Qp01ZGRVHQePw4DtTUYHdVFVJSUrReEpmcKcPou6Rt5syZvKSNhGHK84wN9fWIiooK3S0Tie6AKcNIJCLTH8AhEgXDSCQIw4ZRURScaG7WehlEATNkGCVJQk52Nq5d+1zrpRAFzHCnNk40N6Nqzx6Uv/wy0tLStF4OUcAME0b/S9oONzRofPNgouAZok0de0kbg0h6ZIjK+IujR3lJG+keT/oTCcIQbSqRETCMRILQTRhlWYbL5dJ6GUQho4swnmhuRkb6Uq2XQRRSQh9NVRQF5WVlGBgYEODBo0ShJWxl9F3SFhsbh1cqKxlEMjwhK2NDfT0O1NTwkjYyFeHCKMsyPvvsM94Og0yHJ/2JBCHsPiOR2TCMRILQLIwulwuSJGm1eSLhhD2MiqJgV0UF/mnPHtxzzz3h3jyRsMIaRlmWsaGwEABwsLaWR0uJ/IT1aKokSejt7YXdbg/XJol0g6c2iAQx/ZP+g63Y+Zfr8dbQBO9F2vH0S0/ikVVWzOZxW6IpqRaRyIJD6Oy5hIsjf90415SBT3asw8aqDlxXa0NEBhXCejUDUffl4flt9+PTqiocl26EblNEBhCm5vEKLsqsjURTCU8YIzOx3MrTGERTCWEYb+LzjlrsqvgI9xWvxJJoHsEhmopqI1RD9ethrR/zYnI+dv7jYazIsSJKrQ0RGZRqYYwsOITTZZmIVusLiUyGvSORIBhGIkEwjESCYBiJBMELxYkEwcpIJIj/A57/aMlpD3r+AAAAAElFTkSuQmCC"></p>
<p>B is moved slowly away from M along the line MP. The graph shows the variation with distance travelled by B of the received intensity at M.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the received intensity varies between maximum and minimum values.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain the wavelength of the sound measured at M.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>B is placed at the first minimum. The frequency is then changed until the received intensity is again at a maximum.</p>
<p>Show that the lowest frequency at which the intensity maximum can occur is about 3 kHz.</p>
<p style="text-align:center;">Speed of sound = 340 m s<sup>−1</sup></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Loudspeaker A is switched off. Loudspeaker B moves away from M at a speed of 1.5 m s<sup>−1</sup> while emitting a frequency of 3.0 kHz.</p>
<p>Determine the difference between the frequency detected at M and that emitted by B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>movement of B means that path distance is different « between BM and AM »<br><em><strong>OR</strong></em><br>movement of B creates a path difference «between BM and AM» ✓</p>
<p>interference<br><em><strong>OR</strong></em><br>superposition «of waves» ✓</p>
<p>maximum when waves arrive in phase / path difference = n x lambda<br><em><strong>OR</strong></em><br>minimum when waves arrive «180° or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi></math> » out of phase / path difference = (n+½) x lambda ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wavelength = 26 cm ✓</p>
<p><br>peak to peak distance is the path difference which is one wavelength</p>
<p><em><strong>OR</strong></em></p>
<p>this is the distance B moves to be back in phase «with A» ✓</p>
<p> </p>
<p><em>Allow 25 – 27 cm for <strong>MP1</strong>.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>λ</mi><mn>2</mn></mfrac></math>» = 13 cm ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo></math>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>c</mi><mi>λ</mi></mfrac><mo>=</mo><mfrac><mn>340</mn><mrow><mn>0</mn><mo>.</mo><mn>13</mn></mrow></mfrac><mo>=</mo></math>» 2.6 «kHz» ✓</p>
<p> </p>
<p><em>Allow ½ of wavelength from (b) or data from graph for <strong>MP1</strong>.</em></p>
<p><em>Allow ECF from <strong>MP1</strong>.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>=</mo><mi>f</mi><mfrac><mi>v</mi><mrow><mi>v</mi><mo>+</mo><msub><mi>u</mi><mn>0</mn></msub></mrow></mfrac></math> (+ sign must be seen) <strong><em>OR</em> </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo></math>= 2987 «Hz» ✓<br>« <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Δ</mi><mi>f</mi></math>» = 13 «Hz» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>Attempted use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>Δ</mi><mi>f</mi></mrow><mi>f</mi></mfrac></math>≈ <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>v</mi><mi>c</mi></mfrac></math><br><br>« Δf » = 13 «Hz» ✓</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was an "explain" questions, so examiners were looking for a clear discussion of the movement of speaker B creating a changing path difference between B and the microphone and A and the microphone. This path difference would lead to interference, and the examiners were looking for a connection between specific phase differences or path differences for maxima or minima. Some candidates were able to discuss basic concepts of interference (e.g. "there is constructive and destructive interference"), but failed to make clear connections between the physical situation and the given graph. A very common mistake candidates made was to think the question was about intensity and to therefore describe the decrease in peak height of the maxima on the graph. Another common mistake was to approach this as a Doppler question and to attempt to answer it based on the frequency difference of B.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates recognized that the wavelength was 26 cm, but the explanations were lacking the details about what information the graph was actually providing. Examiners were looking for a connection back to path difference, and not simply a description of peak-to-peak distance on the graph. Some candidates did not state a wavelength at all, and instead simply discussed the concept of wavelength or suggested that the wavelength was constant.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was a "show that" question that had enough information for backwards working. Examiners were looking for evidence of using the wavelength from (b) or information from the graph to determine wavelength followed by a correct substitution and an answer to more significant digits than the given result.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates were successful in setting up a Doppler calculation and determining the new frequency, although some missed the second step of finding the difference in frequencies.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>An experiment to investigate simple harmonic motion consists of a mass oscillating at the end of a vertical spring.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>The mass oscillates vertically above a motion sensor that measures the speed of the mass. Test 1 is carried out with a 1.0 kg mass and spring of spring constant <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>k</mi><mn>1</mn></msub></math>. Test 2 is a repeat of the experiment with a 4.0 kg mass and spring of spring constant <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>k</mi><mn>2</mn></msub></math>. </p>
<p>The variation with time of the vertical speed of the masses, for one cycle of the oscillation, is shown for each test.<br><br></p>
<p> <img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the frequency of the oscillation for both tests.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>k</mi><mn>1</mn></msub><msub><mi>k</mi><mn>2</mn></msub></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the amplitude of oscillation for test 1.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In test 2, the maximum elastic potential energy <em>E</em><sub>p</sub> stored in the spring is 44 J.</p>
<p>When <em>t</em> = 0 the value of <em>E</em><sub>p</sub> for test 2 is zero.</p>
<p>Sketch, on the axes, the variation with time of <em>E</em><sub>p</sub> for test 2.</p>
<p style="text-align:center;"><img 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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The motion sensor operates by detecting the sound waves reflected from the base of the mass. The sensor compares the frequency detected with the frequency emitted when the signal returns.</p>
<p>The sound frequency emitted by the sensor is 35 kHz. The speed of sound is 340 m s<sup>−1</sup>.</p>
<p>Determine the maximum frequency change detected by the sensor for test 2.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>1.3 «Hz» ✓</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>∝</mo><mi>m</mi></math> <em><strong>OR </strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>m</mi><mn>1</mn></msub><msub><mi>k</mi><mn>1</mn></msub></mfrac><mo>=</mo><mfrac><msub><mi>m</mi><mn>2</mn></msub><msub><mi>k</mi><mn>2</mn></msub></mfrac></math> ✓</p>
<p>0.25 <em><strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>4</mn></mfrac></math> </strong></em>✓</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>v</em><sub>max</sub> = 4.8 «m s<sup>−1</sup>» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo></math>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>v</mi><mi>ω</mi></mfrac><mo>=</mo><mfrac><mrow><mi>v</mi><mi>T</mi></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mo>.</mo><mn>8</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>80</mn></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac></math>» = 0.61 «m» ✓</p>
<p> </p>
<p><em>Allow a range of 4.7 to 4.9 for <strong>MP1</strong></em></p>
<p><em>Allow a range of 0.58 to 0.62 for <strong>MP2</strong></em></p>
<p><em>Allow <strong>ECF</strong> from <strong>(a)(i)</strong></em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>all energy shown positive ✓</p>
<p>curve starting and finishing at <em>E</em> = 0 with two peaks with at least one at 44 J<br><em><strong>OR</strong></em><br>curve starting and finishing at <em>E</em> = 0 with one peak at 44 J ✓</p>
<p> </p>
<p><em>Do not accept straight lines or discontinuous curves for <strong>MP2</strong></em></p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>read off of 9.4 «m s<sup>−1</sup>» ✓</p>
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>=</mo><mi>f</mi><mfenced><mfrac><mi>v</mi><mrow><mi>v</mi><mo>±</mo><msub><mi>u</mi><mi>s</mi></msub></mrow></mfrac></mfenced></math> <em><strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>=</mo><mi>f</mi><mfenced><mfrac><mrow><mi>v</mi><mo>±</mo><msub><mi>u</mi><mi>o</mi></msub></mrow><mi>v</mi></mfrac></mfenced></math> </strong></em>✓</p>
<p><em>f</em> = 36 «kHz» <em><strong>OR</strong> </em>34 «kHz» ✓</p>
<p>«recognition that there are two shifts so» change in<em> f</em> = 2 «kHz» <em><strong>OR</strong> f</em> = 37 «kHz» <em><strong>OR</strong> </em>33 «kHz» ✓</p>
<p> </p>
<p><em>Allow a range of 9.3 to 9.5 for <strong>MP1</strong></em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>
<p><em><strong>MP4</strong> can also be found by applying the Doppler effect twice.</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>ai) The majority managed to answer this question correctly.</p>
<p>aii) A very well answered question where most worked correctly from the formula for the period of oscillation of a spring.</p>
<p>aiii) Quite a few answers had <em>v</em><sub>max</sub> from the wrong test.</p>
<p>aiv) Most common answers were a correct 2 peak curve, a correct 1 peak curve and a sine curve. Several alternatives were included in the MS as the original data provided in the question was inconsistent, i.e. 44 J is not the maximum kinetic energy available for the second test, and that was taken into account not to disadvantage any candidate´s interpretation.</p>
<p>b) Many got the first three marks for a correct Doppler shift calculation from the correct speed. . There were very few good correct full answers, might be a question to look at for 6/7 during grading.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">Monochromatic coherent light is incident on two parallel slits of negligible width a distance <em>d</em> apart. A screen is placed a distance <em>D</em> from the slits. Point M is directly opposite the midpoint of the slits.</span></p>
<p><span style="background-color: #ffffff;"><img 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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Initially the lower slit is covered and the intensity of light at M due to the upper slit alone is 22 W m<sup>-2</sup>. The lower slit is now uncovered.</span></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The width of each slit is increased to 0.030 mm. <em>D</em>, <em>d</em> and λ remain the same.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Deduce, in W m<sup>-2</sup>, the intensity at M.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">P is the first maximum of intensity on <strong>one</strong> side of M. The following data are available.</span></p>
<p><span style="background-color:#ffffff;"><em>d</em> = 0.12 mm </span></p>
<p><span style="background-color:#ffffff;"><em>D</em> = 1.5 m </span></p>
<p><span style="background-color:#ffffff;">Distance MP = 7.0 mm</span></p>
<p><span style="background-color:#ffffff;">Calculate, in nm, the wavelength λ of the light.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Suggest why, after this change, the intensity at P will be less than that at M.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Show that, due to single slit diffraction, the intensity at a point on the screen a distance of 28 mm from M is zero.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">cii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">there is constructive interference at M<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">the amplitude doubles at M ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">intensity is «proportional to» amplitude<sup>2</sup> ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">88 «<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">W m</span><sup style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:11.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">−2</sup>» ✔</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s = \frac{{\lambda D}}{d} \Rightarrow » \lambda = \frac{{sd}}{D}/\frac{{0.12 \times {{10}^{ - 3}} \times 7.0 \times {{10}^{ - 3}}}}{{1.5}}">
<mi>s</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>λ</mi>
<mi>D</mi>
</mrow>
<mi>d</mi>
</mfrac>
<mo stretchy="false">⇒</mo>
<mrow>
<mo>»</mo>
</mrow>
<mi>λ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>s</mi>
<mi>d</mi>
</mrow>
<mi>D</mi>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mn>0.12</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>7.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.5</mn>
</mrow>
</mfrac>
</math></span> ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda = 560«{\text{nm}}">
<mi>λ</mi>
<mo>=</mo>
<mn>560</mn>
<mrow>
<mo>«</mo>
</mrow>
<mrow>
<mtext>nm</mtext>
</mrow>
</math></span>» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">«the interference pattern will be modulated by»<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">single slit diffraction ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">«envelope and so it will be less»</span></p>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em><strong>ALTERNATIVE 1</strong></em><br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">the angular position of this point is <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta = \frac{{28 \times {{10}^{ - 3}}}}{{1.5}} = 0.01867">
<mi>θ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>28</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.5</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.01867</mn>
</math></span>«rad» ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">which coincides with the first minimum of the diffraction envelope</p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta = \frac{\lambda }{b} = \frac{{560 \times {{10}^{ - 9}}}}{{0.030 \times {{10}^{ - 3}}}} = 0.01867">
<mi>θ</mi>
<mo>=</mo>
<mfrac>
<mi>λ</mi>
<mi>b</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>560</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>9</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>0.030</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.01867</mn>
</math></span> «rad» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">«so intensity will be zero»</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"> </span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em><strong>ALTERNATIVE 2</strong></em><br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">the first minimum of the diffraction envelope is at <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta = \frac{\lambda }{b} = \frac{{560 \times {{10}^{ - 9}}}}{{0.030 \times {{10}^{ - 3}}}} = 0.01867">
<mi>θ</mi>
<mo>=</mo>
<mfrac>
<mi>λ</mi>
<mi>b</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>560</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>9</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>0.030</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.01867</mn>
</math></span>«rad» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">distance on screen is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 1.50 \times 0.01867 = 28">
<mi>y</mi>
<mo>=</mo>
<mn>1.50</mn>
<mo>×</mo>
<mn>0.01867</mn>
<mo>=</mo>
<mn>28</mn>
</math></span>«mm» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">«so intensity will be zero»</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"> </p>
<div class="question_part_label">cii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered by those who attempted it but was the question that was most left blank. The most common mistake was the expected one of simply doubling the intensity.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was very well answered. As the question asks for the answer to be given in nm a bald answer of 560 was acceptable. Candidates could also gain credit for an answer of e.g. 5.6 x 10-7 m provided that the m was included.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many recognised the significance of the single slit diffraction envelope.</p>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Credit was often gained here for a calculation of an angle for alternative 2 in the markscheme but often the final substitution 1.50 was omitted to score the second mark. Both marks could be gained if the calculation was done in one step. Incorrect answers often included complicated calculations in an attempt to calculate an integer value.</p>
<div class="question_part_label">cii.</div>
</div>
<br><hr><br><div class="specification">
<p>A small metal pendulum bob is suspended at rest from a fixed point with a length of thread of negligible mass. Air resistance is negligible.</p>
<p>The pendulum begins to oscillate. Assume that the motion of the system is simple harmonic, and in one vertical plane.</p>
<p>The graph shows the variation of kinetic energy of the pendulum bob with time.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>When the 75 g bob is moving horizontally at 0.80 m s<sup>–1</sup>, it collides with a small stationary object also of mass 75 g. The object and the bob stick together.</p>
<p style="text-align: center;"><img 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CCAAAL2BQgX9s1pEQEEEEAAAQQQQAABJwUIF06WlUEhgAACCCCAAAIIIGBfgHBh35wWEUAAAQQQQAABBBBwUoBw4WRZGRQCCCCAAAIIIIAAAvYFCBf2zWkRAQQQQAABBBBAAAEnBQgXTpaVQSGAAAIIIIAAAgggYF+AcGHfnBYRQAABBBBAAAEEEHBSgHDhZFkZFAIIIIAAAggggAAC9gUIF/bNaREBBBBAAAEEEEAAAScFCBdOlpVBIYAAAggggAACCCBgX4BwYd+cFhFAAAEEEEAAAQQQcFKAcOFkWRkUAggggAACCCCAAAL2BQgX9s1pEQEEEEAAAQQQQAABJwUIF06WlUEhgAACCCCAAAIIIGBfgHBh35wWEUAAAQQQQAABBBBwUoBw4WRZGRQCCCCAAAIIIIAAAvYFCBf2zWkRAQQQQAABBBBAAAEnBQgXTpaVQSGAAAIIIIAAAgggYF+AcGHfnBYRQAABBBBAAAEEEHBSgHDhZFkZFAIIIIAAAggggAAC9gUIF/bNaREBBBBAAAEEEEAAAScFCBdOlpVBIYAAAggggAACCCBgX4BwYd+cFhFAAAEEEEAAAQQQcFKAcOFkWRkUAggggAACCCCAAAL2BQgX9s1pEQEEEEAAAQQQQAABJwUIF06WlUEhgAACCCCAAAIIIGBfgHBh35wWEUAAAQQQQAABBBBwUoBw4WRZGRQCCCCAAAIIIIAAAvYFCBf2zWkRAQQQQAABBBBAAAEnBZKdHBWDQgABBBDwBMrLy/WPf/xDH330kXbt2q2ysn0qKChQz5491bt3b+Xn57eKVH07f/+7duzY6Z0zLS1VvY4+Wscee6x69OjRKu1wEgQQQACB+BYgXMR3fegdAgggcEQCRUVFmj17jl6ZP1+dunZVXVKyfElJSkrP0LN/LFB1VaV8tTWqC4V07XXXatRFFyk3N/ew2zLtPPvMM1qycJHS0tJUWVnpnaNDhw7e97q6OmVlZ8vn8+na66/TRRdffETtHHbHeAMCCCCAwLci0KHO/Jc/5tE/r4+KN22MeYUfEUAAAQQSRcDMIDzwwDT9ZckSZXbqrJzO35E/M6DUlGT5fEneh3ypTrWhkGpralS2d6/+Z+sW7dq6RQ889KBGjx7doqGadqZOmeKFiurqaiUlJys5OVlJScnq4Oug2HARqq1VTXW1ampqZP4vZ+r0abp8zJgWtcNBCCCAAALxJXCorEC4iK960RsEEEDgiAU2b96skT87T3UpqerW62hlBgLKSE9XamqqUlJSlZyUpMiEgkKhOu/DfnVNtSorKrV71y5t/rxYx/3LAD33x+eVkZHRZD9MO+ed+1Pt2b3bCxXm/KmpaUpOSZEvyackX5IXMMwJ6kImyITDhQkh1ZGZjRMHn6w/zp7dbDtNdoBfIIAAAgh8awKEi2+NnoYRQAABewLmA//Pzv2p/Lmd1eW73ZWZmalMvz8cLtJSlZqcoqRkEy7Cy5Vqa0Oqra1VVXWVKiurVF5Rrn37gir59BP16dVDcwrmHPSDv2nnpyN+or2lpUpLT/eWQqV6ASYcLszshVkCFW3HzFSYGZKa2hpVV1apqqpKFRXlqggGddL3BmvuCy8ctB17crSEAAIIIHA4AocKF1wt6nA0OfbgAqWFmnxcH5k/tsZfJ4yfoUWFRSqLfWdog+aOHKgTJhWqNPb1Nvk5pLKiNzXz/j+pKBRuIFRUoAvyztDkwu1t0uIRnbRsg5ZMGhnxG6O5RRVHdJojf1OpipY9rSkvblCYqUJFBWPU/7j7VVgagTvyk/PONhbYuXNnfbDo1qOncnKyldOxo/fVsWO2juqYo5ycjsrNyVFu7lHe905H5Si3Y8fw7yLH5nTM0THHD9LGf2zWbbfedkCvTTvRYJGekaEMv99bcmWWXZlZEhNo/Oa1xl8m6JhjsrLkNz8HAgpkZemjD1frlgkTDmiHFxBAAAEEEleADd2JW7u467l/zBwtnz5M2fU9Mx9Y5+rRG67U63c8ryfGDVTA/M43QGOXrNfY+uPa8oedWjV3up5ae5XOjTTjyx+nRZvGtWWjh3nuChW9Ok0TF/bV4+++opHdUw/z/a1weOlqvXDTLK27Y3jkZOnKHzdPxfHE1ArDdPUU995zr5L9merSvYeyswPKDmSHP8CbD/kZ4dmFtJQUJXnLosIzF6G68LKoqqpqBSvKlWJ+b5YzdeigfgOO1d9WrdIrr7yiiy++uJ7t7rvuqp+xiIaLDH+mN3th3u+dIym8r8PMXphZC2/mwuy5qKnx9mSYmQ1vdqND+Pcr3vl/emXBAl18ySX17fADAggggEDiCjBzkbi1S4CeZyv/rGs15aEhWjnlPj2/encC9Pnb7GK2OgbI+99mBdqibXM1JbP5ua0e7733nlauXKkuPXoqK5CpQGaWAoGAOgYylZ0VUHZWljoGwq8FMjMV8Pu9r6zMTGUFTBAJKCc7Wx3NsYGAd46OOTnq2be/Hn7wofq+m3beXb7CCxDp6eFZCxMs0iNLo8x3s0/DfJmZi/Csxv6ZDPN6/bEZGUozz/1+yefTQ9MfrG+nrZw4LwIIIICAHQHChR3ndtxKqrqfd50mnvjfmr3wo/AyqAbLokIqLbxfJ+SN1OTZj+kab3nV/iVLoW0faF79cqGBOndSgQqLGi2mCm3T6hcn6dzIsqwTxv9ef/WO2a7CSaM0ft6X0pqpGtE3fN4Dl0WZpVOFmttkO9E+jtGcwndi+nOqrpnxporKDrFsqKxIhQX7+9d/xCTNjS4V8yy+pxFTVkjBFzT+hH5NLBczYzlD/Uc+piVv/j7i1EfmXPNWb1GpWfo1/tTwsqrjrtbvP9gWWd5k/vQOMT6zrG3IVZofDGrtlHN0jLcUKniQZVGlKios0OQRAyPLt0ZqckFhzPijfXxWhR+8vP+4467WzGWNlsa1o/9FjPjx2frFuHEyIaMtHk/OfFKZuZ29QJGRnqHMTL+318IEjGiYMLMXJkyYsNGxY46yO3aMBJHwzEZmRiR0BMzypfBeje907arkdL8WLVrkdXvGE0+oPBhUSmqaUtPTlJYWmRFJS/NCQzQ8eN9NcDCvp6WF92XEBA9zuVqzATwcNNLl92dqX1mZFr72WlvwcE4EEEAAAcsChAvL4O2yOV8n9R7UWcG1m/R1k5/DP9aSd7tp4t9K9NnKObrqlFyFtizWjT+6We90uUvLP9+o4k3v6Yn+7+vmkfdryZaqMGXoSy351QW65OUkXfPmGhVvWqNXTv9Et3jHZGvY9Nf0/JijpRPv1+ufv61pwzo3KkFIZRte1m0j79aKaDufL9PULit084+v0swGsy0r9OAjy5Q19kXvcs2frZyu7m/cqVue+7DhnpLYFsrWa+4tV+rm5T01deUGFW/aoOUP9NSKG87XpTM+UJm3ROxDvT5lqOS/Us9/XKKPGywtiz2ZpDVz9L/f7qXb/1ai4s9X6Pn/tVZTLhyq0x8p0enT3/bG/593JOu5sY/oPzyjFowve5imrZyjy/x+DZryX/rsk6kalt34Pw2l2lBwp0bdsEJdHlimzzZt1Gcr71KX5XdrxMVPa3VswFrzez26xK8rX1kbHu+sPL35y7va7czV62++odxOnWRCxqO//W2r/gu92QPx6fr1yu3SVekZ6fKbmYP0dGX6M+RPD3+ZD/Fe4DCzFllZysoKh4ysrCwFMgMKBDKVnpYif0ZmeNbBBAHvK0Nde/bU3IK5Mpu413+81pu1SDWbw03ASEsLP09N9ZZFmdBgvlK8K0eFXzPHhK8kleodb56b/oSvXpXiBQ/zs9kYPregoNEfO08RQAABBBJRoPEniEQcA31OFIGijdoc+yG0Qb+P1sgx52hAwCdft77qG9ipd2bN0Bv51+r2G09VN+8vNVsDxk3T7y5crcmz3vVmQUIlf1XB66m67M6bNDLf7PbI1oALL9VIvaGCNzbG/Ot9g8ZinuzUqhef08oz7tSUaDu+bjrl5of1uzHb9dTUxfUbwaWjY9qRfN1O1LDvZWlD4XptPWhoCql01QI9/u4QTXvgFzqlm9lLkapu379Gj826SF89+aReO9yN2/6LdPsd5yk/4DMd0OAzT5JfQzXxznGR82crf+gP1C+4Wqs+MzM8hzO+GJbGP5au1rzffqTTH5qsX32/m0w5fN1O1U1PPKzLvnhW014t2m8d20cz3sFDNdj/33r746/3H9P4/A4/N3fAfnrWLD0+c4b+MOsZnTtihMwSo9Z4rF69Wr60DKWZD+ip6UpLD88WmHCQnpbu3dvCzFqY2YhApj88kxGZmTBXkvJnmqVKZhmTOUeyMtLSlJGR7n03QaFLt67atnWrVixf7t0cz1xq1nyZvRVm30Q0OET3W5jXTHjwlkaZDdyZ4cBi+hc93hwbfZ95zZzP7N/YumWrTFjigQACCCCQ2AKEi8Sun7u9L12nZQu/lH9Qnro2+CsNqEf/XgoufEurS4MqWbFUa9VL/Xt4W8XDHuZf4j9Zr0XjBngfgptF8trZrn4/ODYSYKJHh9tRs4HoUMfs1OqlhQrmn6jjvGARPbdPgR591E9fqXhzg+toRQ9ove/faHzRboRUuvotLQn20w8GdmloGviu+udLJcVbm569ackx0aYc/j7y/PP1t9Uf6rShQ3XFZaM16d57v/GH6ffff19p/ozwDIL50J+c4gWN8If9JKVHli95YSPDLJnKVFZWwPsyV23KSEtXht8sb0pXeEbC3A/DfPhPUaoXIFKVkp7h7ekwpTF3+E5OCgcCszncfJmAYN5jbqJnZiZMsAgEspSdna2srGzvKlEmPJjzJfl8Xpgw74l9v3mv2QC+Y8cOh/8CGBoCCCDQPgTYPdo+6hwfo8zvox7mX9wP4xGcd5UGzzvIG/z9DvLi4b8U+nqT1gWbeV+wRF98XaXBzRzS5K9CO/TF2uYud7td6zbtUCh8Da0mT9PgF4dp2NLxqWuDVho9qdLXm0rULJO35O34Ru/jaWOB3NxcTX/wQQ0780w9NH263l2xQhNuuUUmeBzJY9vWbfJnZYc/5JsP/eZDe3KSUpKSIx/kzXKk8EyD+dBvQkZaWqrqQiFVVIaXFpp7XVSnpiilMvwe897oh38TJDKzs/XZhg3eh38TDkzAMEEgGg5in5sZCTMTYsKFmcEIhUIKBoMNrhiVFArVv9c7h+mzL0lVlVX6ZP16mZkeHggggAACiStAuEjc2iVOz6OzEBdGZiEOuoToYMMxewAW6rUmZyAq9E23yPq65ul4v7TuYM2b1/z91LtrqrS5qQOaeT2y10Rrmzqms47P69RwJqCpQ4/w9RaPr9nzp6prXj/5VdLkUdEZpiNhMvdGac+PibfcquMGDjyiD9VlZWXenbB9vg7h7x06KKmDuTu2rz4MmEBgPsSneEuW0ryrOIVqa7wP/FXV1d7vogHBXIbWnMuEh/BXB2+mwbvaVYcO6tAhfHM8c1z4WJ98MT+bUGL2Y5irReXk5HiXnzWXoq2qqlRlZUW4X5Hjo+eo/+4LXyK3Pf8tMHYEEEDABQHChQtVjOsxVGnLX5doSXCoJo4dEnMPjEN0Ovt4nXVhZy15/1Ntu3KAutdPeOzW6hm/1CWFP9Pri8ap39DhGqQ54eVF+enhk5orMF1woabpdr2+6KfNN9RkO2XaXPyVlD/8sGdb9jeYq8HDh8m/cI0+2Val/Pr7V4RUtnmjStRL58cu59r/xtb7qaXja3Z1lk/Zg8/USP8ben/9P3VF/tH7A1HZVhUXSf0u+O7hzL80GF/xpo0NnreHJ2vWrNGtEyboy01feHsxjvRf680VobT9wKVETX1MNx/km3sc7Lfm7tqBjIzm3tbgd/VhISZENDigiScmhPBAAAEEEEh8gfqPbIk/FEYQfwLmJnp/0JR7VmrIlLs1Kvrhv0Ud7awf3nCrTn/7EU156j1t82Y7SlW0eIYmPyndeP/5yjd7mvudrQljczT/kT+ocJtZ5lGlbe+8qgVr/iVyTGRfhNdmhcrKasArPFgAABcFSURBVBq1nqtTrrhaQxq1s6Fgsm6e17m+nUZvauFTn7JPuUQTT1upyffN1iqvf+GrN/36hlfVa8KEwzRpYbMNDmvh+Lx9EWnhdwbLdMC+++zBGnPHSVp+zzQ9Hb3MrbkS1m13a37v6zT5ovz9gaNB+zyJFTAbls0Vo0aNPN/be/H2iuVHvCTKnLfbd7upMhhUKFSnulCdzI3xQnUhbzmSWZJUG/0yS59qalRRUeFdTraiolKVVdXezII5LlRb673HfLz3zmFe877qtK+0VH369o3cEC8U+R6+OZ53TORGeeZnc6M8M0thlkLt2rVLe/bs8a6OVV1dLbP8yizHMueP3lwv9rvpg5nB4YEAAgggkNgCzFwkdv3iqvcH7o/wa8CYibp+3iL9ZHD4CkOH02Ff9/P02yU5em3ub3R634+9t/qH36xpC5/WzwbnhE/l665h9/9BC156SpOHDNB48+qxl2vKwqc1OnJMv3Ou0pg/3awRfR/1llm9MjS2Fz4FBozWE0t6xrRj+n27fvfmhRrmXYGqxeu4Yk8c/jkwUGNnvqDer87V/UMGaEOkf5NnLdaoYflH/K/9BzbU1CstGZ/ZqdtH/3brKC0Yd46OmTJUk998Sqc1OKW5Utcjei1voV647ywd86nZgXGCLpvysF6/6Ifhq1c1OJ4njQWWLl3q7bMwrz/7/HMaPjx6N/TGR7b8+cknn6yFf/6L98G9prbG+3BvPuDXhGq9YFFTXaWqylSlJlerInIjP/NB31uqVF2jyooKVVZXqbq6xgsfNbW14XPV1Hjfa2trVF0e1L/+67/q9b/8p3fOaBAxYcIEhuhzb+9GVZUqKsq985sgU1cXUlVVlbckqrqqKhx2IkHGHO99mbZCtd5m8E6dOrV88ByJAAIIIBCXAh3qGs1Fm/XP7XGZQlxWh04hgEDCC5h7RDwza5b+/aWX9fPLR+u2iRNlNna3xsOc+5wfn61/OeUH6pSbq9yjjtJRHTsqp2O2sjKz5M9IU2Yg4N33wtzQzlzVyeyvUF2dTJCorq5SMFih8vKgysr2KVheodKyvdq1e4927tmjr778Qnu2bdEf58zW2T86y3tvprk/RiBL5mpT3p24I3feNpu5zWVlzXfv6lFJSaYZmYBiAob58mY2Kiu92Qyzj8N8le3dq927dqpLl+/ojaVLW4OFcyCAAAIItKHAobICMxdtiM+pEUAAgTOGnq6j83rrtSWLdeKJJ7YqSI8ePTRw0CD98+uvvZvjVZgP7pWVSq+sjFwe1iefmbGoM0uWapWSmuJt1DadCM80VHszDcFgeXjZlFnSZJZOVZoN2JXa+tWXuu7qX8q0Y8bweXGJd8M7M/thgoL5bjaLm83f0f0cZkbDvG42envtRGc4zOuRkGGChjnGO091tTeDMnbcuFa14WQIIIAAAt+OAOHi23GnVQQQaCcCL85/WSeddJJ3/4e2GPL1N1yvG391k7r26KG0tArvUrPePSrMh/7oB3wvCNQoOdncmyLZm1EIhcJLoSrKK7xgsa+8XEFvNqFCFZUV2rVzh/bt3qVzzjnH6/add9+t66++xgsEZl9FSmXKQYOFmbUwS6WiD7OPw2wKj4YRE1qiwcIsyzKzF+aytReOGhV9C98RQAABBBJYgHCRwMWj6wggEP8Cp556apt28owzztCJJwzSFxs/V+qAAd5duZN9ZjYhPHNgNnvXpqWpurZWSd6lZn3engizsdps+DYf9MsrKrxgsbdsn/aVB7UvWK7P1n2sibf/un4J17Bhw3TyKd/Th3/7IHwjPXPju6Sk+hkLs8I2uqnbzGaYmQwTLMwmbjNL4i2JisxcmIDh7feorFBVRbnuuveeNgtfbYrPyRFAAAEEDhAgXBxAwgsIIIBAYgk88uhv9bNzf6otX36p5L595esQvhBgqDbkzUqYTdtpKalKSjL3pQj/zmyiNleQqg8XwXKVlQe1d+8+rf/7h+qXl6fRo0c3gHj0scf00xE/UTC4T74ksxQqfC4TLKIBwrsxXkzoiG78Nr+PLofyZiyCQe3ZuVMnfW+wLh8zpkE7PEEAAQQQSFwBwkXi1o6eI4AAAp6A2RMxZ26Bd4lbcwO9Xnm9w7MIoVrvalAZaWneRuvo/og61ckLHtU1MjfS8/ZqlJd7MxbrPvpQ3bt8R7PnzD5A17RT8OILXjtmI7Z5mCtCmWVQNamp3uxEtI3YPRjRgGGCjLmZXlVFpbfsatCJJ+iPsw9s54CGeQEBBBBAIGEEuFpUwpSKjiKAAALNCxQVFWnUBRfK3/Eo9T/uOAUyA95yo7TIFZzMnovwbEN0CVN4NqGyqlJ7du9R8Sfr1KvHdzV7zpxmlymZmwCOu+JK754Z/syA0jLSvTtze1eJMsulGm3wDm/yrlKNCTLl4atT9ejRXYv//Odm22l+tPwWAQQQQODbEDjU1aK4id63URXaRAABBNpAwFwaNlhWprye3fXJqr9p0+fF2r79f7Rr927t3GW+dnk3t9u5c1f4+e7d+vqfX2vt3/+u5f/3/2jsFZcfMliYbpurXi0rfEtn/OhMmXtp7Nm1W3v37NHe0lKVma+95muv97WvbK/2lu7R3j2l2vHPf2rXju26cuyVqqys0kcffdQGCpwSAQQQQODbFGDm4tvUp20EEECglQTMPS+uuPxyPfjwwzKbyM0sxiOP/FaFS5eq43e6KCe3kzej4A8EvABSU1OtquA+VQSDuvSyn2v8+PH1m7cPp0umnd889LDefust7/xJycneZu7k5GRvH4bZj5GekeFt7P756Mt09TXXeO2Y94348dkydyk3y614IIAAAggkhsChZi4IF4lRR3qJAAIINCnQOFjEHrhz505t2LDB+9q9e49Kios16IQTdNRROd4lcvPz82MPP+Kfo+3896eferMjJSWfa9CgQerUKVcnnXyyDtbOe++9p3vvvlsvvvQSAeOI5XkjAgggYFeAcGHXm9YQQAABqwLNBQurHTnCxpYsXqx/nz9fswsK2H9xhIa8DQEEELApcKhwwZ4Lm9WgLQQQQKAVBcwN6B568EFdcunPvaVQrXhqa6caef75OmPYmfr1xIneDfWsNUxDCCCAAAJtIkC4aBNWTooAAgi0rYAJFuYD+aBBJ+i6669r28ba+Oym/0cddZTmFsxt45Y4PQIIIIBAWwsQLtpamPMjgAACrSzgUrCI0tw7aZLWrv1Yzz7zbPQlviOAAAIIJKAA4SIBi0aXEUCgfQuYGYu8vLyEn7GIrWJGRoamTZ+uBX/6d5mN3jwQQAABBBJTgHCRmHWj1wgg0E4Fov+yf+NNNzknkJub6105ylxBioDhXHkZEAIItBMBwkU7KTTDRACBxBcwwcIsHXrs8cedvbKSuefFjCef9C5Ra66ExQMBBBBAILEECBeJVS96iwAC7VSgPQSLaGnNHcDNzQDNTQEJGFEVviOAAAKJIUC4SIw60UsEEGjHAuZeEGYvgtmTYPYmtIeHucv4L8eP9y61azaw80AAAQQQSAwBwkVi1IleIoBAOxUwew+enDnT24tg9iS0p8flY8Z4l9o1G9h5IIAAAggkhgDhIjHqRC8RQKAdCphgYTY3v/jSSzJ7EdrjI3oPj+hG9vZowJgRQACBRBIgXCRStegrAgi0GwGCxf5Smw3sZiP7S/Pm7X+RnxBAAAEE4lIgOS57RacQQACBdixgNjFfcdlovTj/5XY7YxFbfrPP5J577/U2ePft109mPwYPBBBAAIH4FGDmIj7rQq8QQKCdCnjB4vLLvWDBh+j9fwRmWZhZHmaWia1Zs2b/L/gJAQQQQCCuBAgXcVUOOoMAAu1ZIBoszGVYCRYH/iWYgGFsbp0wgUvUHsjDKwgggEBcCBAu4qIMdAIBBBJGILRBc0cO1gUFGxT6hp0OFRXogrwxmltU4X1YNvd1uGfSJIJFM64mdEXvgbFz587wkS2qyXYVTjpD/Y+7X4Wl37RysR0sVdGypzXlxW/+9xB7Vn5GAAEEElWAcJGolaPfCCDgnIC5r8Pw4cOdG1drD8gEjEsu/bkW/GnBYZy6s4ZNf1vFn0zVsOxW/L++0tV64aZZWlN7GF3hUAQQQMBhATZ0O1xchoYAAokjYJb8mPs68GiZQPQStS07mqMQQAABBGwJtOI/39jqMu0ggAACcSCwa72WzbhaJ+T1Uf+8U3XNjDdVVBa73CaksqJCzZ00Uv29Ywbq3EkFKiwqbdT5Wu1a/1+aOf7U8HHHXa2Zy4pU1uiodv20rEiFBZN0rufYR/1HTNLcwoMYNVuTgy2LqtK21S9r8oiBkRqN1OSCwkZ1lELbPtC8+jrG1Lq0UJOHXKX5waDWTjlHx7T6kqt2XXUGjwACCSpAuEjQwtFtBBD4NgUqtfbJR/VK0i/0xucbVbyuQOfueEojLn5aq72AEVLZhpd128i7taLLXVpujvl8maZ2WaGbf3yVZq7eHdP5lXrqnv9U0rWL9NmmEn205FzteOxSXTrjAwKGUSpbr7m3XKmbl/fU1JUbVLxpg5Y/0FMrbji/kdGhahJD7v1YpS2L79TZY95SlweW6bNNpo4Pqf/yuzXq9j9rSyQnhrYs1o0/Gqf5ukqvrytR8brnNXT9feFjAsM0beUcXeb3a9CU/9Jnrb3kqnGXeY4AAggkgADhIgGKRBcRQCD+BPwj7tSUG09VN/Nf0cAAjbzjVl32xatatMpsMt6pVS8+p5VnxBzj66ZTbn5YvxuzXU9NXayi+kmObjr7ocn61fe7ySefAvnn6fY7f6avnvuLVrXqxuP4Mzx0j0IqXbVAj787RNMe+IVO6ZYqKVXdvn+NHpt1kb568km9VlRRf5rma1J/WPiH0nf1zD1vqN8dv47YmzoO1NgnHtbIt2fomXe2S6pQyRuv6g1dpNvvOE/5AZ8UOFYXjDlbev1VvVmyv+1GZ+cpAggg0G4FCBfttvQMHAEEjlwgTf1+cGw4WERPEviu+udv15Kl61Rauk7LFm4/8BgF1KN/L6loozbXL6Hqpx8M7KL9/zH2KdCjj/oFC7VsdeRqSNE22t33nVq9tFDB/BN1nBcsogARI32l4s3RBWSHqEn0rd73kEpXv6Ulwc46Pq9TjL0JGDF1DH2hdxf9Xcrvox4mWHgPn7KHTdXHm+ZpbH565DW+IYAAAghEBdjQHZXgOwIIINBKAqGvN2ldsJmTBUv0xddVzRzArzyB0A59sdbMIDT12K51m3Yo9MOmfn+o17/U/HHf1/yDHOYfdJAXeQkBBBBA4JAChItDEnEAAgggcHgCvq55Ot4vrWvqbf5+6t01Vfq6qQN43RPwdVLvQZ2ltU15RGcedjR1wCFeH6rJbz7f9AxEaMMh3s+vEUAAAQQaC0TneRu/znMEEEAAgSYFKlVSvLXhhuuyrSou6qyRw49XdvbxOuvCzip5/1Ntq99bYU5Wps3FXzVaZhO7tMccE1LZ5o0q8Q/TWYNzm+xB+/hFrgYPHyZ/0Rp9si12pidipF7q3yMQoThETRqA+ZQ9+EyN9Jfo/fX/bHgzxLIPNHNE5CaJvt467YKTGy1jk8I3PxzYKjdSbNAtniCAAAIOCBAuHCgiQ0AAAfsCwXkz9OjiDeGAYa5odNvdWnLGrbr+h50l5eqUK67WkLcf0ZSn3osEjFJtKJism+d11o33n6/8+v/6fqn5j/xeS7xL1IavMvXrG97Q6Q/9Uj9szZu92SdqhRZ9yj7lEk08baUm3zdbq7yAETV6Vb0mTNComH0PzdekUXeyT9P1Dw3R8num6ekPtoUDRtkGLfnNdD2lqzT5onz5lK5+51ylMb3/Q48+/la4jqEtemfeIq099rrwMd4ejbTwyYNlqt9K06g5niKAAALtRYBlUe2l0owTAQRaUSBNgyaM1Q83PqbT8pYqqG760YQH9NrVZ6m7Fxp8CgwYrSeW9NRrc3+j0/t+LMmvAWNu1+/evFDD8rNj+jJEN157sjY+8m/qv3Sb5B+uG3//gsafdXTDjcYx72hXP5orOM18Qb1fnav7hwyQt1Dp2Ms1edZijRqWr+i8hXSomjRWS1X386fqtZyFeuG+s3TMp2aTjKnjnVow5ycaHNnA7et2lu6b8we9/NR0nd53fKSO92rBnIsix/TRv906SgvGnaNjphximVXjLvAcAQQQcFCgQ11dXV3suMzNnoo3bYx9iZ8RQAABBBBIcAFzE71RGr/2Kr2+aFzMzFGCD4vuI4AAApYFDpUV6ifmLfeL5hBAAAEEELAu4B+Up678P591dxpEAIH2I8CyqPZTa0aKAAIItEOBkEoLp+r0cS8o6D9HkxcNVuyitHYIwpARQACBNhVgWVSb8nJyBBBAAAEEEEAAAQTcEWBZlDu1ZCQIIIAAAggggAACCMS1ACtP47o8dA4BBBBAAAEEEEAAgcQRIFwkTq3oKQIIIIAAAggggAACcS1AuIjr8tA5BBBAAAEEEEAAAQQSR4BwkTi1oqcIIIAAAggggAACCMS1AOEirstD5xBAAAEEEEAAAQQQSBwBwkXi1IqeIoAAAggggAACCCAQ1wKEi7guD51DAAEEEEAAAQQQQCBxBAgXiVMreooAAggggAACCCCAQFwLEC7iujx0DgEEEEAAAQQQQACBxBEgXCROregpAggggAACCCCAAAJxLUC4iOvy0DkEEEAAAQQQQAABBBJHgHCROLWipwgggAACCCCAAAIIxLUA4SKuy0PnEEAAAQQQQAABBBBIHAHCReLUip4igAACCCCAAAIIIBDXAoSLuC4PnUMAAQQQQAABBBBAIHEECBeJUyt6igACCCCAAAIIIIBAXAsQLuK6PHQOAQQQQAABBBBAAIHEESBcJE6t6CkCCCCAAAIIIIAAAnEtQLiI6/LQOQQQQAABBBBAAAEEEkeAcJE4taKnCCCAAAIIIIAAAgjEtQDhIq7LQ+cQQAABBBBAAAEEEEgcAcJF4tSKniKAAAIIIIAAAgggENcChIu4Lg+dQwABBBBAAAEEEEAgcQQIF4lTK3qKAAIIIIAAAggggEBcCxAu4ro8dA4BBBBAAAEEEEAAgcQRIFwkTq3oKQIIIIAAAggggAACcS1AuIjr8tA5BBBAAAEEEEAAAQQSR4BwkTi1oqcIIIAAAggggAACCMS1AOEirstD5xBAAAEEEEAAAQQQSBwBwkXi1IqeIoAAAggggAACCCAQ1wKEi7guD51DAAEEEEAAAQQQQCBxBAgXiVMreooAAggggAACCCCAQFwLEC7iujx0DgEEEEAAAQQQQACBxBEgXCROregpAggggAACCCCAAAJxLUC4iOvy0DkEEEAAAQQQQAABBBJHgHCROLWipwgggAACCCCAAAIIxLUA4SKuy0PnEEAAAQQQQAABBBBIHAHCReLUip4igAACCCCAAAIIIBDXAoSLuC4PnUMAAQQQQAABBBBAIHEECBeJUyt6igACCCCAAAIIIIBAXAsQLuK6PHQOAQQQQAABBBBAAIHEEUg+WFf75/U52Mu8hgACCCCAAAIIIIAAAgg0KdChrq6ursnf8gsEEEAAAQQQQAABBBBAoIUCLItqIRSHIYAAAggggAACCCCAQPMChIvmffgtAggggAACCCCAAAIItFCAcNFCKA5DAAEEEEAAAQQQQACB5gUIF8378FsEEEAAAQQQQAABBBBooQDhooVQHIYAAggggAACCCCAAALNCxAumvfhtwgggAACCCCAAAIIINBCAcJFC6E4DAEEEEAAAQQQQAABBJoXIFw078NvEUAAAQQQQAABBBBAoIUChIsWQnEYAggggAACCCCAAAIINC9AuGjeh98igAACCCCAAAIIIIBACwUIFy2E4jAEEEAAAQQQQAABBBBoXuD/A1eMCTjQHRGvAAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in m, the length of the thread. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Label on the graph with the letter X a point where the speed of the pendulum is half that of its initial speed.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The mass of the pendulum bob is 75 g. Show that the maximum speed of the bob is about 0.7 m s<sup>–1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed of the combined masses immediately after the collision.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the collision is inelastic.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the axes, a graph to show the variation of gravitational potential energy with time for the bob and the object after the collision. The data from the graph used in (a) is shown as a dashed line for reference.</p>
<p style="text-align:center;"><img 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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="text-align:left;">The speed after the collision of the bob and the object was measured using a sensor. This sensor emits a sound of frequency <em>f</em> and this sound is reflected from the moving bob. The sound is then detected by the sensor as frequency <em>f</em>′.</p>
<p style="text-align:left;">Explain why <em>f</em> and <em>f</em>′ are different.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iv.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>identifies T as 2.25 s ✔</p>
<p>L = 1.26 m ✔</p>
<p>1.3 / 1.26 «m» ✔</p>
<p><em>Accept <span style="text-decoration:underline;">any</span> number of s.f. for MP2.</em></p>
<p><em>Accept <span style="text-decoration:underline;">any</span> answer with 2 or 3 s.f. for MP3</em>.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>X labels any point <span style="text-decoration:underline;">on the curve</span> where <em>E<span style="font-size:11.6667px;"><sub>K</sub> </span></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4}">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math></span> of maximum/5 mJ ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> mv<sup>2</sup> = 20 × 10<sup>−3</sup> seen <em><strong>OR </strong></em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> × 7.5 × 10<sup>-2</sup> × <em>v</em><sup>2</sup> = 20 × 10<sup>-3</sup> ✔</p>
<p>0.73 «m s<sup>−1</sup>» ✔</p>
<p><em>Must see at least 2 s.f. for MP2</em>.</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.40 «m s<sup>-1</sup>» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>initial energy 24 mJ and final energy 12 mJ ✔</p>
<p>energy is lost/unequal /change in energy is 12 mJ ✔</p>
<p>inelastic collisions occur when energy is lost ✔</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>graph with same period but inverted ✔</p>
<p>amplitude one half of the original/two boxes throughout (by eye) ✔</p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>mention of Doppler effect ✔</p>
<p>there is a change in the wavelength of the reflected wave ✔</p>
<p>because the wave speed is constant, there is a change in frequency ✔</p>
<div class="question_part_label">b.iv.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was well approached by candidates. The noteworthy mistakes were not reading the correct period of the pendulum from the graph, and some simple calculation and mathematical errors. This question also had one mark for writing an answer with the correct number of significant digits. Candidates should be aware to look for significant digit question on the exam and can write any number with correct number of significant digits for the mark.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was well answered. This is a “show that” question so candidates needed to clearly show the correct calculation and write an answer with at least one significant digit more than the given answer. Many candidates failed to appreciate that the energy was given in mJ and the mass was in grams, and that these values needed to be converted before substitution.</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates fell into some broad categories on this question. This was a “show that” question, so there was an expectation of a mathematical argument. Many were able to successfully show that the initial and final kinetic energies were different and connect this to the concept of inelastic collisions. Some candidates tried to connect conservation of momentum unsuccessfully, and some simply wrote an extended response about the nature of inelastic collisions and noted that the bobs stuck together without any calculations. This approach was awarded zero marks.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates drew graphs that received one mark for either recognizing the phase difference between the gravitational potential energy and the kinetic energy, or for recognizing that the total energy was half the original energy. Few candidates had both features for both marks.</p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was essentially about the Doppler effect, and therefore candidates were expected to give a good explanation for why there is a frequency difference. As with all explain questions, the candidates were required to go beyond the given information. Very few candidates earned marks beyond just recognizing that this was an example of the Doppler effect. Some did discuss the change in wavelength caused by the relative motion of the bob, although some candidates chose very vague descriptions like “the waves are all squished up” rather than using proper physics terms. Some candidates simply wrote and explained the equation from the data booklet, which did not receive marks. It should be noted that this was a three mark question, and yet some candidates attempted to answer it with a single sentence.</p>
<div class="question_part_label">b.iv.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">The lens of an optical system is coated with a thin film of magnesium fluoride of thickness <em>d</em>. Monochromatic light of wavelength 656 nm in air is incident on the lens. The angle of incidence is <em>θ</em>. Two reflected rays, X and Y, are shown.</span></p>
<p><span style="background-color: #ffffff;"><img style="margin-right: auto; margin-left: auto; display: block;" 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" width="414" height="320"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The following refractive indices are available.</span></span></p>
<p style="padding-left: 180px;"><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Air = 1.00<br>Magnesium fluoride = 1.38<br>Lens = 1.58</span></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The thickness of the magnesium fluoride film is <em>d</em>. For the case of normal incidence (<em>θ</em> = 0),</span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">Light from a point source is incident on the pupil of the eye of an observer. The diameter of the pupil is 2.8 mm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Predict whether reflected ray X undergoes a phase change.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">state, in terms of <em>d</em>, the path difference between the reflected rays X and Y.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">calculate the smallest value of <em>d</em> that will result in destructive interference between ray X and ray Y.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">discuss a practical advantage of this arrangement.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Draw, on the axes, the variation with diffraction angle of the intensity of light incident on the retina of the observer.</span></p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Estimate, in rad, the smallest angular separation of two distinct point sources of light of wavelength 656 nm that can be resolved by the eye of this observer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">there is a phase change ✔<br>of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math> <em><strong>OR</strong> </em>as it is reflected off a medium of higher refractive index ✔</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">2<em>d</em> ✔<br><em>NOTE: Accept 2dn</em></span></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>d</mi><mi>n</mi><mo>=</mo><mfrac><mi>λ</mi><mn>2</mn></mfrac></math> <span style="background-color: #ffffff;">✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo>«</mo><mfrac><mi>λ</mi><mrow><mn>4</mn><mi>n</mi></mrow></mfrac><mo>=</mo><mfrac><mn>656</mn><mrow><mn>4</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>38</mn></mrow></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>119</mn><mo> </mo><mo>«</mo><mi>nm</mi><mo>»</mo></math> ✔</span></p>
<p> </p>
<p><em><span style="background-color: #ffffff;">NOTE: Award<strong> [2]</strong> for bald correct answer</span></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">reflection from «front surface of» lens eliminated/reduced<br><em><strong>OR</strong></em><br>energy reaching sensor increased ✔<br></span></p>
<p><span style="background-color: #ffffff;">at one wavelength ✔<br></span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Accept reference to reduction of glare for MP1</span></em></p>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">standard single slit diffraction pattern with correct overall shape ✔<br></span></p>
<p><span style="background-color: #ffffff;">secondary maxima of right size ✔</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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" width="468" height="206"></span></p>
<p> </p>
<p><em><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">NOTE: Secondary maximum not to exceed 1/5<sup>th</sup> of maximum intensity<br></span></span></em></p>
<p><em><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Ignore width of maxima</span></span></em></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>22</mn><mi>λ</mi></mrow><mi>b</mi></mfrac></math><span style="background-color: #ffffff;">✔</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup></math> <span style="background-color: #ffffff;">«rad» ✔</span></p>
<p> </p>
<p><em><span style="background-color: #ffffff;">NOTE: Award <strong>[2]</strong> for bald correct answer</span></em></p>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>A buoy, floating in a vertical tube, generates energy from the movement of water waves on the surface of the sea. When the buoy moves up, a cable turns a generator on the sea bed producing power. When the buoy moves down, the cable is wound in by a mechanism in the generator and no power is produced.</p>
<p style="text-align: center;"><img 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"></p>
<p>The motion of the buoy can be assumed to be simple harmonic.</p>
</div>
<div class="specification">
<p>Water can be used in other ways to generate energy.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline the conditions necessary for simple harmonic motion (SHM) to occur.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A wave of amplitude 4.3 m and wavelength 35 m, moves with a speed of 3.4 m s<sup>–1</sup>. Calculate the maximum vertical speed of the buoy.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a graph to show the variation with time of the generator output power. Label the time axis with a suitable scale.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, with reference to energy changes, the operation of a pumped storage hydroelectric system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The water in a particular pumped storage hydroelectric system falls a vertical distance of 270 m to the turbines. Calculate the speed at which water arrives at the turbines. Assume that there is no energy loss in the system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The hydroelectric system has four 250 MW generators. Determine the maximum time for which the hydroelectric system can maintain full output when a mass of 1.5 x 10<sup>10</sup> kg of water passes through the turbines.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Not all the stored energy can be retrieved because of energy losses in the system. Explain <strong>two</strong> such losses.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>force/acceleration proportional to displacement «from equilibrium position»</p>
<p>and directed towards equilibrium position/point<br><em><strong>OR</strong></em><br>and directed in opposite direction to the displacement from equilibrium position/point</p>
<p> </p>
<p><em>Do not award marks for stating the defining equation for SHM.</em><br><em>Award <strong>[1 max]</strong> for a ω–=<sup>2</sup>x with a and x defined.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>frequency of buoy movement <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{3.4}}{{35}}">
<mo>=</mo>
<mfrac>
<mrow>
<mn>3.4</mn>
</mrow>
<mrow>
<mn>35</mn>
</mrow>
</mfrac>
</math></span> <em><strong>or</strong></em> 0.097 «Hz»</p>
<p><em><strong>OR</strong></em></p>
<p>time period of buoy <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{35}}{{3.4}}">
<mo>=</mo>
<mfrac>
<mrow>
<mn>35</mn>
</mrow>
<mrow>
<mn>3.4</mn>
</mrow>
</mfrac>
</math></span> <em><strong>or</strong></em> 10.3 «s» <em><strong>or</strong></em> 10 «s»</p>
<p><em>v</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi {x_0}}}{T}">
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mrow>
<msub>
<mi>x</mi>
<mn>0</mn>
</msub>
</mrow>
</mrow>
<mi>T</mi>
</mfrac>
</math></span> <em><strong>or </strong></em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi f{x_0}">
<mn>2</mn>
<mi>π</mi>
<mi>f</mi>
<mrow>
<msub>
<mi>x</mi>
<mn>0</mn>
</msub>
</mrow>
</math></span>» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\ = \frac{{2 \times \pi \times 4.3}}{{10.3}}">
<mtext> </mtext>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mi>π</mi>
<mo>×</mo>
<mn>4.3</mn>
</mrow>
<mrow>
<mn>10.3</mn>
</mrow>
</mfrac>
</math></span> <em><strong>or</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times \pi \times 0.097 \times 4.3">
<mn>2</mn>
<mo>×</mo>
<mi>π</mi>
<mo>×</mo>
<mn>0.097</mn>
<mo>×</mo>
<mn>4.3</mn>
</math></span></p>
<p>2.6 «m s<sup>–1</sup>»</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>peaks separated by gaps equal to width of each pulse «shape of peak roughly as shown»</p>
<p>one cycle taking 10 s shown on graph</p>
<p><img 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"></p>
<p><em>Judge by eye.</em><br><em>Do not accept cos<sub>2</sub> or sin<sub>2</sub> graph</em><br><em>At least two peaks needed.</em><br><em>Do not allow square waves or asymmetrical shapes.</em><br><em>Allow ECF from (b)(i) value of period if calculated.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>PE of water is converted to KE of moving water/turbine to electrical energy «in generator/turbine/dynamo»</p>
<p>idea of pumped storage, <em>ie:</em> pump water back during night/when energy cheap to buy/when energy not in demand/when there is a surplus of energy</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>specific energy available = «<em>gh</em> =» 9.81 x 270 «= 2650J kg<sup>–1</sup>»</p>
<p><em><strong>OR</strong></em></p>
<p><em>mgh</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{1}{2}">
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>mv</em><sup>2</sup></p>
<p><em><strong>OR</strong></em></p>
<p><em>v</em><sup>2</sup> = 2gh</p>
<p><em>v</em> = 73 «ms<sup>–1</sup>»</p>
<p> </p>
<p><em>Do not allow 72 as round from 72.8</em></p>
<p> </p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total energy = «<em>mgh</em> = 1.5 x 10<sup>10</sup> x 9.81 x 270=» 4.0 x 10<sup>13</sup> «J»</p>
<p><em><strong>OR</strong></em></p>
<p>total energy = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}m{v^2} = \frac{1}{2} \times 1.5 \times {10^{10}} \times ">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>1.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mn>10</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
</math></span> (answer (c)(ii))<sup>2</sup> =» 4.0 x 10<sup>13</sup> «J»</p>
<p>time = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4.0 \times {{10}^{13}}}}{{4 \times 2.5 \times {{10}^8}}}">
<mfrac>
<mrow>
<mn>4.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>13</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mn>2.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>» 11.1h <em><strong>or</strong> </em>4.0 x 10<sup>4</sup> s</p>
<p> </p>
<p><em>Use of 3.97 x 10<sup>13</sup> «J» gives 11 h.</em></p>
<p><em>For MP2 the unit <strong>must</strong> be present.</em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>friction/resistive losses in pipe/fluid resistance/turbulence/turbine or generator «bearings»<br><em><strong>OR</strong></em><br>sound energy losses from turbine/water in pipe </p>
<p>thermal energy/heat losses in wires/components<br><br>water requires kinetic energy to leave system so not all can be transferred</p>
<p> </p>
<p><em>Must see “seat of friction” to award the mark.</em></p>
<p><em>Do not allow “friction” bald.</em></p>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iv.</div>
</div>
<br><hr><br><div class="specification">
<p>Two loudspeakers, A and B, are driven in phase and with the same amplitude at a frequency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>850</mn><mo> </mo><mi>Hz</mi></math>. Point P is located <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">m</mi></math> from A and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>.</mo><mn>3</mn><mo> </mo><mi mathvariant="normal">m</mi></math> from B. The speed of sound is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>340</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASsAAADACAYAAABcUEVBAAAZN0lEQVR4Ae2d328cVZbH5z9pS/1ka7wYMkOSnVFGA9kdx4RsZmaFdnG8P7DDOBMFEKtABmc92VF2JTJgM1aYiIcdZzcgIR5oS7wtGbXCAxIJLfGAVla/IYj6IQJktUQUWa0z+pb7tK/Lt6qruuvXrf6WZHX1rVtVtz63+5vzPXW68j3hQgIkQAIOEPieA2PkEEmABEhAKFb8EJAACThBgGLlxDRxkCRAAhQrfgZIgAScIECxcmKaOEgSIAGKFT8DJEACThCgWDkxTRwkCZAAxYqfARIgAScIUKycmCYOkgRIgGLFzwAJkIATBChWTkwTB0kCJECx4meABEhgeAKtmpyujEnV8jc5vyIbjZZ0hjwLxWpIgNydBEhARDyxelhO177ci6NzV+rLJ6RamZXrzft7t8V8R7GKCYzdSYAELASCxApdt+pycXxMDqw0ZNuya9QmilVUUuxHAiQQTCBMrLYbsjo1JpNLddkKPkLfLRSrvojYgQRIoC+BELHqNNflZGVCTq5vDpW3olj1nQV2IAES6EsgQKw6rdtyY+mEVMdfkI27D/oeJqwDxSqMDreRAAlEI+CJle1u4ITMLK1LvTmMAdwZAsUq2lSwFwmQQBiBgMgqbJe42yhWcYmxPwmQwH4CFKv9TNhCAiRQQAIUqwJOCodEAiSwnwDFaj8TtpAACRSQAMWqgJPCIZEACeRCgAn2XLDzpCRAAnEJUKziEmN/EhhhArdufSTPnTsnzy48Kyuvr8hXX32VGQ2KVWaoeSIScJsAxOnHf/1jOX/+gly6dFnOLJ71HgnTbDYzuTCKVSaYeRIScJsABOmRh6Zk9Y2rcvXNt3p/zz//ohyfeSKTi6NYZYKZJyEBtwm8/fY78swzCz2RMgXrB48ckK+//jr1C6RYpY6YJyAB9wlArGD7TJHS9cd++lgmuSuKlfufI14BCaRGABHT2zduyOGDB+XQowf32UDkrmamj6V2fvPAFCuTBtdJgAQ8Ap999pksvfJK75nqP/3JT+Sf5ubkZ3/zM3llaVmu/H5VkK86MPWIfHrn00yoUawywcyTkEDxCSCK2qjV5B+eesr7g0DhP4BAZPXdd995F/Duu+/K7NOzXvuFly9IVncCcXKKVfE/QxwhCaRKAIJz5dVXPQG69sdrPcFCZJVlHVW/i6RY9SPE7SRQQgKIlD788MNeFIWICsIE0UJEhW1FWyhWRZsRjocEUiQAQUL0BHsHYUJuCgvECiKFbWr5UhzGQIemWA2EjTuRgDsEID4ff/yx/PrMGU+QkIPSuihYQOSosC3L/NMg9ChWg1DjPiTgAAEIEiIlREzIP0GwdMG2Ils+Haf5SrEyaXCdBEpAAKIEcVJb50+SIx+l24pq+WzTQLGyUWEbCThGQMsOIEKwdBAsvxDB5mGbC5bPhp9iZaPCNhJwhAAS5GbZgS3vBNFSO1jEu3xRUVOsopJiPxIoCAGIj1l2gHV/FKVDddXy6fjNV4qVSYPrJFBgAoiabGUHtiG7bvls10SxslFhGwkUhAAiJuSf9CcwqIfSsgPbEMti+WzXRrGyUWEbCeRMQIs3bWUHQUNTy4ccVpAtDNrXhXaKlQuzlMAYO63bcmPphFe5jOrl6viCrNYa0ursHjxKn93e3TXvv2Aa2z0ujl0ZkwMrDdne15kN/QiYZQdm8WbYfmr5EH3ZEuxh+7q0jWLl0mwNOtb2bVmdnpDJ+Wtyp/VARLakWVuWmcqEzKzcljaOG6XPvvN3ZKu+LJOVWbnevL9vKxuiEYCtgzCFlR3YjmRaPtjDsi8Uq7LPsKigHJPVhidL3Su+J/WlI1IdX5b61nZXdML6GCFYj9l9aa7Pdo9h297ryBULAX1mlBZo+os3Lbv0mkzLF5bD6u1QghWKVQkmcbBLaEtj5ZhUK+dkoxVk2Pr16QrefE1aoYPYllbtnFQrJ+Tif/9eTo93beP4gqzd3pTNm2u7bdPLstHcCj2ayxu1eFMT5mFlB7brhKChqLPsls927RQrG5VRaOtsyvUTE1KdWpFGkFb167PdkNWpMZn8lwX5VxUgCNL/3t6TCxNRsRqT6vRlqcOKdm0n8ltqTzutm/Lb6QmpnliXZskCNbPsAOUHcXNLsHxqFUfB8tm+ghQrG5XSt3Wk3VjzclYn1zfFrgv9+3Sa63LSE5sbstnuHqX9uVyfP7KbC/NYqlgdkYv1e126XQtZMdv6RXJuTQwEBpGTRlH9yg6Crg5Jd1hF3OUbFctnY0GxslEpe5sm0xdrcteuVL3IZzKsj5WTCpOZdNc2MyembaYNLYdYadkBokb8oFifGWXFFdKI42D/UbR8NiwUKxuVMrd5kc8hqU6vSUOjIf/1Runj36f3XkXIJky2tnKIFaIoREDIJyEKilp20MNmrNDyGTCMVYqVAaPsq53Wx7I2D6Hq5o0sFxylj2U3o2m0xMosO/A/M8qAEnmVli8YFcUqmE2JtnSkvXlj545boFBF6WMi0ZIIM+eE7bZyhjABczOyMos3kTCPU3ZgUtR10/INahv1WGV9pViVdWaN6+rcrckZ3K0bf0E27qIodP8Spc++vTT3Nb+bYN+5o3dEztS+MBL35RArf9kBBAuWbZhFLR/yW0jAD3u8YcZS9H0pVkWfoaHHp0nr/T+JwRekWkEeqdWtuQrr0xbplipUjbqqTqshGysLMtn9mY33M56bzZ2q+N7Y3RarKM+M6l1qjBW1fLCPo3yXLyoyilVUUuw3UgQQ4ZhlB3GLN8Ng0fKF0QneRrEKZsMtI0jALN5EXVOS+SMIIKweLd9gHyyK1WDcuFeJCEBEYMm07GDQ4s0wJBA91EvR8oVRCt9GsQrnw60lJgA7ps8mT6LswIYKuSgcG0KVZJRmO1fZ2yhWZZ9hXt8+Av6ygzSS27R8+7AP3UCxGhohD+ACAQiS/hAYdi+JsoOg66blCyIzXDvFajh+3LvgBCAc5n9VNWzxZtjl0vKF0Rl+G8VqeIY8QsEIQDSQJNenHSRZdmC7VNPyIXrDey7JE6BYJc+UR8yJgL/sIO4zowYZtmn50ozaBhlb2fahWJVtRkfsehDFmMWbaZQd2JCq5cMTFpD/4pI+AYpV+ox5hhQI+MsOsioLoOVLYTIjHpJiFREUuxWDgFm8Ocwzowa5GthKLeyk5RuE4HD7UKyG48e9MyBgKzvI4LS9U+D8uKNIy9dDkssKxSoX7DxpFAL+4s08ohnkwPTJn7zLF2XW0utDsUqPLY88AAF/2UGaxZthw6PlC6OTzzaKVT7ceVYfAYiDWbyZRdmBbwjeW1o+G5VitFGsijEPIzkKW9lBnlaLlq/YH0OKVbHnp5SjQ9SEpx3guU5JPzNqEGBq+fCbwbwiukHGPWr7UKxGbcZzul5ETHmWHdgu27R8KCzlUmwCFKtiz4/zo4MgpP3MqEEgqeXD2PK0noOMfVT3oViN6synfN3+sgOIVhEWWr4izMJgY6BYDcaNe1kIQJA0Ykn7mVGW04c2IXrSCI+WLxRVYTdSrAo7Ne4MzP/MqKIlqSFOKOyk5XPnM2UbKcXKRoVtfQkgUkEUldUzo/oOyNIBookIj3f5LHAcbKJYOThpeQ4ZAoAIRcsOihZFgQ0tX56fkPTOTbFKj21pjowvPxLmGkUhoipKwtwPmZbPT6Q87ylW5ZnLxK/E/8woCFZRF1q+os5McuOiWCXHsjRHKlrxZhhY0/Ih4uNSXgIUq/LObawrg63L6r+qijWwkM5q+fCTnaLa0pDhc1NMAhSrmMDK1h1lB/gfg/XWfh7PjIrLVC0fcmhFTPDHvR72j0aAYhWNU6l6afGmJswRocBOFX2h5Sv6DKU7PopVunwLdXREIUV4ZtQgUJBHQ/RHyzcIvXLsQ7EqxzwGXgWiEUROGkUVuezAdhGwpbCptHw2OqPVRrEq6Xxr2YEWb2b1X1UlhRMiqwl/3uVLiqrbx6FYuT1/e0aPL7hLZQd7Bm+8oeUzYHC1R4Bi1UPh7opZdgDLhC+7iwstn4uzlt2YKVbZsU78TBAl18oObBDU8sGy0vLZCLENBChWjn0OtOwAd8aK9syoQVCq5YPosrBzEIKjsw/FypG5Lvozo+JiNC2fa8n/uNfK/skQoFglwzGVo/jLDlwp3gyD4bd8eM+FBKIQoFhFoZRxHxRvms+MKkvkgeuAfaXly/gDVZLTUawKMpGIMJC/QfEjvtCuFW+GYUQuCgKFayuL8IZdL7elQ4BilQ7XyEfV4k2NOFwtO7BdMAQYoqt3+Wj5bJTYFpUAxSoqqYT7mWUHqNQu250wRFCIpGj5Ev7gjPDhKFYZTj4ESX9CUoayAxs6Wj4bFbYlQYBilQTFPsdAlGE+7QDWr2wLLV/ZZrR410OxSmlOEGEgXwMrhL8ylB0EoaLlCyLD9iQJUKySpCniPblSyw7wWuYnWarlw82BMt0YSPgjwcMlRIBilQBIWCCXnxkVF4Fp+ZCD412+uATZfxACFKtBqHX38ZcdjEINkWn5yph7G+LjwF1TJkCxigkYUQQsD+7mwf6UsezAhoSWz0aFbVkSoFhFpI0vq5YdoHZolHI0uFGgwkzLF/EDw26JE6BY9UFqFm8iYT5K1gc3B7Swc7jrfiCtxjtycXrCq2ZHRfvk/IpsNFrSsfL/Vhorv5Bq5ZxstLatPXYaO9Ju/p+szh/qHveQnF6pSaP1IGQfbnKVQOnFSpPBcSbIX3YAwRqliALXj7qwZO7ydaTdWJOZyiE5/YePpQV1am/KxtIJqVZ+IauNb31To/3H+opV525NzoxPyMxSTZrtjnRaN+W3EMTpNWm07TLoOxnfOkTAabGCgCDawZfLXNCuNg3r+Jc8yuIv3ixz2UEQj+Qt3z2pLx2R6tSKNMwgaasuF8fHZHKpLlvmYNq3ZbUXgYVFVveluT4r1cqsXG/e7x5hW1q1c1KtHJPVRts8KtdLQMBZsYJAIckNIVJRQU4JCywL7IsuYWIFMfOXHaBt1JbkLF9EctsNWZ0ak+p8TVq9Xbr2b3pZVpeO9o2serv1VoLE6kvZmH9YqtNL8qeVBZmsIGqDFb0md5qfy597bbtRWu+QXCkMASfFCmKkCV8ku1Ws0KZRlilQ5rqSxz5avAnLMwplB3rt5muyls88cvh6p7kuJytjcmClITsBl9o/WMMvpbFyLKZYIX9V8/Jik4s1ubvHBXbFqjIhM8s3pdXRc0G01J4+kFb9ssxUJuTk+mZALi38mrg1XQIpipWG6ZZQf4hrgr2D+KjNM8UK6yo6pkAhAoM4qT3UsgNYHhW3IYbk7K5q+SDa2UaTmkA3LJxn/x6WmZXb0pZ2PLHqbMr1E93k/fiCrN32J+67YjW+LPWtrorpPmabNdpzdnpLN/D0xKr74fvb6aMyuSevEI8hRMf8Q/SkkRS+YP88Nyevvfa6vP32O/L6a6/1/ncU2EC9g/VvL74ov/uP33nR2KiVHdhogx/4qIjb+qTXplHNITlT+6Ibwaj908R4TLHqDVajI/PY2NgVqz15s26baUMpVj2SRVxJSaw6slVf9kTqT7WrcnKI0NqMkLCOaAALhGru1Jwcf+K4nFk8K888syBTkw/J4rO/8rZDlN577z3veUrfHx/3xGqUoyhAMS0f8nTZLx1pb96Q07iD50VQGIGKl3lncFCxwuG6UdaJdWn2rCDFKvu5Tv6MKYlV9w4QQuxv/38nRN/z4Yl+IUFideXVKzI7OydX33yr97f6xlWZmvwrL8KCQM3Nznp28eWXXupFY9HPXK6e+Vk+5fhAWrev7QiVlzfSdhWmvRH0bjT9sJyufamdI7yGCBMjqwj8itslHbHac1tac1dGfiIGjyCxQjvEyRQrrCPKmn9mQZ5/7rmeQJl5rRinLkVXWD7YvXwsnyLcks31RZnsJbi1PehVBSysdMH4B1HzUDhcN7Lam2QPETDawKBJKFx7CmKlFvCIXKzf8y54587PYHdZwsTKL1R4f/78BVn+92XP/mluaxTFCjYZiXPk+PKxfPpZfyB3ay945QJ7BUS3216jiJXax0Nyev1z2amq2pJmbVlm9hWbUqxslF1rS16sOl/IxuIhqZq2T/MI5p2XiKSCxOr4zBPyytLyvsjq73/5lHzwwQcjLVYQJ4hU9nf5LJOqSWvfjRLMq/e3x5rp/jaxsrXhZzw14+c2qJ1akz8395SZMsGuWB1/TVystH6m92HUD6X3uhttReUWJFaf3vlUDkw9IpcuXfYEC5YQOaxHHpryku9mNGWuRz2vi/2KYflcJMcxu0AgYbEKyU/tyWNFR+MXPRRw6nLr1kdy8IeP9kobnjz+pLz//vveZuyntUNlF6viWD6dGb6SQPIEkhUra3JTBx2QENXNEV7xpUSiGPZGF1OIzCSyGZGZle26X1le1fJBxFWcy3JtvA4SMAkkKlY7FjDI6mni3V+wZw6n/7pfsEyx0mgKfUyxMtf7n8GNHmr5UNypNxLcGDlHSQKDEUhQrLpVyGFJdP1FvZl8H2DcKljmLXn98uJwWIeI6VImscK1610+LZDV6+QrCZSZQIJilS0mfGkhSBAiiBOqs/XnNfjdoOa2/E9gyHaUyZ7NtHyjXo2fLFkezQUCzoqVwsUX2P/FhUCpcPmjLN3PpVdcC6JIWj6XZo1jTZqA82LVDwiETJ/E0K9v0bYjetTnvtPyFW12OJ6sCZRerLIGmtT5YGVxFxN21h85JnUOHocEXCJAsSrYbMHyIRdHy1ewieFwcidAscp9CnYGQMtXkIngMApLgGJVgKmh5SvAJHAIhSdAscpximj5coTPUztHgGKVw5Sp5UONGO7y4T0XEiCBcAIUq3A+iW9Vy4ckOu/yJY6XBywxAYpVRpNrWj5X674yQsXTkICVAMXKiiW5Rlq+5FjySKNNgGKV4vwjgkK9FC1fipB56JEhQLFKYaqRi9LCTlq+FADzkCNJgGKV4LTD8uHuHu/yJQiVhyKBLgGKVUIfBVq+hEDyMCQQQIBiFQAmajMtX1RS7EcCwxGgWA3Iz7R8eIwLCzsHBMndSCAiAYpVRFBmN9PyoX6KCwmQQPoEKFYxGKvlw3OmUInOhQRIIDsCFKsIrGn5IkBiFxJImQDFqg9gPMNdCztp+frA4mYSSJEAxSoALiwfHilMyxcAiM0kkDEBipUFOAo7IVK8y2eBwyYSyIkAxcoAT8tnwOAqCRSMAMVKxHuuFC1fwT6ZHA4J+AiMvFjR8vk+EXxLAgUlUHqxQqIcd/P8i1o+/E/HvMvnp8P3JFA8Ak6LFSrJkQiH8JgLxAe2Thc8BUEX8y4f/ut5LiRAAm4QcFasIDQQKvM/A9UICoKEbbqoWKnlu/bHa/wtn8LhKwk4QsBJsYLYQIwQQeEhdxpZwdLpugoU5uFHhw7LL3/+czG3OzI/HCYJkECXQMJi1ZbGyjHv4XMQiz1/00tyvd6U9hDo8bMXiBNER59yYIoVrJ/+Zg/n/uabbzw7+P3xcfmf69eHODN3JQESyJtASmJ1TjZa27vX1mnJnT8syGTliFys39ttj7C2R/AqY574qFDB7p38u5NyavaULP5qUX5z4YL3pE4cdu7UKS+iQhT28ksv9SKuCKdkFxIggQISyEascOFbdbk4PiaTS3XZigECYqUL1pF3wgIL+OgPfihnFs/KpUuX5ZWlZTn6+FE5+vjjXuT1o8OHRRPoZvSlx+IrCZCAWwQyFqsJObm+KZ0YjILE6uyvz8rzz78oV998q/e3+sZVOXzwsKytre3JZVGsYgBnVxIoKIFsxKprAw/M35DNdhypEi/vpezMyArrplDpOgTsyqtXKFYKja8kUBICKYmVL7neTbZPzl+TO60HsdAFRVZBYnX+/AWKVSzC7EwCbhBISax8CXbZkmZtWWYqYzK5WJO7MYKrILGaOzW3zwYiukLe6tatjxhZufH54yhJIDKBjMQK47kn9aUjUq34hSx8rEFiZSbY//O/XvUS7MefeFJmpo95BzRrqpizCmfMrSTgAoEMxWpbWrVzA4kVBEv/tBgUcCFYx2eekKOPPS6zT8/K0//4tHzyySced1PkTOFyYVI4RhIggf0EMhSrbmQ1viz1rRg+0DdmPBDPFCwzasLPbSBgWEyxMtd9h+NbEiABRwhkJFYPpFW/LDOV+KULNo6oUlfBUrEyfw8IwdLfCWJ/ipWNIttIwC0CKYnVrm2DUHh/4wuyenO4n9uYaFWw9IfM+E2gPmkB6xAxLKh2p1iZ5LhOAm4SSFissoUAwYIQ6Y+X9eyoXIddxIJtyFlxIQEScJuA02IF9JqjCpoGM8oK6sN2EiCB4hNwXqyiINYfPkfpyz4kQALFJDASYlVM9BwVCZBAHAIUqzi02JcESCA3AhSr3NDzxCRAAnEIUKzi0GJfEiCB3AhQrHJDzxOTAAnEIUCxikOLfUmABHIjQLHKDT1PTAIkEIcAxSoOLfYlARLIjQDFKjf0PDEJkEAcAhSrOLTYlwRIIDcCFKvc0PPEJEACcQhQrOLQYl8SIIHcCFCsckPPE5MACcQhQLGKQ4t9SYAEciNAscoNPU9MAiQQhwDFKg4t9iUBEsiNAMUqN/Q8MQmQQBwCFKs4tNiXBEggNwIUq9zQ88QkQAJxCPwFpgarTuD2slsAAAAASUVORK5CYII="></p>
</div>
<div class="specification">
<p>In another experiment, loudspeaker A is stationary and emits sound with a frequency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>850</mn><mo> </mo><mi>Hz</mi></math>. The microphone is moving directly away from the loudspeaker with a constant speed <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>. The frequency of sound recorded by the microphone is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>845</mn><mo> </mo><mi>Hz</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce that a minimum intensity of sound is heard at P.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A microphone moves along the line from P to Q. PQ is normal to the line midway between the loudspeakers.</p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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" width="370" height="161"></p>
<p>The intensity of sound is detected by the microphone. Predict the variation of detected intensity as the microphone moves from P to Q.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When both loudspeakers are operating, the intensity of sound recorded at Q is <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mn>0</mn></msub></math>. Loudspeaker B is now disconnected. Loudspeaker A continues to emit sound with unchanged amplitude and frequency. The intensity of sound recorded at Q changes to <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi mathvariant="normal">A</mi></msub></math>.</p>
<p>Estimate <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>I</mi><mi mathvariant="normal">A</mi></msub><msub><mi>I</mi><mn>0</mn></msub></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the frequency recorded by the microphone is lower than the frequency emitted by the loudspeaker.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>wavelength<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>340</mn><mn>850</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>40</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo>»</mo></math> ✓<br><br></p>
<p><span class="fontstyle0">path difference </span><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>8</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo>»</mo></math> <span class="fontstyle3">✓<br><br></span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>8</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo>»</mo><mo>=</mo><mn>4</mn><mo>.</mo><mn>5</mn><mi>λ</mi></math> <em><strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>20</mn></mrow></mfrac><mo>=</mo><mn>9</mn><mo> </mo></math> </strong></em><span class="fontstyle2">«</span><span class="fontstyle0">half-wavelengths</span><span class="fontstyle2">» ✓<br><br></span></p>
<p><span class="fontstyle0">waves meet in antiphase </span><span class="fontstyle2">«</span><span class="fontstyle0">at P</span><span class="fontstyle2">»<br></span><span class="fontstyle3"><em><strong>OR</strong></em><br></span><span class="fontstyle0">destructive interference/superposition </span><span class="fontstyle2">«</span><span class="fontstyle0">at P</span><span class="fontstyle2">» </span><span class="fontstyle4">✓</span></p>
<p> </p>
<p><em><span class="fontstyle0">Allow approach where path length is calculated in terms of number of wavelengths; along path A (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">56</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">25</mn></math>) and<br>path B (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">60</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">75</mn></math>) for MP2, hence path difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">4</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">5</mn></math> wavelengths for MP3</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«</span><span class="fontstyle1">equally spaced</span><span class="fontstyle0">» </span><span class="fontstyle1">maxima and minima </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle1">a maximum at Q </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle1">four </span><span class="fontstyle0">«</span><span class="fontstyle1">additional</span><span class="fontstyle0">» </span><span class="fontstyle1">maxima </span><span class="fontstyle0">«</span><span class="fontstyle1">between P and Q</span><span class="fontstyle0">» </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">the amplitude of sound at Q is halved </span><span class="fontstyle2">✓<br></span><span class="fontstyle3">«</span><span class="fontstyle0">intensity is proportional to amplitude squared hence</span><span class="fontstyle3">» <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>I</mi><mi mathvariant="normal">A</mi></msub><msub><mi>I</mi><mn>0</mn></msub></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></math> </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">speed of sound relative to the microphone is less </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle2"><br></span><span class="fontstyle0">wavelength unchanged </span><span class="fontstyle3">«</span><span class="fontstyle0">so frequency is lower</span><span class="fontstyle3">»<br></span><span class="fontstyle4"><em><strong>OR</strong></em><br></span><span class="fontstyle0">fewer waves recorded in unit time/per second </span><span class="fontstyle3">«</span><span class="fontstyle0">so frequency is lower</span><span class="fontstyle3">» </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">d(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>845</mn><mo>=</mo><mn>850</mn><mo>×</mo><mfrac><mrow><mn>340</mn><mo>-</mo><mi>v</mi></mrow><mn>340</mn></mfrac></math> ✓</span></p>
<p> </p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>00</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</span></p>
<div class="question_part_label">d(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was answered very well, with those not scoring full marks able to, at least, calculate the wavelength.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates were able to score at least one mark by referring to a maximum at Q.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates earned 2 marks or nothing. A common answer was that intensity was 1/2 the original.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>HL only. The majority of candidates answered this by describing the Doppler Effect for a moving source. Others reworded the question without adding any explanation. Correct explanations were rare.</p>
<div class="question_part_label">d(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>HL only. This was answered well with the majority of candidates able to identify the correct formula and the correct values to substitute.</p>
<div class="question_part_label">d(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>A mass–spring system oscillates horizontally on a frictionless surface. The mass has an acceleration <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> when its displacement from its equilibrium position is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<p>The variation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> is modelled in two different ways, A and B, by the graphs shown.</p>
<p><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline <strong>two</strong> reasons why both models predict that the motion is simple harmonic when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> is small.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the time period of the system when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> is small.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, without calculation, the change to the time period of the system for the model represented by graph B when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> is large.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph shows for model A the variation with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> of elastic potential energy <em>E</em><sub>p</sub> stored in the spring.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Describe the graph for model B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>For both models:</strong></em><br>displacement is ∝ to acceleration/force «because graph is straight and through origin» ✓</p>
<p>displacement and acceleration / force in opposite directions «because gradient is negative»<br><em><strong>OR</strong></em><br>acceleration/«restoring» force is always directed to equilibrium ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempted use of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>ω</mi><mn>2</mn></msup><mo>=</mo><mfenced><mo>-</mo></mfenced><mfrac><mi>a</mi><mi>x</mi></mfrac></math> ✓</p>
<p>suitable read-offs leading to gradient of line = 28 « s<sup>-2</sup>» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>ω</mi></mfrac></math>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><msqrt><mn>28</mn></msqrt></mfrac></math>» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn></math> s ✓</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>time period increases ✓</p>
<p> </p>
<p>because average ω «for whole cycle» is smaller</p>
<p><em><strong>OR</strong></em></p>
<p>slope / acceleration / force at large x is smaller</p>
<p><em><strong>OR</strong></em></p>
<p>area under graph B is smaller so average speed is smaller. ✓</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>same curve <em><strong>OR</strong> </em>shape for small amplitudes «to about 0.05 m» ✓</p>
<p>for large amplitudes «outside of 0.05 m» <em>E</em><sub>p</sub> smaller for model B / values are lower than original / spread will be wider ✓ <em><strong>OWTTE</strong></em></p>
<p> </p>
<p><em>Accept answers drawn on graph – e.g.</em></p>
<p><em><img 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"></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This item was essentially encouraging candidates to connect concepts about simple harmonic motion to a physical situation described by a graph. The marks were awarded for discussing the physical motion (such as "the acceleration is in the opposite direction of the displacement") and not just for describing the graph itself (such as "the slope of the graph is negative"). Most candidates were successful in recognizing that the acceleration was proportional to displacement for the first marking point, but many simply described the graph for the second marking point.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was well done by many candidates. A common mistake was to select an incorrect gradient, but candidates who showed their work clearly still earned the majority of the marks.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates recognized that the time period would increase for B, and some were able to give a valid reason based on the difference between the motion of B and the motion of A. It should be noted that the prompt specified "without calculation", so candidates who simply attempted to calculate the time period of B did not receive marks.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates were generally successful in describing one of the two aspects of the graph of B compared to A, but few were able to describe both. It should be noted that this is a two mark question, so candidates should have considered the fact that there are two distinct statements to be made about the graphs. Examiners did accept clearly drawn graphs as well for full marks.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">The diagram shows the direction of a sound wave travelling in a metal sheet.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdIAAAEECAYAAACcB7UEAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACqeSURBVHhe7d0LXJR1ojfwH9AmKhJjduTiKyJeUjDxctTNFCTKdb0cELVWS3zHcvPg1uYhzTqaaWYlry4dOe7akY94ySuXRTueSgi3NOSAwYFMwAHtVcB3lfECqCnD+/8/84AgoOAD4zD8vn3m08xzm2dm8PnN/zp21QKIiIjogdir/yci6nhMpxAz0R12drMQk39DLLiIlKUjxWN3TIw5BZN5K7J52j53BikREbWIqSQT8ZFrEKt8+WiCqQSZ8RvwTqztfyFhkBIR1eqBwI8zUF1djC/1T/IC2RhRit86bypC38pGlbqooRvI3/oGRoauQ2bTG9kM/p0QUcdRno+vI8PgbmcHO/cwRH6dizJ1lVljVXxXkf/1BoS5i33kfuLmHrYBX+dfVdYq6h53wjuIP5XWRJXxEIR99L75WO7vIOWqeIa6+yo3sU3kl8gvl88uAilmlrLc/V9i8OWGO+e+Ib0EpvJTiF860bz+7nOqp+b5R2Jp/Ld1nm+ieHwK5epWCnE+KTFLMUFZL24TliI2UzyXXCerwicFYv5XJeLBPswf2BnuS1PEO1SXPOe5GDh/n7hfgq/mD4JDzWsVRynPT0GMes7yfZ6wdDsyS35R9mzcLyjJ3I6lE+T7aT4n97BIxNeck+LubcTrik1HSe0GzfgMG7hrn7rvw91kZyMiIptXdaY6Tu8rO1c2cptZvSXvutjo79XJS0aIx27Vz2/5qbpK/HctY311QGP7PL+lOq+qieO6PV0d8LSbuH/3cetus6w6+cql6ox1k+svV241z3+9Om/LzEbWi5tbcPXc2Xc9b805NdDI89feas5RuHa8el2APO+7t/Gt1sedqa6q+ql6y/P117stSa6+Yt5b1cg5K6/1VtPvpVt4ddy5m+r+9VXlbal+/p77NPUZuVUHrDtefa05n2GDz/1m9bm48Gq3BvtMrl6XYZQ71MMSKRF1CKbTyfhLTK64Vuqx5acrohBRhWs/bcVccbVsmj2cRryJb6qrZaFDuVWdi4Ne7pNzGudEqbHhcW+ieIe49B+TpbaG3PRxOFcljpP/DsY4d8eIiIO1x5b7igs43ERJLievuH5JMWAlkotvQoQdRNiJwl4ivnZ833ysvC0Qz1h7TvfiNncrfrpWBfEFAOILgFjyHfZ8d0aUtEy4mp6I9aklYpuNOC6fS76W5JUIQC5iFv0FqeUDoD+UAhGmYr+ZEAGM4o8D4awcuYYjBui3QYSpuO8msuonVBV/iEDny0jfuxOp8MXc9d+hWJx3ddU5JC8TZ14SjUWffndXyVYSJdhzp5Ej7onAhgjsO+9V8UZM93hUrCmrPa4Ie4hcVD+jEqSuT0S6OOj9PsMGTIX48i/xKHELhwhrsU/N38oXWL/3RIPzZJASUQdQ54L88hzMeFJe+kVIDhgN/yH3TFIzWd0ZH4/4+M+w7KVFiKnNyMaO+yjcAl7Ay0rY3G0EXp4zHh7iymvv5IQuyjJZ3Zkqji2OH7McL4VGixhtyG3UOIx0E8HRxRndZX7UPZZrH/g142XIYBviPxoDnOROXeHSo5O6XCpDxpdfiecWxw17AaPkc9V9LSWncab0XlWw93H1f/Dl9kxxClMRNv/XcJPpY++BgHkvKF8CSrLOoLRBptnDeVQwFosvDiWfPIvH1CrWmPi/IqWmWrbOcecE/S8l1Ow9pmNLsQxbGeByidDkZ9iQ6fQx7JHV1yLgQ3t1gp2dA7oNmodtctH2w8hQqqnvUJ+BiIgaEiGXuQETugVg9fFLgIs/lv91B5Y0K7Sa4zIyI6eh28C1OH5ZHP6ZZfhr8jIRd23FHX59erSvC7/TKER8cwp5yYmIi9uMJdiO+aHBeHbgbERmijftvtr6M2SQElGHIEqfvfphiLhXsn0n9p+SpZlfUJKRjCM59yia1FYbPo6+o59HcGAfXMv4Fum1uzRx3NQ92K50yLmPqyewd/0XojTVH6MnTkFgvwpkHM5stETa9rpj5MTnRYhnYnvsHvEaZemzzmsJ+DWGuitF4Qfj/BQmvjxCvFEHELvle3NHINN5pG7dg6/EswY85wv3JhPJGQMC/wnTp7+Kj78pVKuN1WrWusfdf9JcHV6ejkil45Hs7HX+Pp9hQ7Ul/Nrq+jvVwvVKuSoGKRF1CPYDpmHpEnnBjcH8QY+Ji2wnuI9epFTX3V8uYkL7wEHu8+wBESre6nJx3H7P4veyrbHucVfno7dsx2yumipEh1549sgvaMmuradONeq2RRjtLqs05etdKULoeSxbPgvDlCrhHujj5y62b6rXrvQoXPv0E/FYt9euC0bNmqO0t25b/AzcHezMr3ftV+L9/D2Wz/GDk7r3HSZcTXmnTo9meeus9giejMWzhouI7X7nuPOHoJvcpttovJUqDrsuArMGdDYf6h6fYQPOz+D1jeFwq/1Ma57bHRMi0+u3XQsMUiLqIHogcPnn+GrdXLXq9Hks2bcb6xpty6wh99mBuCVKVx5RQpmL9cf3YdPLw0X4/Q9OFIgIsffE9Kh9tdsoHXV2LIF/cwpvzgFYnhqHJWpyKvvu/RNeHiIiKD0bBffpONTqZDXqgVQkb1kigkkVsARbM7big0APNTBEcP3vP6idtNww8AmnRoJEhvJsfDBXdmYSBj6Bx+xlx603cCAvGVtq3k9ZEl2yDRmfL0Og0iZ7N3GcwLeRmryl9j1SKOf0GRaPcBEP5HHD8XnGtjrbiM92yw785bWRIpyb8Rk28Cg8pn+I1K/W1+mMJo65NRGfLx7VIPA51y4RkQam/BhMGjgfX2EEliT/Fz4O7AHT+Xi8+o+hiMEyJJ/6oEFVINkWBikRkRams4h/dQpC5RCYu8ihLv/92XSlZy3ZLn68RERa2Hsi+IOtiKutMpZ8MXddHA58MIUh2gE0WSKVDatERNaIFWlkTe4ZpAkJCeojIiLrEBISwiAlq8JKByIiIg0YpERERBowSImIiDRgkBIREWnAICUiItKAQUpERKQBg5SIiEgDBikREZEGDFIiIiINGKREREQaMEiJiIg0YJASERFpwCAlIiLSgEFKRESkAYOUiIhIAwYpERGRBgxSIiIiDRikREREGjBIiYiINGCQEhERacAgJSIi0oBBSkREpAGDlIiISAMGKRERkQYMUiIiIg0YpERERBowSImIiDRgkBIREWnAICUiItKAQUpERKQBg5SIiEgDBikREZEGDFIiIiINGKREREQaMEiJiIg0YJASERFpwCAlIiLSgEFKRESkAYOUiIhIAwYp3cdtGA05MBhvq4/v5yLSohYiJCoNRnVJ81XBmPZnhIT8GWnGKnVZ2zAZDcgwGGFSHxMRPSgGKd1TleEg3onYi5yy5gZpO1BlQNI7EdiSU4ZqdRER0YNikBIREWlgVy2o9+uxs7NDQkKC+oisn6wW/Qz6zTcR9jsdMv89AbliqS5gAZZO6YX8g1sQk3pWLPFDyNJXMGuMBxzlbiYjDOlHcHBzLFKVulix/vXZmOrfH85FiVgUEYtSuVhwDYvExmBPXDVk4MjB3YhVjifd2UdnL6t2l+NjhCHmjTHQqVvcUYni7GTsi4pRn88TAWFhmPmboXB3rDa/ho8vICSsNwpik5TXAN9QLF04HWPcu8hHSrVs+pGD2Bybaq4+9g3B6/Omwt9bp34zlNXRdc9RJzaZi3lTn4G381kkLopA7J0XhciNwfB2UB+T1QsJCUETly2ih4IlUltjzEZmyQAs3LUfuza+jqHZm/F2RDyuBK5AXMIORIY5IOHjz/Fd8S2xcQUMSdGI2HwePqt3ii9OcWKf8TBuX4v1SQW45R2MjZFhcIUvwiJ3YVOwN+yKU/FpxG6c9VmMXeKLVkJcDD7RuyD107/gwI9XzefQJBMqc+LxrytP4PE3t4jzkc/3T0DSv+Gz70rqtFdmIfVsH7y2Kw4Ju6IQ3iMDH392DMVygxsFSFq/BpvPPoXVcn3CTmz0v4btEdFIMlSIDUy4YTiE9XXPcddK+BsTEbH+EAy3vBC8MRJhruYvBvs3MUSJSBsGqc0ZBP+gEaJ05wBHtwHw8RRlwoCJmDyku/iwu6LPEF8RjFdRfr1KFA4LcTSpEH6zgxHoIUt79nD0eAYzZw9CbtJxFFQ27Ipj7x6E9xL+hDeCeptLtPY6eI/wEeXKChgrflG2aVo1blaUi1KkA5y6dBLPJp9vAt6IicF7QR51/hifxuyZz8DDUSxx9MCI0U+KbD2Nn6/cRmXBcSTlDrqzHl3gERiM2X6FSDpaKMq75Sg4egS5flMwM1A9R8feCJw5BX65R3C0oFwuISJqNQxSm9MNTp3Vj9W+E5xcOsHV8wk4m5fUY7p8AUVGI7KiFyE0JESpMgsJmYXw6GOiZFuOiptNVJ8p1cFpSEsTt8Pb8F54tChDNocDdH6/RXjARcRGvIQQfRQSj6UhvUHv2TqvoZ7buHyhRATxMUSHz1LPV9xCFyE6ywijsQI3TddwoahMBG80wkNrXlMIQpVzbE7YExG1DIO0w/NGyKpYpT28/u01jNE1rPM0GbOx471/QcSBfFH2E5yG47XIf4afsrYZROkw6I312BW9GksXDAf+ezfWRvwL3tuRDWNzx6LoQrFqp6zWveuc67TJ6kJWYefd6xM24Y0xPdQtiIhaB4O0A7N36QkvnQGpP5xFpbrs3m6hNPMrxJ0PxKplLyFozBiMGTMYusoLqOl21Dz2cHT3FfuOQ/Ab60TpchBy475H3pX7JekjcOnpBp0xCz8Ymqiite+Gnl7dYUzNhqGRqmkiotbGIO3IuvTF2GkjYEyIR3xOmVK9ajKewoGoPyLk/cNK5x6H7q54EtdxtVJWiTqoQWZAtuGy2N6EG8Xp2L83pZmTL9xGWdpm6PVROFCgVufeKMHJH88Dfv3Q+7H7/TnaoUv/0ZjmW4aEvYeQo0wScRvGgkOI0uvx/uHz4phO6D/WH77GFOyNzzGXck1GFByIgj5kHQ7LTlYOj8H1SVfcvFqJm8pxiYgeHIO0Q+sK72nhiHzdC3kr5ivtpKH6P6PQ80WxLADu8q/jsQEIDO2GhBVhCIlKx02fyVimd0GKsn0ofrcpH+6TpiFAV4rs/JL7lGwfQfdRM/HuyzqkL9Gb22V/txJHdMF3nu9+HPtj2uJleL3/KazQz0RIyEzo1+bDc8G7eD1QdlgSpV3vSVgcORf980R4ynbSUD3WFnpiQeQrCHT/lTiICwYGBsAjYQXmWGAWJSKybRxHSkTtiuw8xnGkZE1YIiUiItKAQUpERKQBg5SIiEgDBikREZEGDFIiIiINGKREREQaMEiJiIg0YJASERFpwCAlIiLSgEFKRESkAYOUiIhIAwYpERGRBgxSIiIiDRikREREGjBIiYiINGCQEhERacAgJSIi0oBBSkREpAGDlIiISAMGKRERkQYMUiIiIg0YpERERBowSImIiDRgkBIREWnAICUiItKAQUpERKQBg5SIiEgDBikREZEGDFIiIiINGKREREQaMEiJiIg0YJASERFpwCAlIiLSgEFKRESkAYOUiIhIAwYpERGRBgxSIiIiDRikREREGjBIiYiINGCQEhERacAgJSIi0oBBSkREpAGDlIiISAMGKRERkQYMUiIiIg0YpETULly6dAn/+Z//qdw/d+6c8n8ia8AgJSKrVlRUhNjYWHz00Ufo3LmzsqxXr17K/4msgV21oN6vx87ODgkJCeojIiLL+eWXX3Dy5EkcOnRIeRwSEoK+ffvi0UcfVe43cdkieigYpERkNa5du4aMjAylCtfX1xfjx4+Hl5eXutaMQUrWhlW7RPTQFRcXK+E5d+5cXL9+HW+//TbCwsIahCiRNWKJlIgemlOnTiE5ORlnzpxBaGgohg8frlTf3gtLpGRtGKREZFGy/fPEiRP45ptv4OzsjGeffRZPPvmkuvb+GKRkbRikRDakypCIRRGxKFUf3+GJgLAwzPzNULg7PpwWHdn++e233yoBOnr0aDz99NNwd3dX1zYfg5SsDYOUyIaYgzQTEyPfRbC3o7rUhBvF6di7aTNS+7+JjXOHoIu6xhJk++fXX3+N3NxcTJgwAePGjUO3bt3UtS3HICVrw85GRDbPHo7uIxDkPwjG1GwYKk3q8rYjq29l++fatWuVMaBDhw7FmjVr8Nvf/lZTiBJZIwYpEbUaWX2blpaGd999F8ePH1dKj8uWLYOfn999OxERtVcMUiKbJ6t2M3H4SCF8p41G/y6t/8++Zvo+OXylrKwMb775pjJ8pSWdiIjaK7aREtmQpjsb+SEkfDqCnvFp1c5GsvpWljxl+6ccvuLj49PmVbdsIyVrwyAlsiGNdzZqXfeavs8SGKRkbVi1254Z0xAVshBRaRfVBURtR7Z/yqErsv0zOzsbL774otL+Katv2f5JHRmDlIjuSQ5f2b9/f+30fStWrOD0fUR1MEiJqFGy/TM6OhobNmxQfrZsz549HL5C1Ai2kd5NVpfqdwNhQdBlxiMh1ygW+iFk6SuYNcYDSquTyQjDkQPY+mkCcuVjXQDCFkyB/yhv6ORXE/UYpgBX5KQehxFPI/z9f8SP7yXWP67YT790CgbkH8THMaliOx18QxZg4axR5g4h8nnSj+Dg5likytOQfEPw+ryp8PfWwV55nlhg6Wq8MaaHugF1ZFrbSLVO32cJbCMla8MSaaPOIjXzMgYs3Ci+TOxAZJgDEj7+HN8V3xLrKmBIikbEdiNGfRKDuIR9iFk2AGc3r8H6pALcMB9AOIu/XfTBu7v2Imb9CxjhIS9qdY67KwrhQ4sQ8/Ya7LgSgP8TF4ddkSFAwmZ89l0JTLiF4pT/QMTm8/BZvVP5UhMXsxb6Hifw6Zov8KMFBtVT++PgHYxNCatbHKKy/VMOX3nhhRdw7tw5peo2PDycw1eImoFB2igd/PwnYJS7nEitK7xGjRFl0kL8+PMVoLIQR5MK4Td7Bib3F6VCPAJd/yDMnD0IuUnHUVAbcPIYw+Hl+CvovHqbS6p1j+vohsE+HmLZKEye7CvW28Oxz2CMcDWitPwGqvEruAe9hYSYcAR5mCd0s9d5Y4Tcx1iOipv8Rk7ayfZPOfPQqlWrlMfbtm3DjBkzHmgOXKKOikHaqE5wcepU++bYd3aCi3q/qsSA740eGOr1eJ03zwEuPd2gM5bgwuUqdVn9Y5jVXWaPzk7dAFdXPOHsoCxpjMloQHpaGtLSjuHwtg8RHn1MXUP0YDh9H1HrYpC2imrcrChHTTNm67gNY84evKdfgwP518RjezgNC0Nk+NPm1UT3IQNTljhlta3E6fuI2gaDtIUc3Lzxa915ZBddwp1WShOul4uLlc4NPV2aLl22iOkCMuO/xPmQN7Fs7nMYM2YMxgzpjsriC+oGRE2TIfrOO+8o7Zxy2Mr27ds5fR9RG2GQtlSXvhg7rS+yPt+PLwqMIkJFybHgMPZ9/lPrzmNq3w09vbqLY5+EwXhbLKhEcVoS9iYYzOuJ7kHOPFRaap4o8JFHHkFRUZHS/imrb9n+SdS6GKQt1hXe08IR+bIO6Uv0CA2ZCf3afHgueBeLp/U3D49pFc7wmfoK9D2+xwr9TISELMKm/J6YFBYAHU4j/1yFuh3RHbIkmpWVhX379qGiwvw30qVLFwwcOJDtn0RthONIiWyAbP/MyMhQhrD4+vpi/PjxOHPmDD799FNMmzZNuT3++OPq1u0bx5GStWGQErVjsjPRsWPHsHPnTrz66qsYN26czZc8GaRkbRikRO2QHL6SnJyslDrlz5cNHz68w/S8ZZCStWGQErUT7WH6PktgkJK1YWcjC5IXAKKW4vR9RNaNQUpkpTh9H1H7wCAlsiKcvo+o/WGQElkBTt9H1H4xSIkeokuXLintn5y+j6j9Yq9doodAVt/Kkmdubq4yfMXHx4dVt83EXrtkbRikRBYi2z/lHLiHDh1SHstA6Nu3L6tuW4hBStaGVbsWxOEvHZNs/5RjP2X7Z3Z2Nl588UWl/VNW3zJEido/BilRG5HDV/bv36+0f16/fh0rVqxQ2j+9vLzULYjIFjBIiVpAdg6Sw1LuRbZ/RkdHY8OGDejVqxf27NnD4StENoxBStRMso3zo48+UsZ23k2uk8NX5PhPOQeunL5v3bp1yg+ys/qWyLaxsxFRM8ig/Oyzz5RqWVm6rCHbP7/99ltl3Zw5c/D0009z5qE2xs5GZG1YIiVqhqSkJDg5OdWGKKfvI6IaLJES3YfscSuHrciOQnLS+Jp/F5MmTcLgwYNZdWthLJGStWGJ1II4/KX9kR2HDh48qATm+++/z+n7iKgBBilRE2QpVAZmYWGhMnyF0/cRUWNYtWtBsiTD99T61UzfJ3vhenp64tatW8oPatfo168ffH19lftdu3ZV2kbJcli1S9aGQWpBDFLr1ZLp+2RPXXmTOnXqhMcff1y5T5bBICVrwyC1EHnhjY+PV+737t0bnTt3Vu67uLjA2dlZGazPAfuWJz+XjIwM5RdYZClz/PjxnHnIyjFIydowSC1IDpmQfv75Z+X/kuwFWlFRofwKyOnTpxEcHKwEbZ8+feDh4cHOLG1EfhbHjh3Dzp078eqrr2LcuHH8ItNOMEjJ2jBIrYgsHV28eBEXLlxAXl4eEhMTERQUhLFjx8Lb25sX+lYg2z/lzENnzpxRfr5s+PDhD/RlxVR8GKvD/wteq1Zg7hBnseQqcratwoqi3yB6eRDc7e/axqcKhvQjOLg5FqlG8zHgG4LX502Fv7cDfrxrX7E3KnM+x6IVJZgd/UcEudvBaMjAkYO7EZt6VqzXid3nYt7UZ+Cte0Tu0GEwSMnasNeuBckLwL3IoJTVinJaOdk7tGaOVll6kgP/5fytMghkex41X1tM32fv0hNeujIUXbgmIk+oPIsfUg1A1mn8fKVKLLiF0pM/IEvnh2HenVCc8h+I2HwePqt3Kl9Q42LWQt/jBD5d8wV+rOwK72F+0GX9gJOlt+TRhHIYfsiC0W8YBrs64IbhENZH7MZZn8XYJfZP2LUS/sZERKw/BMMN5QyI6CFhkFoxeZGvmZJuzZo1SgDI3qTy57hkMNR0eKHGyfdHtn2+8MILShW6/HISHh7eOsNXunhiWEB3ZB39CaUix6pKDPgeT8L3ybPIP1chNriOS8UXoAsYCu8uneAe9BYSYsIR5NFF2d1e540RPh6AsRwVN8XhvIciQPcTjp78f3WCuQx+YwfB1b4cBUePINdvCmYG9oajXO/YG4Ezp8Av9wiOFpTLJUT0kDBI2wkZqjIAZBi8/fbbKCsrU36eS866wxJqfUVFRbXT98lOXW0zfZ9TnVJkBS4UFeBmwD9hxuhHkPrDWVQqQQgEDPOEOToBk9GAdPEFKC3tGA5v+xDh0cfUNUK9YDah0pCNVOMgjB38D7A3XRPHLxOl3WiEh4YoNRvyFhoejSxUwFjBz5/oYWKQtkNyuIUspcqAkBMF1JRQOzL5ZUJWe8vq2927dyu/0CJL8RMmTGijtmV7tRR5AcV/L8LJo2UiNAehv/dA4PsCFOTJIOwJ98dl7+zbMObswXv6NTiQL2sR7OE0LAyR4U8rRzJzQv+x/vBVgrmsTrXur9T1gC5kFXbKat16t014Y0wPdQsiehgYpBbU2p23ZEDIQJUz7sjOSTJEanoGdxSy+lZ+iZBfJiw+fZ9jd7h7liF1/x4kZ4n7j3cxh+vNY9gff/ROEJouIDP+S5wPeRPL5j6ntM2OGdIdlcUX1ANJ9nD0Gg5/v0IcTfsbMlJvI2jiULjKf6H23dDTqzuMqdkwVLI9lMjaMEhtgKyylFW+chJ1+WPSHaG6V35hkO2fsnpbVnPL6m6LT99n/w8YPHYQjLm5OFUTml3cMGCoHM50U23flNupQVhwEgbjbbGgEsVpSdibYFAOU0s5Xl9kbd+OJIzE+KceV/+BqqVVYwr2xufAKLPUZETBgSjoQ9bhcHFNByUiehgYpDZElsJWrFihjFOVv4956dIldY3tkNW3sv1TfmHo3r27Ur0tS+UPZ3ahX8F18DD4QXcnNPEYevv0Ff9X2zflIjjDZ+or0Pf4Hiv0M0WpeRE25ffEpLAAsedptXOSVHM8qJ2Uav55itKq9yQsjpyL/nkiPGU7aageaws9sSDyFQS636n+JSLL4zhSC5LVjpZ6T2V1Z1xcHObPn9/uJ1mXpevmTt9Htk9+/hxHStaEJVIbJdvhZNvpli1blKre9qhm+Ips/8zOzlaqbmX7p/xiwBAlImvBILVhsu1Uth3K0pwMpPZCtn/u379faf+UZHW1DNHWHb5CRNQ6GKQ2TrYdyrlk5dhKaw9T2f4pZ2+SbaC9evWqndmJUyMSkTVjG2kHIdsZZQekmpmSrIU8L/lbn7I9V07UL2dvau9tutS22EZK1oYl0g5CtilaU8n07un7ZHtuq03fR0RkQSyRdjA1JdPBgwcrs/5Ymgzyv/3tb8rPxsmS8ciRI1l1Sy3CEilZG5ZILUheAJp2A4bE5co29W4LE2GQPyZytxsFSFyux8JEA8yrzdPQLZf7LN+DHGXgf0OyZPriiy8qpUHZJmkJMrwtO31fa6qCMe3P4rP4M9KM4p02piEqZCGi0i6q69uC+CwNOerkDXc9PxFZHQap1SjH389ebDif6qZgeDuom9Qw/R1pW6IRm1vzw5bSZeSllGNyzF7ETC5HSt5ldXlDsgNSzdCYtpy04aFO39dWdGPwRhvPb1tlOIh3IvYip0wGqYN4ytfE38JrGKO7+w+BiKwBg9RaVF1B6amb8HTvbv6ZrCbdRll6AjYflj/uXJcLBgY64Qv9LOi/cELgQBd1eePkUBL5w9ayhChLjK3JKqbvIyKyEAaplTBdKEJ2aXd49ex2zw/FVJaBXZtLELjiLbzsqi5UPALdkBewWpZiV7+AIbpH1OVNk5M2ODk54ejRo+oSbaxr+r4HVYni7AOI0qtV68u34Uh+ncnl61XtXkRa1ELoN0Rhg7K9Hu8fPg+TUjWbhsSoP5qPIZYv35aqVtWqbhQjO1HOlWt+Hn3UAWQXV4rSaCIWRcSiFLmIjfgdFibm4eLdVbsmIwzfbDNX48ubPgqJaQbzHLw1VcFy2dd1tlm+A2ni+ETU+hikFtR05y0TblwqxVlUoGDvKvOFr9GL789I2b4fpdNmY8ZTPVvlw5s+fbpSenzQX42RpdmsrCyl/VO+vtGjRyvtnzKk218nIvE5GJKxaeUJ6BZsxK6EfYiZ64qzqVnq+sYZ/3YNXu/uQFzMSswd8QR+MRzC+ojdOOuzWBxDfLHZtRL+xkRErD8Eww2RdkrV/CdYmdQZC7bsE+ujMBvJWPmv8TjpNg0bI8PgCl+ERe7CpuB+qF+hWwFDUjQithsx6pMYxMlzXDYAZzevwfqkAtxQt4IxG5klA7BwV5w4/icIQwo+/uwYivnjMUStjkFqFapw+UIJjPDAiHnvq+2jG/Ga+49YU3PxlRfQ/9qG6Iv+mPcb7/tU/zafDLs5c+YoJcmWsM3p+8pRcPQIcv3GImiUh3iPRSm//1gEBnir65vgNwajvLrCXtcbXrob6jGmYGZgb/Pn5NgbgTOnwC/3CI4WlMNUmo0vD1+F3+zJGNX9EWV90Bt/QkLMSxhSO1F9EyoLcTSpUOw7A5P768Q/YHmOQZg5exByk46joLKmN+sg+AeNgLujOJ5jH4zyHwRkncbPV9hhiai1MUgtSJY0G/cruAe9JcLzXxHs3VVd1gVugwfCU7n4XhMlpRRsFVkXNi8Q3vLi2Ipk5x/ZZtqcHwe36en7qv4Ow/cGuA71Qs/at7greg3op95vgosTOtdsb7qGC0VlIrSiES5/pUWtWg0Nj0aW+DJkrPgF1dfLUYpOYrdOLf4HWFViwPdGDwz1qvmJNckBLj3doDOW4MLlmhqMbnCqPSl7dHbiECOittLSf8dkQfadneCiXHyv4nxOOnKRidiIl8wX5xkRiC0FSmMjMKOpITIt8NxzzymzCzXV8YjT97VMg97Xyq2tevtW42ZFOer24SYiy2GQWoWryNkWgZD3D9drwzKJkstl9IVPb1d4B6+uf1HeH4kwV8A1LBL7Gxsi00KyRCnHdR4+fFhdYm7/lKXUt956C8nJycr0fbL6VrZ/2uSvrzg8Ae9fe6M0uwgXaj8HE66XX1PvN0PNj3inZsNQ2XiDpJ34guSKm7hcflMcvWUc3Lzxa915ZBddqrOveo46N/R0uX8nMyJqXQxSq+CE/mP94ZuVhvQi9UeeTWX4MeUozgaNw3BXy/xw87hx45RZj0pKSjro9H01n8NB7Ev5GTdk79uCw9j3+TF1fXOoxzCmYG98jrknrcmIggOyh+46HC6+BXvXoZgY5Iysz79AuhwrKj7rnB3vI0Rd79DdFU/iOq5WNlI70KUvxk7rK/bdjy8KjCJCa87xJ/hOG43+XezUDYnIUhikVsEejt6TsDjyGVzd+gdz1W3oKqQ4TcMH80ehu4U+pYsXL+Kpp57Chx9+iM6dOyvDV2bMmNGBfr6s5nMIhu7ISvwuZCb020rhGeCnrm+OmmPMRf88EZ6ynTRUj7WFnlgQ+QoC3cWXIvsnMGb+Eqycdh2b588U6+djRZ4XXq9Z/9gABIZ2Q8KKMIREfY/6U2Z0hfe0cES+rEP6Ej1C5TmuzYfngnexeFr/VuuERkTNx7l2OzhZfVtYWFj7WU+aNEmZh9cmq27JJsgvmpxrl6wJg7SDksNXfvzxR6WDka+vrzL+kzMPUXvAICVrw6pdC5IXgIeN0/cREbUuBmkHYRvT9xERWR8GqQ2zren7iIisE4PUBtnm9H1ERNaJQWpDbHr6PiIiK8VeuzZAtn/KmYeuXr2qzE40fPhwljzJZrHXLlkbBmk7Jds/T5w4oQxf6dOnjzJ9H3veUkfAICVrw6pdC2qN4S817Z8db/o+IiLrxCBtJ4qKipThK6tWreqg0/cREVknBqkVk9W3sv1TDl/ZvXs3hg4dqgxfke2gHL5CRGQdGKRWSFbfyp8vk8NXjh8/rlQJy+Er8ge42YmIiMi6MEitCKfvIyJqf9hr1wrI6ltZ8szNzUVoaCh8fHxYdUvUBPbaJWvDIH1IZPvnyZMncejQIeWxvDj07duXVbdE98EgJWvDql0LkhcATt9HRGRbGKQWIkugEqfvIyKyLfes2iUiskas2iVr0mSQUuuTX074dhMR2RZW7RIREWnAILUglkaJiGwPg5SIiEgDBmmL/F/Eh/WDXVg8StQlLXH/DlwmlOenYn9kGNzFtnJ7O7uJWBpzEJkl5l6/RERkXRikLfK/MD32NKpjp8NNXdJ6fkFJympMHfgHHMBspF6rUqqCq4pXY3Dev2HkiIWIOXVV3ZaIiKwFe+1a0D177V5NwdInX0L64kQciBgFJ3WxwnQW8a9OQei5N5F3SI8B/PpDRGQ1eEmuR5QKM+MRGTZErVZVq1Zj01FikuvrVu3eRkn8a7BzD0HYHHX7iTHIV7ZrqRvI3/9nfIJ5WL5gZP0Qlew9Ebz0TTz/1b9jS+pFdSEREVkDBmkdpvwdmDfyPeT478I1UXKsrirG8fWu2D7vn/GnpgKs5Dh+HrYF18S2Jz6ahH4P9I6W41xeIfDcSAxybvwA9q594OdWjKwzF/FAWU1ERG2CQVqH/QA9vqzOQaze11wqtHfDyMn+GILLKL18XdmmoWfw8rSn4CS2HTbM7Z5vaNO16NdxufSyer8JXR7DE11KYCirYJASEVkRBundTCXI/Gs84uPFLWYpnh04H1+pqxrXHS7dHlHvP6jOcHF1gUhrXGsqJSuv4O+V6n0iIrIaDNI6TCVf451nR2Dkn46LMqjgMgmbMjbjeWWtdrIdtXFO6DWwL5BzGufKG09SU+kZZJWMQOhwT2iNbSIiaj0M0lo3cPrQZ1ibNw/Jf10L/fTpmD59PNyvFCFH3aLtOGLAjNewBFuxenMGypVlN5AfMwvuYZGITz+K+I834Cu35zFxZHdlLRERWQcGaa1H4dqnH9xKMnE4owQmZXKERKxZvfWBJl9oMedn8Mcdvwfemo/wyC+RX/4oBsz6ALFDcrBo9DOYGQPoN/4eAU10RiIiooeDV+Va9nAO+AMS17ti67O94GDngG6/P46B4Ysx182Ar48XoG2nQ3gUboHLcSDv3zAVnyOgmwPsug3E81+4Ym3GGZxLnoHCRSuw/ut8tcRKRETWgBMytBtyjOthpGMYpo64d+9gIiKyHAYpERGRBizYEBERacAgtaCmh78QEVF7xSAlIiLSgEFKRESkAYOUiIhIAwapBbGDNBGR7WGQEhERacAgJSIi0oBBakEc/kJEZHsYpERERBowSImIiDRgkBIREWnAILUgDn8hIrI9DFIiIiINGKREREQaMEgtiMNfiIhsD4OUiIhIAwYpERGRBgxSIiIiDRikFsThL0REtodBSkREpAGDlIiISAMGqQVx+AsRke1hkBIREWnAICUiItKAQUpERKQBg9SCOPyFiMj2MEiJiIg0YJASERFpwCC1IA5/ISKyPQxSIiIiDRikREREGjBIiYiINGCQWhCHvxAR2R4GKRERkQYMUiIiogcG/H9frDHqdFX5oQAAAABJRU5ErkJggg=="></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The sound wave in air in (c) enters a pipe that is open at both ends. The diagram shows the displacement, at a particular time <em>T</em>, of the standing wave that is set up in the pipe.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">A particular air molecule has its equilibrium position at the point labelled M.</span></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">Sound of frequency <em>f</em> = 2500 Hz is emitted from an aircraft that moves with speed <em>v</em> = 280 m s<sup>–1 </sup>away from a stationary observer. The speed of sound in still air is <em>c</em> = 340 m s<sup>–1</sup>.</span></p>
<p><span style="background-color: #ffffff;"><img 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"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Particle P in the metal sheet performs simple harmonic oscillations. When the displacement of P is 3.2 μm the magnitude of its acceleration is 7.9 m s<sup>-2</sup>. Calculate the magnitude of the acceleration of P when its displacement is 2.3 μm.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The wave is incident at point Q on the metal–air boundary. The wave makes an angle of 54° with the normal at Q. The speed of sound in the metal is 6010 m s<sup>–1</sup> and the speed of sound in air is 340 m s<sup>–1</sup>. Calculate the angle between the normal at Q and the direction of the wave in air.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The frequency of the sound wave in the metal is 250 Hz. Determine the wavelength of the wave in air.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">On the diagram, at time <em>T</em>, draw an arrow to indicate the acceleration of this molecule.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">On the diagram, at time <em>T</em>, label with the letter C a point in the pipe that is at the centre of a compression.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">dii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the frequency heard by the observer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ei.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the wavelength measured by the observer.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">eii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">Expression or statement showing acceleration is proportional to displacement ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">so </span><span style="background-color:#ffffff;">«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7.9 \times \frac{{2.3}}{{3.2}}">
<mn>7.9</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mn>2.3</mn>
</mrow>
<mrow>
<mn>3.2</mn>
</mrow>
</mfrac>
</math></span>» = 5.7«ms<sup>–2</sup>» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sin \theta = \frac{{340}}{{6010}} \times \sin {54^0}">
<mi>sin</mi>
<mo></mo>
<mi>θ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>340</mn>
</mrow>
<mrow>
<mn>6010</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mi>sin</mi>
<mo></mo>
<mrow>
<msup>
<mn>54</mn>
<mn>0</mn>
</msup>
</mrow>
</math></span></span><span style="background-color:#ffffff;"> ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta = {2.6^0}">
<mi>θ</mi>
<mo>=</mo>
<mrow>
<msup>
<mn>2.6</mn>
<mn>0</mn>
</msup>
</mrow>
</math></span> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda = « \frac{{340}}{{250}} =» 1.36 \approx 1.4 «{\text{m}}»">
<mi>λ</mi>
<mo>=</mo>
<mrow>
<mo>«</mo>
</mrow>
<mfrac>
<mrow>
<mn>340</mn>
</mrow>
<mrow>
<mn>250</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mrow>
<mo>»</mo>
</mrow>
<mn>1.36</mn>
<mo>≈</mo>
<mn>1.4</mn>
<mrow>
<mo>«</mo>
</mrow>
<mrow>
<mtext>m</mtext>
</mrow>
<mrow>
<mo>»</mo>
</mrow>
</math></span></span><span style="background-color:#ffffff;"> ✔</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">horizontal arrow «at M» pointing left ✔</span></p>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">any point labelled C on the vertical line shown below ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em>eg</em>:</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><img 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" width="416" height="175"></span></p>
<div class="question_part_label">dii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f' = 2500 \times \frac{{340}}{{340 + 280}}">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mn>2500</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mn>340</mn>
</mrow>
<mrow>
<mn>340</mn>
<mo>+</mo>
<mn>280</mn>
</mrow>
</mfrac>
</math></span> ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f' = 1371 \approx 1400">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mn>1371</mn>
<mo>≈</mo>
<mn>1400</mn>
</math></span>«Hz» ✔</span></span></p>
<div class="question_part_label">ei.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ' = \frac{{340}}{{1371}} \approx 0.24/0.25">
<msup>
<mi>λ</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mfrac>
<mrow>
<mn>340</mn>
</mrow>
<mrow>
<mn>1371</mn>
</mrow>
</mfrac>
<mo>≈</mo>
<mn>0.24</mn>
<mrow>
<mo>/</mo>
</mrow>
<mn>0.25</mn>
</math></span>«m» ✔</span></p>
<div class="question_part_label">eii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was well answered at both levels.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many scored full marks on this question. Common errors were using the calculator in radian mode or getting the equation upside down.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was very well answered.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very few candidates could interpret this situation and most arrows were shown in a vertical plane.</p>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was answered well at both levels.</p>
<div class="question_part_label">dii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was answered well with the most common mistake being to swap the speed of sound and the speed of the aircraft.</p>
<div class="question_part_label">ei.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Answered well with ECF often being awarded to those who answered the previous part incorrectly.</p>
<div class="question_part_label">eii.</div>
</div>
<br><hr><br>