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<h2>SL Paper 2</h2><div class="specification">
<p>A pipe is open at both ends. A first-harmonic standing wave is set up in the pipe. The diagram shows the variation of displacement of air molecules in the pipe with distance along the pipe at time <em>t</em> = 0. The frequency of the first harmonic is <em>f</em>.</p>
<p><img 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"></p>
</div>
<div class="specification">
<p>A transmitter of electromagnetic waves is next to a long straight vertical wall that acts as a plane mirror to the waves. An observer on a boat detects the waves both directly and as an image from the other side of the wall. The diagram shows one ray from the transmitter reflected at the wall and the position of the image.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An air molecule is situated at point X in the pipe at <em>t</em> = 0. Describe the motion of this air molecule during one complete cycle of the standing wave beginning from <em>t</em> = 0.</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 speed of sound <em>c</em> for longitudinal waves in air is given by</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = \sqrt {\frac{K}{\rho }} ">
<mi>c</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mi>K</mi>
<mi>ρ</mi>
</mfrac>
</msqrt>
</math></span></p>
<p>where <em>ρ</em> is the density of the air and <em>K</em> is a constant.</p>
<p>A student measures <em>f</em> to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m<sup>–3</sup>. Determine, in kg m<sup>–1</sup> s<sup>–2</sup>, the value of <em>K</em> for air.</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>Demonstrate, using a second ray, that the image appears to come from the position indicated.</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>Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.</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>«air molecule» moves to the right and then back to the left ✔</p>
<p>returns to X/original position ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wavelength = 2 × 1.4 = «2.8 m» ✔</p>
<p><em>c</em> = «<em>f λ</em> =» 120 × 2.8 «= 340 m s<sup>−1</sup>» ✔</p>
<p><em>K</em> = «<em>ρc</em><sup>2</sup> = 1.3 × 340<sup>2</sup> =» 1.5 × 10<sup>5</sup> ✔</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>construction showing formation of image ✔</p>
<p><em>Another straight line/ray from image through the wall with line/ray from intersection at wall back to transmitter. Reflected ray must intersect boat.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>interference pattern is observed</p>
<p><em><strong>OR</strong></em></p>
<p>interference/superposition mentioned ✔</p>
<p><br>maximum when two waves occur in phase/path difference is nλ</p>
<p><em><strong>OR</strong></em></p>
<p>minimum when two waves occur 180° out of phase/path difference is (n + ½)λ ✔</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>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 air between the slits and the screen is replaced with water. The refractive index of water is 1.33.</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>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.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the wavelength of the light in water.</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>State <strong>two </strong>ways in which the intensity pattern on the screen changes.</p>
<div class="marks">[2]</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>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>evidence of solving for <em>D</em> <strong>«</strong><em>D</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{sd}}{\lambda }">
<mfrac>
<mrow>
<mi>s</mi>
<mi>d</mi>
</mrow>
<mi>λ</mi>
</mfrac>
</math></span><strong>»</strong></p>
<p><strong>«</strong><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}}}}">
<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>
</math></span> × 2<strong>»</strong> = 4.27 <strong>«</strong>m<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[1] </em></strong><em>max for 2.13 m.</em></p>
<p><strong><em>[2 marks]</em></strong></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{{633.0}}{{1.33}}">
<mfrac>
<mrow>
<mn>633.0</mn>
</mrow>
<mrow>
<mn>1.33</mn>
</mrow>
</mfrac>
</math></span> = 476 <strong>«</strong>nm<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>distance between peaks decreases</p>
<p>intensity decreases</p>
<p><em><strong>[2 marks]</strong></em></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">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><span style="background-color: #ffffff;">The solid line in the graph shows the variation with distance <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></em> of the displacement <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></em> of a travelling wave at <em>t</em> = 0. The dotted line shows the wave 0.20 ms later. The period of the wave is longer than 0.20 ms.</span></p>
<p><span style="background-color: #ffffff;"><img style="margin-right: auto; margin-left: auto; display: block;" src="data:image/png;base64,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" width="612" height="296"></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">One end of a string is attached to an oscillator and the other is fixed to a wall. When the frequency of the oscillator is 360 Hz the standing wave shown is formed on the string.</span></p>
<p><span style="background-color: #ffffff;"><img style="margin-right: auto; margin-left: auto; display: block;" 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" width="521" height="172"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Point X (not shown) is a point on the string at a distance of 10 cm from the oscillator.</span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate, in m s<sup>–1</sup>, the speed for this wave.</span></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><span style="background-color: #ffffff;">Calculate, in Hz, the frequency for this wave.</span></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><span style="background-color: #ffffff;">The graph also shows the displacement of two particles, P and Q, in the medium at <em>t</em> = 0. State and explain which particle has the larger magnitude of acceleration at <em>t</em> = 0.</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;">State the number of all other points on the string that have the same amplitude and phase as X.</span></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><span style="background-color: #ffffff;">The frequency of the oscillator is reduced to 120 Hz. On the diagram, draw the standing wave that will be formed on the string.</span></p>
<p><img src="data:image/png;base64,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"></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><em>v = </em><span style="background-color: #ffffff;">«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>05</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>20</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfrac><mo>=</mo></math>» 250 «m s<sup>–1</sup>»✔</span></p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;"><em>λ </em>= 0.30 «m» ✔<br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> = «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>250</mn><mrow><mn>0</mn><mo>.</mo><mn>30</mn></mrow></mfrac><mo>=</mo></math>» 830 «Hz» ✔</span></p>
<p><em>NOTE: </em><em><span style="background-color: #ffffff;">Allow ECF from (a)(i)<br>Allow ECF from wrong wavelength for MP2</span></em></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">Q ✔<br>acceleration is proportional to displacement «and Q has larger displacement» ✔</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">3 «points» ✔</span></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">first harmonic mode drawn ✔</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Allow if only one curve drawn, either solid or dashed.</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(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.</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 vertical tube, open at both ends, is completely immersed in a container of water. A loudspeaker above the container connected to a signal generator emits sound. As the tube is raised the loudness of the sound heard reaches a maximum because a standing wave has formed in the tube.</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>Describe <strong>two</strong> ways in which standing waves differ from travelling waves.</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>Outline how a standing wave forms in the tube.</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>The tube is raised until the loudness of the sound reaches a maximum for a <strong>second time</strong>.</p>
<p>Draw, on the following diagram, the position of the nodes in the tube when the second maximum is heard.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" 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>Between the first and second positions of maximum loudness, the tube is raised through 0.37 m. The speed of sound in the air in the tube is 320 m s<sup>−1</sup>. Determine the frequency of the sound emitted by the loudspeaker.</p>
<p> </p>
<div class="marks">[2]</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>energy is not propagated by standing waves <strong>✓</strong></p>
<p>amplitude constant for travelling waves <em><strong>OR</strong> </em>amplitude varies with position for standing waves <em><strong>OR</strong> </em>standing waves have nodes/antinodes <strong>✓</strong></p>
<p>phase varies with position for travelling waves <em><strong>OR</strong> </em>phase constant inter-node for standing waves <strong>✓</strong></p>
<p>travelling waves can have any wavelength <em><strong>OR</strong> </em>standing waves have discrete wavelengths<strong> ✓</strong></p>
<p><strong><em><br>OWTTE</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«sound» wave «travels down tube and» is reflected <strong>✓</strong></p>
<p>incident and reflected wave superpose/combine/interfere <strong>✓</strong></p>
<p><strong><em><br>OWTTE</em></strong></p>
<p><em>Do not award <strong>MP1</strong> if the reflection is quoted at the walls/container</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>nodes shown at water surface <em><strong>AND </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac></math>way up tube (by eye) <strong>✓</strong></p>
<p><em><br>Accept drawing of displacement diagram for correct harmonic without nodes specifically identified. </em></p>
<p><em>Award <strong>[0]</strong> if waveform is shown below the water surface</em></p>
<div class="question_part_label">b.ii.</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>0</mn><mo>.</mo><mn>74</mn><mo> </mo><mo>«</mo><mtext>m</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mo>«</mo><mfrac><mi>c</mi><mi>λ</mi></mfrac><mo>=</mo><mfrac><mn>320</mn><mrow><mn>0</mn><mo>.</mo><mn>74</mn></mrow></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>430</mn><mo> </mo><mo>«</mo><mtext>Hz</mtext><mo>»</mo></math> ✓</strong></p>
<p><em><br>Allow <strong>ECF</strong> from <strong>MP1</strong></em></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.</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>A loudspeaker emits sound waves of frequency<em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></em> towards a metal plate that reflects the waves. A small microphone is moved along the line from the metal plate to the loudspeaker. The intensity of sound detected at the microphone as it moves varies regularly between maximum and minimum values.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The speed of sound in air is 340 m s<sup>−1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain the variation in intensity.</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>Adjacent minima are separated by a distance of 0.12 m. Calculate <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></em>.</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>The metal plate is replaced by a wooden plate that reflects a lower intensity sound wave than the metal plate.</p>
<p>State and explain the differences between the sound intensities detected by the same microphone with the metal plate and the wooden plate.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«incident and reflected» waves superpose/interfere/combine ✓</p>
<p>«that leads to» standing waves formed <em><strong>OR</strong> </em>nodes and antinodes present ✓</p>
<p>at antinodes / maxima there is maximum intensity / constructive interference / «displacement» addition / louder sound ✓</p>
<p>at nodes / minima there is minimum intensity / destructive interference / «displacement» cancellation / quieter sound ✓</p>
<p> </p>
<p><strong><em>OWTTE</em></strong></p>
<p><em>Allow a sketch of a standing wave for <strong>MP2</strong></em></p>
<p><em>Allow a correct reference to path or phase differences to identify constructive / destructive interference</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wavelength = 0.24 «m» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> = «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>340</mn><mrow><mn>0</mn><mo>.</mo><mn>24</mn></mrow></mfrac></math>=» 1.4 «kHz» <em><strong>OR</strong> </em>1400 «Hz» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>relates intensity to amplitude ✓</p>
<p>antinodes / maximum intensity will be decreased / quieter ✓</p>
<p>nodes / minimum will be increased / louder ✓</p>
<p>difference in intensities will be less ✓</p>
<p>maxima and minima are at the same positions ✓</p>
<p> </p>
<p><em><strong>OWTTE</strong></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) On most occasions it looked like students knew more than they could successfully communicate. Lots of answers talked about interference between the 2 waves, or standing waves being produced but did not go on to add detail. Candidates should take note of how many marks the question part is worth and attempt a structure of the answer that accounts for that. At SL there were problems recognizing a standard question requiring the typical explanation of how a standing wave is established.</p>
<p>3aii) By far the most common answer was 2800 Hz, not doubling the value given to get the correct wavelength. That might suggest that some students misinterpreted adjacent minima as two troughs, therefore missing to use the information to correctly determine the wavelength as 0.24 m.</p>
<p>b) A question that turned out to be a good high level discriminator. Most candidates went for an answer that generally had everything at a lower intensity and didn't pick up on the relative amount of superposition. Those that did answer it very well, with very clear explanations, succeeded in recognizing that the nodes would be louder and the anti-nodes would be quieter than before.</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">b.</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 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"></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The frequency of the sound wave in the metal is 250 Hz.</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;">State the frequency of the wave in air.</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;">Determine the wavelength of the wave in air. </span></p>
<div class="marks">[1]</div>
<div class="question_part_label">cii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<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;">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></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">Expression or statement showing acceleration is proportional to displacement ✔<br></span></p>
<p><span style="background-color:#ffffff;">so «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7.9 \times \frac{{2.3}}{{3.2}} » = 5.7 « {\text{m }}{{\text{s}}^{ - 2}}">
<mn>7.9</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mn>2.3</mn>
</mrow>
<mrow>
<mn>3.2</mn>
</mrow>
</mfrac>
<mrow>
<mo>»</mo>
</mrow>
<mo>=</mo>
<mn>5.7</mn>
<mrow>
<mo>«</mo>
</mrow>
<mrow>
<mtext>m </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math></span>» ✔</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><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^\circ ">
<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>
<msup>
<mn>54</mn>
<mo>∘</mo>
</msup>
</math></span> </span><span style="background-color:#ffffff;">✔<br></span></p>
<p><span style="background-color:#ffffff;">θ = 2.6° ✔</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><em>f</em> = 250 «Hz» <em><strong>OR</strong> </em>Same <em><strong>OR</strong> </em>Unchanged ✔<br></span></p>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><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>
</math></span>»</span> <span style="background-color:#ffffff;">✔</span><span style="background-color:#ffffff;"><br></span></p>
<div class="question_part_label">cii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">any point labelled C on the vertical line shown below ✔<br></span></p>
<p><span style="background-color:#ffffff;">eg:</span><span style="background-color:#ffffff;"><br></span></p>
<p><span style="background-color:#ffffff;"><img src="data:image/png;base64,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" width="378" height="152"></span></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 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>Many used a ratio of the speeds to produce a new frequency of 14Hz (340 x 250/6010). It would have helped candidates if they had been aware that the command term ‘state’ means ‘give a specific name, value or other brief answer without explanation or calculation.’</p>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">cii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was answered well at both levels.</p>
<div class="question_part_label">d.</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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"></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>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 sound sensor gives a graph of the variation of output voltage with time along the track that is similar in shape to the graph shown in the resource. Explain how this effect arises.</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>«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><em><strong>ALTERNATIVE 1</strong></em></p>
<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">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">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A beam of microwaves is incident normally on a pair of identical narrow slits S1 and S2.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">When a microwave receiver is initially placed at W which is equidistant from the slits, a maximum in intensity is observed. The receiver is then moved towards Z along a line parallel to the slits. Intensity maxima are observed at X and Y with one minimum between them. W, X and Y are consecutive maxima.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="text-align:left;">Explain why intensity maxima are observed at X and Y.</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 style="text-align:left;">The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.<br><br>Determine the frequency of the microwaves.</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 style="text-align:left;">Outline <strong>one</strong> reason why the maxima observed at W, X and Y will have different intensities from each other.</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>two waves superpose/mention of superposition/mention of «constructive» interference ✔</p>
<p>they arrive in phase/there is a path length difference of an integer number of wavelengths ✔</p>
<p><em>Ignore references to nodes/antinodes</em>.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>path difference = 0.062 «m» ✔</p>
<p>so wavelength = 0.031 «m» ✔</p>
<p>frequency = 9.7 × 10<sup>9</sup> «Hz» ✔</p>
<p><em>If no unit is given, assume the answer is in Hz. Accept other prefixes (eg 9.7 GHz)</em></p>
<p><em>Award <strong>[2 max]</strong> for 4.8 x 10<sup>9</sup> Hz.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>intensity varies with distance<em><strong> OR</strong></em> points are different distances from the slits ✔</p>
<p><em>Accept “Intensity is modulated by a single slit diffraction envelope”</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;">
<p>Many candidates were able to discuss the interference that is taking place in this question, but few were able to fully describe the path length difference. That said, the quality of responses on this type of question seems to have improved over the last few examination sessions with very few candidates simply discussing the crests and troughs of waves.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates struggled with this question. Few were able to calculate a proper path length difference, and then use that to calculate the wavelength and frequency. Many candidates went down blind paths of trying various equations from the data booklet, and some seemed to believe that the wavelength is just the reciprocal of the frequency.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This is one of many questions on this paper where candidates wrote vague answers that did not clearly connect to physics concepts or include key information. There were many overly simplistic answers like “they are farther away” without specifying what they are farther away from. Candidates should be reminded that their responses should go beyond the obvious and include some evidence of deeper understanding.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A large cube is formed from ice. A light ray is incident from a vacuum at an angle of 46˚ to the normal on one surface of the cube. The light ray is parallel to the plane of one of the sides of the cube. The angle of refraction inside the cube is 33˚.</p>
<p><img 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"></p>
</div>
<div class="specification">
<p>Each side of the ice cube is 0.75 m in length. The initial temperature of the ice cube is –20 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed of light inside the ice cube.</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>Show that no light emerges from side AB.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the diagram, the subsequent path of the light ray.</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>Determine the energy required to melt all of the ice from –20 °C to water at a temperature of 0 °C.</p>
<p>Specific latent heat of fusion of ice = 330 kJ kg<sup>–1</sup><br>Specific heat capacity of ice = 2.1 kJ kg<sup>–1</sup> k<sup>–1</sup><br>Density of ice = 920 kg m<sup>–3</sup></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline the difference between the molecular structure of a solid and a liquid.</p>
<div class="marks">[1]</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>«<em>v</em> = <em>c</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{sin }}i}}{{{\text{sin }}r}}">
<mfrac>
<mrow>
<mrow>
<mtext>sin </mtext>
</mrow>
<mi>i</mi>
</mrow>
<mrow>
<mrow>
<mtext>sin </mtext>
</mrow>
<mi>r</mi>
</mrow>
</mfrac>
</math></span> =» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3 \times {{10}^8} \times {\text{sin}}\left( {33} \right)}}{{{\text{sin}}\left( {46} \right)}}">
<mfrac>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>33</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>46</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>2.3 x 10<sup>8</sup> «m s<sup>–1</sup>»</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>light strikes AB at an angle of 57°</p>
<p>critical angle is «sin<sup>–1</sup><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{2.3}}{3}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>2.3</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> =» 50.1°</p>
<p><em>49.2° from unrounded value</em></p>
<p>angle of incidence is greater than critical angle so total internal reflection</p>
<p><strong><em>OR</em></strong></p>
<p>light strikes AB at an angle of 57°</p>
<p>calculation showing sin of “refracted angle” = 1.1</p>
<p>statement that since 1.1>1 the angle does not exist and the light does not emerge</p>
<p><strong><em>[Max 3 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total internal reflection shown</p>
<p>ray emerges at opposite face to incidence</p>
<p><em>Judge angle of incidence=angle of reflection by eye or accept correctly labelled angles</em></p>
<p><em>With sensible refraction in correct direction</em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>mass = «<em>volume</em> x <em>density</em>» (0.75)<sup>3</sup> x 920 «= 388 kg»</p>
<p>energy required to raise temperature = 388 x 2100 x 20 «= 1.63 x 10<sup>7</sup> J»</p>
<p>energy required to melt = 388 x 330 x 10<sup>3</sup> «= 1.28 x 10<sup>8</sup> J»</p>
<p>1.4 x 10<sup>8</sup> «J» <em><strong>OR</strong> </em>1.4 x 10<sup>5</sup> «kJ»</p>
<p><em>Accept any consistent units </em></p>
<p><em>Award <strong>[3 max]</strong> for answer which uses density as 1000 kg<sup>–3</sup> (1.5× 10<sup>8</sup> «J»)</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>in solid state, nearest neighbour molecules cannot exchange places/have fixed positions/are closer to each other/have regular pattern/have stronger forces of attraction</p>
<p>in liquid, bonds between molecules can be broken and re-form</p>
<p><em>OWTTE</em></p>
<p><em>Accept converse argument for liquids</em></p>
<p><strong><em>[Max 1 Mark]</em></strong></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>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,iVBORw0KGgoAAAANSUhEUgAAAOsAAAFXCAYAAABDdblvAAAgAElEQVR4Ae2d3+93V1Xn/T8mjhRaylMqFE2F9mlMCxKkiBkRKMXRIqQ8pVgyTEY6RgRMpF6Mg+MFlQw4jiO9GC9wtE0gar2gEyJXQEOakHDzTL3gsoQ/4DN5nfL+sr7r2ft8zo+99/m1dvJ5zvmcs3+uvV57rbXP+XyfnzpFuiSBF1/8f6cvfemLp49//D+c3vOeX7/h87nP/dfTd7/73Utl4ktIoIUEfqpFI2tv44c//GEH6Nve9tbTT//0v+k+t932mhtAfdOb3nhxn/O/+Zv/vfahRf92JIFDwwqkWErABFIAxKr2WU5ZXoHLsS//jnQlhrKwBA4LK1ZRkOLufuMb3xg9FbaOsLKjxRcFRkrgcLBiTYFTlnQKpFbGWFq5z8S5kUICtSRwKFi/9rWvXljTT3/6UyfALZGoB1BZAObCX6I/Ucc+JXAYWIlFgQnXtwZQ1Bmw7hOStYzqELDK6uGulrKmfgIDVi+R+F5aAruHVaByrAUqkxKwllbNqM9LYNewWlD9wEt/D1hLSzTq8xLYLawtQUWoAatXrfheWgK7hBV3l40kPq1SwNpK0sdtZ5ewMp28pMDuLG8otUg8b6U9dp0jhQRqSGC3sCIsXn7AutbcWLKT0nJxsO3G+TEksGtY5ZoSv7ZIAWsLKR+3jV3DyrTq1ULc1NqJl/ppL1JIoIYEdg+rrCuvF9ZOgBqw1pbycevfPaxMLQC1iF31uOi46hQjrymBQ8DKC/wtdmrZeaadVhtaNRUj6l6fBA4BK2InnuRTM8nl5hgpJFBaAoeBVb+6qQlSPGstrZ5Rn5XAYWDFNcVFrf0Yh9i4dht2AuP8OBI4DKxM6Yc+9MHqryCymVXb3T6OesZIrQQOBateQWTDqVbSJlOL57q1xhD1rlMCh4K1hSusTab4A2rrVPgt9+pQsDJRLVzhFrHxlpUu+j5NAoeDVa5wzV1hFoSIW6cpZJTKS+BwsOrxSs2fzukxUfzx77zixZ3xEjgcrIiIP5xW8x1eLQgt3kceP+VRYqsSOCSsQERcWTOxIIQrXFPCx6v7kLC2iFvlCteMjY+nrsce8SFhlZta80+wtHhMdGzVPd7oDwkr09zitUD9ZC5+hXM8sGqM+LCwssFEXFkz6QWJmjvPNfsfda9LAoeFtcUmE1MdG03rUvgt9+awsGoDqPY7vNrMitcPt4zJOvp+WFjlorbYreURTjzGWYfCb7kXh4WVt4t41trC4sm61tx93rISRt+HSeCwsCIeYG21+UPs2uKPtg2b9si1RQkErI3+ew253fEK4hYxWUefDw0rcSS/kGmVaAtr3iJObjWmaKedBA4NK89aa77Q76eRlyNwhWs/3/Xtxvd9SCBgbfzfXeiRUbjD+wCo5SgC1sawMrlyh2v+LaiWShRttZFAwLoArLjDxMu4xLVfymijRtFKCwkErAvAysTqOS/xa7zo30LVt99GwLoQrKiOXpZouSO9fZU97ggC1gVh1e9qY7PpuACOGXnAuiCs2hmOP6w2RmWPm/fQsBIvtnzO6tUsXvD3EonvfRI4NKwt3w32k6B4tcUPCXzb8X2bEghYG70bbNVDbzLFz+asVOL8nAQOC6s2d5b42Zr+SkW8I3xOPeO+lcBhYdWvYFoDw1tLuN/xuMaqYZwPkcBhYVXM2HInFmvOW0u4v/EixBD1jDxWAoeFVf+PqhVGzXPgZPcZq9pygZg7puef/87p6tW7un7ffvttpyef/Hx3zvVIbSVwWFh5ZNNyg0fPVJeIkeeo1IMPvq+DdU4dUbaMBA4LK6C2jBv1LvDWHtXcf//bT3wiLS+BQ8KKS4o7CrDA0yp+JF5tuUDMUS/cXGRkP7jA3g0WzFzHTSa/3GXbPvVhpVXfI49c676T1ybqkdtNXvK99NJLF1loj3pUF+Xt/YuMOzw5LKzErMAq5QGi2uDy32kA7JaSYFSfU7AiQ+ARNI8//olOrs8883RX7Pr16x3A5FGysOma6uZIopxvn++098QTn+3yqA3VsefjIWG1E8qjG0FkwSW2LP1bU+1At35cZMc79tzDIqC0wSR4AEuJcwsU8HoLCNhck2VVGSypTbLwAjjVns2/5/PDw2onl2eggGstrmJbLPEUeCmjTSW531v6lc0QWAWcZAmIFlbcWmtVlY9rKvvUU1/uynD0iTwqT39Uxufb+/eANTPDbAgBGe4xrivKN+VvDFMHZfW4hsc3fLaSSsAKXN5iMn6uCTxZbGSV+tAPUsC6Fc1ZsJ9Y2HO/0MEyk09g0l3tAsu66vnuFCu9xPBLwIplFWx2DCnLei4GDVitBOM8KQHFtbqpWFffOXowdc/uAivPVh7hlIA1FbMiG6yqLKtiVm0cSXaKbXU9YJVk4piVgHdnc5tFFkxVJlda31N5dG9txxKwAiJQKu5kjJzj7gpWrmkXWZtJgEo+LDPnpIC1E0P80ycBWUS5s7ixKJuPYz2Y1OlB91a6r92l75WAlTHknrNSv02Aap+zAiuwKwWskkQceyWARQQ0pVQc68Ekrwc9Z5VV71GOuV3io4x/7DhjN3iExPz7xICLdbXJg6l71vVd+yMcNspKvtUlV1bPZpGJdn+fe+7rElEcz0ggYD0jIHvb7+TmLKQFU+W9e7zWRzgsNqn+axxTjsSbikf1WAaAz+38Tmlrz2UC1hGzyw4wyoblIc2JWz34I7pRLSvWFNceWIE20rokELCOnA9gtW8gTY1b5S6v6REObr5djEaKJrJXlkDAOlLA3n1N7ewKRO0cqwnvXvrvyrfEUX8Xyu9uL9GXaDMtgYA1LZfsVSm1Mihu9W5jCkQft6ZAV70tj7j1WNRzb2i17FO0daMEAtYbZdJ7RYqtX84obvVW1INJpf6xjkBXXb0NV7rJIsPCgjtfcge4UncPXW3AOnL6Bad1F1F04LTJg8k97x4v/QiH9nHrgdV7BnYscb4OCQSsE+bBbyql3FkPpprx7rGPgZWvxZEFBvd3TZtcLca91TYC1gkz5+FMWVGq9WByzbvHSz3CUbt2Z3uCKKJIQwkErBOE7eHMWVEPJk0pTpXbqbItrZvi7thQmjD5CxYJWCcIX4ABrVLKinqoyauY91xZ1Vv6SN/pa2wolZZs/foC1okyRuFxh5VSVjQFNfn9hpR3q1Vn6WNsKJWWaNv6AtaJ8vYv9aesKFWnLK6HU65x7Uc4saE0cbJXUixgnTgR2qDBrSXlrGjK4gpOypBaPMLRYhIbSp3IN/lPwDpx2vxL/VSTsqKCRGCSLxW31nyEo77SxhqSFrg19GVLfQhYZ8yWf6k/ZUVzFtfHrd5Sz+jWpR8aAAaLCB8s+FIJOTBGFgzk9sd//MRSXdlsuwHrjKnz1lBW1FuOlMX1caugnvsIR1abvv3rv754AYe17DOGPKmoFiIgpV/Xrj0cL2NMkGTAOkFoKuJf6s8Bl7K4Pm6lzhTUamvoUS4vYLzyla9oCgWWm3H5hYEFhIVMi5iFd+7iNFQue8gXsM6YRb1cYHdxAc4+0qF6WVyrxLKA3FPy1lbXxxzVFrDqUxMIAKVN/RaWNv34ff9tXvLX7J9ve8vfA9YZsyfgsBRKWFHiUZtkcS2Y3PdxK0qL8lr4bT1DzmXtBaqO5wAaUncqj8bGWGibBexcUp/sMXapz0ntdApYz8uoNwdKal/bk2WTy6fCKRfXW9ISj3C81QII2gaGORtMQEh/7cKksVmPQddyR+umW1g5D2BzUnv5esDaL5+zdz1wsjTeteuLW60l9ZtWZzvgMrB4CALA9f1w2c9+pd+qj+NcC23jVep7zWtePdgin+3szjMErDMnWK6rtS4ppZbFtflSbrSU2VvmXDexllg9yj3wwHtPv/ALd3bKP7S8rTdVhsUDQGljjmVWOywgLADI4/3vf7Cz+roXx34JBKz98jl7V5bUxqMoJBbOplQ+7ns3WvlyFlFwAtDdd991yer9+rvedXrm6Zf/A2Pbdt85EOJ+0g/c5ZZJC531LFq2v7W2AtYCM+Z3gHPWMRe3Yolt8vmweCwGv/zLb7sE54c++MHTX/zFl07f/va3Tz/60Y9sFYPObXzLOW2UsJ6DGjdvckWsOkxiAeswOfXm8jvA2kTx1nFo3IrVvHLl1g4eaz3f/Ob7Tn/6p587/d/nnuvtj78p2P11rCp9bAmo78PcGN3Xt+fvAWuB2U1Z0qlxK/C89a1vubCguLZc+8EPfnCpp1/76ldvuGYz4E5jsYCBvvBZo7tJH+lbKl6244nzeHRTRAdkSbFUSmPj1nvuuft09erdneK+/vU/21lQDyh14/J+//vfP/3hZz7TfdSeP2oBAVbOgXeNSbLzXsga+7p0n8KyFpoBrIONvQSLtxg+HgVw4KQ8bi4Wsy9xn3yATJlcrIpr69vuq3fJe14mS/ZlzW0HrIVmB0uKFVPKWQzFrcD0wAPv6YDjcYs2j2699ZYTG0d9cSmwch8XuS+f+rL2o2Sy9n4u3b+AtdAMKPay1Xlryz3cvVtuufl0yy2v6kC9+eZXnu699xdPH3vssdNf/uX/OP31X/+v07UPf7i7l3KDqYNNJnaB9bFtbvEcmSCrNcbUa5JnwFpoNnBnvcJ5a0tTX/jCn59e+9rburxPP/33pxdffPGGz7e+9a3u/qf+4A+SvUO5iVmxqljhrSfc9dTCtvVxle5/wFpIori1KByxqpLiVvto5Ld/+6HTRx999PTOd/7KDZBacN/xjvtPD/3Wb6mqS0c2mbCqbDT9x49//NK9rX6JRzjnZy5gPS+jwTn820iKW+0u8cc+9lhnDQHbwunP/+RP/svpda+7fXDbbDRhaXGRiWWp375VNbiihTIqjNjKptgSYgpYC0qdlxmAxCa+213iT37y97sYlTj1H//hH5LA/u3ffuV03333nj788MO2qhvOsaxYWFxh2tGHd4Sx6tai31B4ZRe0sMUjnPzEBKx52Yy+o40S+0zTx60vvPBCB9WjH/nICVf3e9/7Xgcscepn/+iPuvdzge7f/8Zv3PDSA+4vbeD66nEPeXnLiQUBC74lQL2A4xGOl8jl7wHrZXnM+qaX8K37KffOQvTQQ7/ZAXvPPVe71wp5XAN0d97586fPfPrTp39+9tnu5QesJhtJcmtlOXl5AisOuHtyG+MRTr/6Baz98hl911sH7RLbuJVKeWPpDW+4o4tLBWHuCMz8nGxvcHrhyjOJRzheMi9/D1jTcpl8Fetgfx6HRQVCG7dSuRTz2Wef7Z4vYo1lhbGaKKyssV8AJndu5QXjEU7/BAWs/fIZfVePa6x7mnosIcW0LjON+R1lrgEvwB4hpWR1hHEPGWPAOkRKI/KkdjVlMWUpVR1gYoltUl57TVb4CO6hxm8XOyuLI58HrBVm37u9ubg1ZTGV14KZc6UrdH3xKlOL3eKdWkkHAtYKE+Ef1+Rgk8W0j3qU174JRReP5B4eJUYfq3oB61iJDcgvV866vcAGxDbl4tZU3lQsbOva03nK49jT+KaOJWCdKrmecilXVgD7YkPjVj3DxRrvPcnjsKHA3sc8ZHwB6xApjcyTcmVTAFNtyork8h7FPZT8WOAi/UQCAetPZFH0zD+CkQL6WFRWZEjcmgK7aKdXVNmRYvShYg9Yh0pqZD7AYlfYplQsOiZuFdhHcA+PFKNbHek7D1j7pDPjnsCyFnNu3CrrfAT38Egx+lA1C1iHSmpkPimbfUMpF4um3Ntc3iO5h0eJ0YeqVsA6VFIT8nllk8s7J249knuYWsQmTMNuigSsFafSv9RPU37jiWuC2FphrqesqCw2bvbek0KJI8ToQ+YyYB0ipYl5UlYwtfFE9X3PW4lVbfIW297b0/mRYvQh8xawDpHSxDyp91xz1iLl8ilu5WhTKq+9v6fzlHexp/GNGUvAOkZaE/L6l/rl8o6JW/3ubw74Cd1bfZGUd7L6TlfqYMBaSbCq1r/Uz/W+uNVDnLIsR3IPjxSjS2dyx4A1J5lC1/Vs1cadfXGrf9k/VZ6upSAu1OXVVXOUGP2c4APWcxKaeV9xp93RzLmxKYhV3setR3IPjxSj96lbwNonnQL35LJa91Zxq39Uk4JY5X3ceiT3MCWXAlOzuSoC1gZTlopRU49qBLEFm+7lXN6juIe5BavB1K2qiYC1wXSk3Nuca5cCOxe35upoMKTmTeQWrOYdWbDBgLWB8OXG4boqpa5xLwV2Lm5VHTYeVv17Ox4pRs/NXcCak0zB63JvbYyaukaTKQBzbmDuesGur6aqI8XoOaEHrDnJFL6eii9LxK1Hcg9TMiw8TauuLmBtND2pl/q5hgL6NCZuPZJ7eKQY3esE3wPWlFQqXMMF5tVD3F8lXbOxLPfGxK1Hcg9TIYJkeYRjwNpollMv9Qs0G8vSnZRS9sWnR3EP+2TQaBoXbSZgbSh+/1I/TadA0+bT0OetR3IPjxSje9UMWL1EKn5PvdRfIm5NWeKKw1i06iPF6F7QAauXSMXvUjTcOaUSceuR3EOFDixQR0sBa8MZ18sN9iUGKd/cuPVI7mEqdGg4jYs1FbA2FL0soI9FU8qXi1tTrjRDkNW2u80Nh9a0qSPF6FawAauVRoNzLKD/zWrqGSxdST1vFZTWlSavLPQR3EPF6P5ngw2mb9EmAtbG4k89Q1Xc6q1iKq8eAaUUNWWhGw+vSXPyUPzPBps0vmAjAWtj4csqpOJWbxVTeelu6hEQ14/kHuKh4HkcKQWsjWdbsajfUMIqAptNyutj3FzcmoPb1rmXc4UD3hvZy/hS4whYU1KpfC3lrpaIW4/kHipG94te5albtPqAdQHxp16EyFmKsXFrPMJZYEIbNRmwNhK0bSa1oaSNo7lxaw562/5ezlML2V7GlhpHwJqSSuVrOTDZOJobt8o99NBXHtIi1StGT+2ML9Khyo0GrJUFnKs+BSYbR6kdzjHPW2kvFRPn+rHl60eK0ZmngHUhbU3t6OZc2JS7J+ucsirkB9gjpCM9wglYF9JogWnfRBKA3oWVu8d9m1LWmfu5/LbsXs4lxyM8wglYF9JaLCKwecuYArDveWvKbT6Se6gY/QiPcALWhWAVUFgGm6bErSmrEo9wrFT3cR6wLjiPAAWcNsmts+4x9/viVu82k1/1pEC27e3hPCWbPYzLjyFg9RJp+D2lZIpbvXuci0NTbjNDkHuYArnhEJs0Jdl4mTVpvGEjAWtDYfumpGSpjSP/i5KxcSttDXmE88QTn+1iZ6D3n/vvf/vpqae+7Lu9uu8KKbzMch196aWXTo88cu1ivFev3nV65pmnL2Vn3IxfMiHPk09+/lKe1l8C1tYSN+0JQL85knqsQ7G+560pd3fIIxzB+vzz3zE9e/n0wQff1ynrFoAd+ggHUAHv8cc/cTFezoHyuee+3l1jvHxHNkqAyrUlgQ1YNRsLHVPWT/Hm3Lg1Z7ntUPtgRbFvv/22E9CuPUlmqUXL9p3xMiafuCaAsagA7RNySF33+Wp9D1hrSXZgvamX+kvFrUPcwz5YGQJKnFLugcNrlk0xuvdSfAe8VfX3+77LdWYR8wmLS91ym3NW2eahDB6NPBhvzX0bAauXSOPvqZf66QIT52Mwuc1YEZtyj3vIc+4RTh+sW7KsjDXlpVg5cc7CAyR8BBaW1MesvhzfAY2PT6pLgFKXBU/3aef69etdcbne9EdtK18u7AhYveQbf5cV9bu2OcjGxq3n3MMcrICqFV+xXGPRjG4utbtuKwEUIAIQ69oLkr5xKo4lr0/U5yGmfq6TVL+FkLboi6+PMnLHfTsBq5fIAt+ZNBTNJqwq133ceu3aw911IFR8lgOe+uQe+sVAbQlW2vIfFE6rvvKv+Zh7K0x9xuVkjB4s7nPNAqwyHCkHRLjBPgm6HGDkF6x2E099ScGaaod6AlYv/QW+p3Z/U4qnDSMLlSDkmgdeQ+lzDwWrVSSV29rxXIyOt4CcUjBwTZbQjhtr3Aeyd3ltWZ0HrJLEDo5yVa0V9YrHd6CzoOqce31xa98jnD3Biir0yYH7AJmyoMDqLS4g9oFKfWFZdwDgmCGkrCjlbdwqV1eA2iP3BLxcY9u+LDL5fNobrLkNO41bFtTv6AKldWW1AZSywqpLRxYAD7rKA3NYVklqB0dZUYCzycatij0tpDoHQsEst9jWo/r97jJ59gar5JR7hINbC1wWTGDimt+pHQIqMhSMHEmKcWXBdd+GGhGzdqLa5j9YUVw4m7zF5b4A1ZFySlzLxa3WSis/x73BypjYMef5dS4BJSBJhpwLJMW1upc6Kq+tHyCxrsrvFwOu23IBq5Xexs5lRW23ZRFlcRWbSiFQSuv29sVrfW6ybXMP5yxYyGhvKXaDVzKjubgyZXHpcup6H5ByD1Nu8kpEUKwb3iMpVvHCFQWsC0+AmtfbST7WSllcyqSunwOy7xGO+rGHozySVIy+5fEFrCuavVSsJSvhd3Jz1wEyF7f2PcJZkRiKdKUvJCjSwAKVBKwLCD3XZOqlflkJxa0qm7tOHUCfSjlXO5V369fOPcLZ4vgC1hXNWk7BUvEp3U5dz9VBfgG+N/cwNYUKCXxYkcq7lWsB64pmSgrmN4Fyu5tT4lYA53OElAortjzugHVls8cjBx9z5tzXKXFr347xykQxuzu5RW52xQtVELAuJPhcs2yMeMunneIScWvOeuf6s+XrWsw47iEFrCubRVk+4kubcOkA2aexcSvlaz7Cod/AwTjsh0WiddpbjB6wttagM+3pHV9vDXIu3ZS4lboAtmSi3+xE6+2q1JHFxj+CKtmHVF17eoQTsKZmeMFrOWtQMm7N1TV12FowWAA490DixmNluQ/EfgNtartDyvXtjg8pv6Y8AeuaZuPHfUm5tiXj1tyCMFYU1ENfARCryve+ZPN7z6Gv3Jx7itH38AgnYJ2jCZXKylL56kvGrUDGZ2qy4I2xlCqHlWUBapH28ggnYG2hLSPbyLmpU+LWnEXRRtZUYNSXMaBKDLJ21NEiqa8t2qrZRsBaU7oT6865vILY76ziUuKK+lgR64V7mkoCZgpsigPnwCaApi4WqTHlrkk+rVzvXD/mXg9Y50qwUvmU6yaIvbXEtQRWrKVNgAqwudQHc64MfaDcHBeaujWWOcDn+uivSz6EF1tOAetKZy8HWgpihgA8/jmsLKC3xBoyoPTBrHz2KIvorbjNM/RcYwSm2mkPj3AC1tpaMrH+HGg5wFKbUnJ1vSVWl+RWDwWvtDVs6Z5KnoxhqylgXenMCTQfUwowby2l+B68Pld3rHsoq1pS4XHfqbd2kjxzC1ft9kvUH7CWkGKlOlKKnFO6HHhyNXNdHPoIp7RVVX/oH659i5QLIVq0XaKNgLWEFCvVkYuzctYyBZ7cP2+J1eWhj3DkZpe0qvRB/Stdr8Znj/IM7LUtnQesK54tgeQ3YHLWUkDZ/DlLrGHrvne3dZ8j9bFA+A0sm2fqOW47HkRf+1Pr9uUUKmz1EU7A6md0Rd+lyF65ZI28tcwpY84Sa6jn7itOrgVU6rGT+lbyqFChRYxcst+qK2CVJGYeAQeIsIb6AI+1cmObkHL554OyhrRnUy5/zhKrLMoLsLl0rnyu3NDrqcdOQ8uOzZcLLcbWs0T+gHWm1AGTjQusQ+oDBMAwNSbLKXLOGk6JW2U5/U4yotHGkl8wZortUvGWm0w5r+RSh1b6JWCdODFYN8AAUGBF4S2QWDksK4pIHuCa4kYqDvXdzFk75bcWPWeJVWfOInO/hXIrNld/ah7PyaJm23PrDlgnSJAJBz4+3hVNVWfBHhsv5axeDqKpcWvKIjOWFm6jxoicWiQW1xqbZbX7HrCOlLAFdYxyYb0AFSs7Bli5oVgfm2ibury1zlnJnCVWnbJu3jugjZouMO1rIy3lhqt/JY+aB+t9lKy/Vl0B6wjJMrmsyljUMaDaJqQoY4ClTWDziX6k6klZyZwlVp0p+GXxakOkBWmIl6L+zjnmvI85dbYoG7COkLLiQSZ7TrLADlndc1aR64Dsk/pp6xaMfUAAv10Ucu369kp8x4J776FEvak6kMtYDydVT+trAetAiWv1t8o8sGgym4DFClqoUplzVlHXretK+Zzl8DD6tugTeZRyllv3Sx5buNu2vy1icdteifOAdaAUZa08GAOLJ7PJzcQ69rnVsoo+Ps1dl+XwseY5S6n+4PYKeN9mciAFLgJPy00fLXR9ci8wrKJVBKwDxQlQWMHSCSiwYHz6wMi5bTnrl4pbBWNOQS3kWpzOWf1S8mgNqxa6vrCg1NhK1ROwDpBk7YmlfuASkClAcm5b7noKNrnyfQoqyFmcWlq61rAy7a3HOEDVerMErL3iefnmOYs0oIqzWQBUcWzKLdajFQ+yrnv3XG4sR5uouy/uVn0sHH1Q2zpLnGtxKVHX0Dokby/ToeVb5wtYB0hcCjwg6+wsLAy4ttpwkSLpWaSHT9e9C0051WE75TeR7D3O5UVQlvNWqaWMNabcgqb7azsGrANmpLUiYSVxCwEGS4hS5eCj++QDQp/k0trrQ7yEm276mROflqm1jBmbZJqSXcuxD20rYB0gqSUUiW4BKbACI/Dec8/dyTiSe+TzSa6lrDP3h8Stcg99fTW/LyXjnOxqjnVq3QHrAMktpUh0DdBoX64x4Pqk/pWKW2V9vcvt2y35XWMoWeeQurb0CCdgHTCjSymS7RrQfuADD3VW1r/+VzpulXuIZW6VFD/6sdVuXzF6y820qWMKWAdITpbGW64BRYtmkQvL4uFT6biVeDflWvt2S33XgtMaVvrPOHGH154C1gEzpNXX77gOKFo8C4qVevSCsgGYT1PjVnkTWqCwtjV3h5eEVTE6Y1xzClgHzk7uTaGBxYtlQ7Hoi0+Cyyuc3Esff+agV73f/Oa/dC73u9/9rosXNlLtKv/c45Kw5mQ0d0ylywesAyWag2Rg8WLZchsiUnYPZS7+9OMhH2WxxFho3Gp9sBSYxAoAABT6SURBVNpYc77Xsq7qP8clUi6MWKIvuTYD1pxk3HWtvku7wn0uOQqX2hRKPW/9q7/6nx181649fAOc5KceC47arbURszSsLEYtY3SnXoO+BqyDxPRyJiZzDROac8nPxa3/9E//mLScgpMFybvRVjy0m4qXbZ6p50vDmvNYpo6nRrmAdYRUtSu8tHUFytSi4eNWAODaW95y34VLi/UVnHfc8brTr/3avxssAUCtFbcuDat22mt5DoOF3JMxYO0RTuoWkKCwfRYoVa7kNQ+l6v6zP/tvHZQezl/6pTd313lOa/utXVCVP3esaX2WhpWxM7cshGtNAevImZFSpWLDkVVNzq4+ACfgomBYTH2uXLm1e1fYurWpuFWeAvUNSTXjVo1paF+G9HdsHuYUGdoFbWwdNfMHrBOkq53R1ooFLFg3DycWASsJfPfdd2/n5vphpRRRrh/AD020VSNuXQOs2kTkuMYUsE6YFVZeXGEUt9UqrAWCld/CqZcWNIwUlNzLKSJ1jXH9/CMftTv3uAZYGQPyZYxrTAHrxFmR8tewMqkuKV48t+qrXz4fiwqK6N33sXGrXGesfMkkF3vpzTvmkwVsjSlgnTErsmItdhClzOfaykHJMEvErXKdz/VjilhZTMa45FPaOFdGi2Lpxehcu0PuB6xDpJTJAxgAgJK1mNyhzzlTUDIELS7WdRd8YyDB8tTwKNYAq+RRYzHKqNHgywHrYFGlMwIpEAGIhSCde97VofFiCkpazrnIa4lb1wArchorj3mzOrx0wDpcVtmciuNqb0yonXNWXFD63eqcizw1bvX1ZwU08MZaYM0tdgOHUS1bwFpItNqt9Rs7harvqhnqognKlGubcpG1COTgoz7GhRLL7a8BVo06p8hfi13NuZzSr4B1itQSZVBo3CdcYqCqlYbGi0CVeiSTshpaBCzcgOvhBCbq5TqKzJhLprXAypjoS21PaazsAtaxEuvJj4IzySlIeoqNujU2bvWV56zGG95wx0Wsxhj0qQmn7xtt2gXD32/5fY2PcALWwhogy1XLhZLLOjdu5adxgOHfhmoJpxc9XslarNkaH+EErF5jZn637nBpN5GupVzWVJdp21oqrH4KTtxqAPnUpz7Z5c/Frak2Sl9j4ajplYzpr+S8pkc4AeuYGRyYV+4wVrZGGvJoAct7++23nV7/+p+9cGmBl7JYT85feOGFi+5JOZd0Q4e6+BedrnwyRM6Vu3Cp+oD1kjjKfdHuMBCUTig1sNkEnFgB2sWd5L4+5Md9Vl+0mHhXfWnllOupftrxLXGukKaGhzRlPAHrFKkNKCNLBSilk+JW6vZwApzg/MIX/rwDNuXaArK3/FLO0v0dWp8WEca3hpTbjFuqbwFrRckDDVCUthRaCKgbKwqwWCXfjvKlXFtiQ9xhm6ScKbhtvprna9pkYpzIuMaCO0WGAesUqQ0sI1hqTDZwntsRpps51xaAUUTr4vlNqYHDLJpNnkLRSmdURn+Q4RpSwFp5FmRdLRSVm7xUvdq/dPF06v5yIbD6uBVru+SOrKz7WlxhxdFDFkYv49LfA9bSEnX1MclAwaQvkRTfplxb+rW2uBUZ4QovuWDYeZJ3tNT82b4ErFYalc6xVku5UlK2LcWtctFTC0ylKeqtNhdK9BaqcDNgrSBUX+XSrhTKRuzlk6CwLvoa4lb6sCbrql1yKycvyxbfA9YGUpZ18y5ng6a7JohbUX6f9KhkbXEr/dRCsobYVXG0l5OXZ+3vAWttCf+4flxh/6ikUdPdCxHEp6lNkrXGrcgGj4BFZmmLRl+QU41d/TE6ELCOkdaMvLIUSyieLHtqk2Stz1sRtSz/Gjab1vBIKWCdAeCYolK8pVyp2nErixAua2m3VYvcUiGE5njpfQf6EbBqNhoccaVQviXSlLj1nNuOW40SY/kYmz6lvQesGnWXXgjGzIO8k6Xmj74GrGNmbGZelH8pl67PMgCCt1y5HVA8A+5hqQUn51yTFSztPQA/slsaWMZ5bgGbqSK9xQPWXvGUvZmzbmVbSdfW93JGX9z61FNfvvg1j+DkSBkWALtpBVTcq7ERswZgcwtYWuLlrwas5WWarVGWJ5uh8g12Voc8byW+/r3f+88XlhMAKQuEWM0+N5f6sUA10tLAMnZksZQ7HrDW0KpMndpk4rhEyu1o8p8so4QPPPCeDkrO+dxyy6tO/G0maz3P9bvP3T5Xdsj9pYFFLtZzIJZtlQLWVpI2jyKWgtWCpM0hxYIo4atedVNnebEcKOEUt6/FRowFlj62TCx4r371zRdxe+plk1r9CVhrSTZRL0oGFEDTOtH2F7/437v2+XMv9IOPNoeA1m+eyO0bu2HUYiOG8WgX2lq6GnJlAWIBA9Sbb37lheyQH9dapYC1laR/3A4T3Gr7HyVjYUChBCfHn/u5O7rr3FdSPA0ESlpcxlqvKRZZbY49AipjYqGxfR9bT19+vBAsqJWhzlsuvAFr3yxVuMck14QVFxtYsG5SKM61OfTQQ7/ZKZ4fmuJpb0VTFteX9d9VV6uNGLn3jHNMfO373fc9B2yt9lJ9CVhTUql4rSascltpA8hYFLwySbGtVdVwKeet6FQrqd1j1V37yMJAm3z8mEu17YGlrZYpYG0p7R+/EF7Lsspt7YvhUDigTFk9YkCsk01aALzFtXlS57jerZXZwpQaX6qfY6/ZNlrGq/QzYB07WzPz17SsdC0FnO8yEKWAVtxqra4WAG9xfZ3+O7Aw1tY73/QdryK3IPl+Tvn+zW/+S/dYq2W8Sj8D1imzNaNMbVjl5mIBcgmL4C0oeXOx5pS4dSrkuT6PuU7bpYFFnshWO9DM49/93f8Z063ZeQPW2SIcV0FtWLEstNG36gtoa0E1Csp6qzs1bp0Cufox91gaWMmARY7zsWHB3PFQPmAtIcURddSGla6gUICSSzkLSv6UGz0lbgUWoGe8qUUh17eS18cCSz9ZyPA8vPtOXUuNQzIJWCWJRscWsMoKoGC5lLKg5J0Tt8pVlAtKG8THS1ghjXsIsPSPBY7+8uG81gaV+jXlGLBOkdrEMigzylBbeWUJ+xQuZUEZVs7q5lxa2sKCemVfylVMTQ3A0j8WjmefffYGC8m8IA+sKudrTQFrw5kRCN7FqtGF3I6v2kpZUN1jQcnFrfzPc3IVZYk44jpyfWlXUWOwR+T92GMfPb3iFf+2Wyx/53c+am9v5jxgbThVAqTPPS3VHeAB2FzSwpGyvt7qkvcDH3jowk0ETiwVQGNZW4wnN45z1+XN0Oe77npTN4b3vvfd54qt8v5oWB955Fr3/35OGc2Qss8883QnUI57Syh3H0Alx6vnnH1uHQrsLSh9eOKJz3Zz8P73P9j1l3z6/Oqv/soqXUXGyWKI++0TspDFVzxfOxTxfSjxvSmsQzq8Z1ixRlitFgnlBLCU8qp9a0Gl7HZziN+zYqFRdqwn+ft2mVVvyyOLjY2Xz/XPxq9r9ghSMgxYU1KpcE3wENe1SrlNIdpHUR999CMd0Hfe+fMXlpMysj7e6rZ041MyknW09wB1bLysEIDxbClNhlWuEqv3/fe//WTdVu7xm8nHH//EhRJwP+UG+3pUxtbH3wG6evWui7qefPLzXf3UZ5Oti36Rby0JSOlTn1tauq+CTkrOkX5gIemLPu985ztu2ByyVlf9kpK3dCFpi3HIeqovc4+Mj5BEsplbX4vyk2Blkh988H2nl156qeujAHvuua933wUNeUgCz8Oq77rPUT+M1jVApT2Bd/369W5x4JqFlbYoq3Kqi76tIWGxULiWiYUBOWF5pOx85xyrCQh8T7nKsqJemXP5+8aFFZ+ySNlFhXMWmlKuqxae1Nj7xrLkvcmwPv/8dy71G8snOAUroNkkOLlGeSZeECqfygo66sVy28Q9ygpWD7TyUjf5fF91v9VR0CzhdmE9kAGLBcruoQEC7vkkZfa7xbn8vjzt0B51037fxhptIRsPIosJH3/dtzX1O2OhX7Xqn9qvXLlJsAKQT1gwLBtJwHlILKwCSdZY9fGdyQVIrCjnHmjy0pZglWUnv02pBYGVFMVACb3i2rIlz7FijMNbqZJt5OpijH3KKAuaykOfx8StgEV+b8Wx7NQFlErk5boWE39f+WoetSCxqGwhTYLVWzoGKkBxjXU+BFafR4ABq87PwQq0THbuQ3+UBI7Ny+rPdRSXCUwprsqPPQIobXmlH1tPrfxSWODxCcvjXXebn7Gh6IJRMqUc17U4SQbW5eQ+oCIX7Tb79lt8Z3wpz6JF22PbKAZrTctqYdMAU5ZVMbTy9B1ROpQEBZI7JGXjiCJxfa4V1uIgxe3r01L3GK8FSf2Q1bV9F6xXrtx6sTjaGFgLHUfky/iR5RvfeOcqoWDcjN+OUeNf23ESrIDiwcA1lls6xLLKxfUgyj3ui1nlKqs9xawqIyHznYnw13XfH5kwlBElxVoo3qIOfcZYYSn2Wq2qxs+ilLIu6v/v/u5/usFlve++ezs5pUIJIJW8ABVZrnXRov/0dQuu8CRYGZzdDdZOrGLGIbCiKLLGgokjCwH165pAlCtMG7jh5BGs1MU1FgyVw4Xmuza9pJhTjijtFCssi732VVvWRVYRBWbBsouVoEMOypeTJeOlTutarxkKPAPmau1pEqyAISAFro09dc9eQxDABYw2yZJSD3Dpu6AjL8Byjzx8yEM93iqrXeVjMaiVhlhh+oHCo/gAf07Ja/X1XL1f+cpXOrnyF/lRXMmPvgMdfZ+SkBFw25iW87UlWf219cv3ZzSsvoIlvsuFlrVdog+5NmWFieluuulnTleuXP57s6Vi4Vz7Q68DEq4fFkVwcgQmuzk0tD7lw4ICuLfKADHEKquelkf6xdinLkqt+rp6WLGg1uVGMHzH0vq4uZXQzrWjyedIGmKFUW4Ueo4VFii5/uGWApK1nnZzKFeu77rfSBL4ssr0ae1pzS66ld3qYcWVBk4pAUfcacXHdjBrOQcAPueSrDAAKb614xxrhbVIAL11uWmHulQ3IGE9p4JEOW+VbUzL4rS1hGyYhzWn1cO6ZuGl+gYYTDzKPCXNscJYZQukgKVOruPi6trYvmGVWQS8VUbB7UbS2HrXkp8FbO2bTAFrYW1BoQFjKhS57gyxwq997ZULWOkD1k7WE2XkMzQBOAuO3RyiThSa61u0nn1jZ1xj5NNXV617AWthyQIIwLZI3grrz5YAlT70R7Eq1/ogY0HAUqK0tjzjoY7SC1ALGQ1tQ17J0PxL5AtYC0odhUbJl3ALAUmA2SNuK5ZQmyja9GLYlOE71hOoVQ5YUV5Z5YIiWm1VAetqp6ZOx7BKKPwSFkixMu0DKH3xsAEk7h6K6a0nwALuEn2vMxvjahWsax5/WNZxc9qbe8m4B+spdzXXScXTFmggj/STP8G6ZnkErAU1FQiwaGtNKOIeN4dKyFueScBaQporr4ONG2AFhkjbk0DAur05m9zjLUz25MEdoOAW5i/c4EKKqJ1gv6lTqPqoprIEAtbKAl5T9dpNXFOfoi/DJUD4QhjT9xx6eG11coZlLSTXgLWQIBeqZgvzF7AWUo4tTHahoe6yGh5r8Rx6zSlgLTQ7AWshQS5UDc/I+aw5BayFZidgLSTIhapZ+zNyxBKwFlKOgLWQIBeoJvXe9ALdONtkwHpWRMMyBKzD5LTGXFvYCUZuAWsh7QlYCwlygWr4UcOQv+yxQNcuNRmwXhLH9C/6kyrxUsR0GS5RUq+JrvmdbsklYJUkZh638AbMzCHusrhc4C0ssgFrIRXUCh0v8hcSaKNqcH+34AIjjoC1oFKw/c/D9UjbkIC8oa0ssAFrQb1a8sfnBYdxmKqYL95aWvNfh7CTEbBaacw8X/LPuszs+uGKy6qyi7+VFLAWnCn9TM7+UbKC1UdVBSWwNavK0APWggpAVRG3FhZoheq0qG7JqiKGgLWwMujPehauNqorJAHiU+0AbyVW1dADVkmi0FEvR4QrXEighavRvsISf9t57lAC1rkSTJTX3+dN3IpLC0pAm0p4P1tMAWuFWdPqvYW3YioMf5VVyv3d0qMaL8iA1UukwHe9zRQvSBQQZqEqsKZs/m3R/ZUIAlZJovBRf/0+rGthwU6oTr+I2sLL+n3DC1j7pDPjnqzr2v9UyIwhbqKoNvz2MA8Ba0WV04q+ZderoniqV60NJX6vurXHNCnhBKwpqRS6todNjUKiaF4N4QebSXzwcvaQAtbKs6jVfauPCyqLp0r1FtQ97RkErFXU5XKlepSzlZ9iXe79tr7tFVRmIWBtpIv6z4v3tNI3Et3gZtgbkOu7RzkHrINVYV5G4qY9K9I86cwvrV1fZLxHUJFQwDpfTwbXIBeNF8n3sDs5eOCVM+qZ9l52fXPiClhzkql0HVeNN2n2rliVxHepWhY8np8iTzbw9r4ABqyXpr/NF7lsWNi9umy1JckuOy4voG7td6lTZROwTpXczHJ73wyZKZ7e4tpdB1agPUoKWBecacWwWIf4/ev5iUBe2lXH/d272+slErB6iTT+zi6xFJCNkqMp4BBxIxNrTY/6vDpgHaItlfOgjNrRJI49kmt3TrR4HIpN2UTay6uD58aduh+wpqSy0DXFsbjFWJIjW1kWLO30soAhm6OngHVlGgCg+qE0FuVosayFlPEfZad3iBoGrEOktEAelBaLgpXluHdoU5Ae2bNIqVzAmpLKiq4B6V6hBUY7PlnSgDStgAFrWi6ru5pS6q1utvAIhg01bRyxGLHDG5D2q13A2i+f1d0FWm284CJzzrW1KzqAsmkmL4G+E5vHxtFwFQtYh8tqVTmxql75eV6LhQKMpROLByBiQS2g6uPaF5el5ZdqP2BNSWVj11JWCxcTq8tuKps3tV1m+oCFZwHRSx5YT1l/FpHafdjYtI3ubsA6WmTrLgAQQOMtmgUH9xOIAQiQ9emzdsCofJSjPPV4MAUn0IaLW1ZXAtay8lxdbQAIZMAFwFhbbewI4KlH3FvqA0wWCNqJVE8CAWs92a6+ZqywrKWABurURzCSL9zZZaY2YF1G7tFqSGC0BALW0SKLAiGBZSQQsC4j92g1JDBaAgHraJFFgZDAMhIIWJeRe7QaEhgtgYB1tMiiQEhgGQkErMvIPVoNCYyWQMA6WmRRICSwjAQC1mXkHq2GBEZL4P8DLtxbFPLvNL8AAAAASUVORK5CYII="></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>
<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> <strong>✓</strong></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> <strong>✓</strong></p>
<p><em>Answer must be to 3 or more sf <strong>or</strong> 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>
<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>
<br><hr><br><div class="specification">
<p>A loudspeaker emits sound towards the open end of a pipe. The other end is closed. A standing wave is formed in the pipe. The diagram represents the displacement of molecules of air in the pipe at an instant of time.</p>
<p><img 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"></p>
</div>
<div class="specification">
<p>X and Y represent the equilibrium positions of two air molecules in the pipe. The arrow represents the velocity of the molecule at Y.</p>
</div>
<div class="specification">
<p>The loudspeaker in (a) now emits sound towards an air–water boundary. A, B and C are parallel wavefronts emitted by the loudspeaker. The parts of wavefronts A and B in water are not shown. Wavefront C has not yet entered the water.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how the standing wave is formed.</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>Draw an arrow on the diagram to represent the direction of motion of the molecule at X.</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>Label a position N that is a node of the standing wave.</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>The speed of sound is 340 m s<sup>–1</sup> and the length of the pipe is 0.30 m. Calculate, in Hz, the frequency of the sound.</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 speed of sound in air is 340 m s<sup>–1</sup> and in water it is 1500 m s<sup>–1</sup>.</p>
<p>The wavefronts make an angle <em>θ</em> with the surface of the water. Determine the maximum angle, <em>θ</em><sub>max</sub>, at which the sound can enter water. Give your answer to the correct number of significant figures.</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>Draw lines on the diagram to complete wavefronts A and B in water for <em>θ</em> < <em>θ</em><sub>max</sub>.</p>
<div class="marks">[2]</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 incident wave <strong>«</strong>from the speaker<strong>» </strong>and the reflected wave <strong>«</strong>from the closed end<strong>»</strong></p>
<p>superpose/combine/interfere</p>
<p> </p>
<p><em>Allow superimpose/add up</em></p>
<p><em>Do not allow meet/interact</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Horizontal arrow from X to the right</p>
<p> </p>
<p><em>MP2 is dependent on MP1</em></p>
<p><em>Ignore length of arrow</em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>P at a node</p>
<p> </p>
<p><img src="images/Schermafbeelding_2018-08-12_om_14.17.43.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/03.a.iii/M"></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wavelength is <em>λ</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4 \times 0.30}}{3}">
<mfrac>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mn>0.30</mn>
</mrow>
<mn>3</mn>
</mfrac>
</math></span> =<strong>»</strong> 0.40 <strong>«</strong>m<strong>»</strong></p>
<p><em>f</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{340}}{{0.40}}">
<mfrac>
<mrow>
<mn>340</mn>
</mrow>
<mrow>
<mn>0.40</mn>
</mrow>
</mfrac>
</math></span><strong>»</strong> 850 <strong>«</strong>Hz<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Allow ECF from MP1</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\sin {\theta _c}}}{{340}} = \frac{1}{{1500}}">
<mfrac>
<mrow>
<mi>sin</mi>
<mo></mo>
<mrow>
<msub>
<mi>θ</mi>
<mi>c</mi>
</msub>
</mrow>
</mrow>
<mrow>
<mn>340</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>1500</mn>
</mrow>
</mfrac>
</math></span></p>
<p><em>θ<sub>c</sub></em> = 13<strong>«</strong>°<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald answer of 13.1</em></p>
<p> </p>
<p><em>Answer must be to 2/3 significant figures to award MP2</em></p>
<p><em>Allow 0.23 radians</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>correct orientation</p>
<p>greater separation</p>
<p> </p>
<p><em>Do not penalize the lengths of A and B in the water</em></p>
<p><em>Do not penalize a wavefront for C if it is consistent with A and B</em></p>
<p><em>MP1 must be awarded for MP2 to be awarded</em></p>
<p><em><img src="images/Schermafbeelding_2018-08-12_om_14.30.57.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/03.b.ii/M"></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<p> </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">a.iv.</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>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,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"></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> </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>
<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>
<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 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>
<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 </em>cm<em> 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 <strong>(b)</strong> or data from graph.</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;">
<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>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by the principle of superposition of waves.</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>Red laser light is incident on a double slit with a slit separation of 0.35 mm.<br>A double-slit interference pattern is observed on a screen 2.4 m from the slits.<br>The distance between successive maxima on the screen is 4.7 mm.</p>
<p><img 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S7y01imTN59oz6eFIgAAggkiwCH+GQZCVPa8bm6Gn8ud849Kl+RJ4fxbrA7lFfxuDbnHFZj69k4rTqj5mertH+FSxtKspVupErP1pLye1TU/K96qyWS76xaG5uk2TM0lXdaHEs2I4AAAtYU4LBvzXEdZq/8Otl5XI7YAMA+RTNmf6H6xj+qZ8iSpqiwulXd1YXKGHJ/eGPgjE4cPaecLGdfEJIorc7I45ojW/EzamjcrlJn+HJKgUt1bafUE305xlmq7S2RSzgjzZewMexEAAEEELhCAQKMMGBVVZVOnjx5hZwplj0UAHTHbbTv6Amdjn+VZEC+gO+Iap/ervaySj2SP6Vvn79bne0TNfX/vqn7IwGDs1Q1DW3yxSu36Vnt8HxFG7y9Cvae1KFvH9V9c6Yr++ku/d0zbQoGP9EHm6/R1iVPa8+pCxfbMNJ8F0tgDQEEEEBgFAUIMMKYGzZs0M0336zXX39dn3322SgSJ3FRoQDAd2UNDHTIXexUmnOeHj3wTa1b+e2+Sy2SAqdP6KjPqWl5D+jV7vD8C+/jmvnbH2vZthb5h6rZcZ+e2LBEmen20OWaOXfkyqG7tXlDufIcEyRlKHPeXOX4/lO/7Yw6vzLSfEO1gW0IIIAAAlcsQIARQ1haWqr58+erqakpZg8vhxSwZ6ussVvB4Bfq3jVTv7i9SA82fBi6A8WeWabGYKOqCqep/42Wnqk7ir+uznU1esv7+ZBFshEBBBBAIPUF+o/7qd+V0evB+++/r+LiYi1ZskRer3f0Ck62ktKdyspxjFKrJshR+LCeWH+t3C8dUle8SyCyK336LOXouDpPDnEOI2eWphtnLy53GWm+y62H9AgggAACwxK4JlEq47kF43np7u7W+fPnrUsQmszpjNu/QZM/46aM2dHepZP+gDIzRhAoxBTFSwQQQACB1BRI+A3Q/8yCyLMLLPw7dvjq6up0+PBhzZ49O3ZX0rw2xufKlnRNz5qpQZM5L3X3R3jehdPlGfIuE8eKOzQn44K87qWyOSvlGfA8jfCzMRxFKp4z+cqaT24EEEAAgaQVSBhgJG2rx7Bh69at08cff6x7771XEydOHMOakqHo6zSr+Acqa9+up1871jfpMuBTS+1PtLF9qVzfz7w4dyK6ufZMLa1ap6z6f9XbHZGJlhfk8zyvTfXf0Ob75yhD1ylz6VptzWpS3dt/ujih0/8nvV33Gy18bqXyOcMRrco6AgggYCkBAozwcC5evFidnZ3asmWLJk8eP39Z26fdIdeuNZpaX6RJxqO805xacjRHz+1bfTEACJ+xuHg2wq703If1xr47dfYnc8OPAJ+hZY0364nm7SrLDj8dIz1Pj77xkhaf3arMyGPCF9VLpS+ptuQrQwcvlvp40RkEEEBg/ArYgld+nn386tFzBBBAIAUEjPl0HOpTYKAs1kTOYFhsQOkOAggggAACySBAgJEMo3AV22A8SIwFAQQQQACBsRYgwBhr4SQq/8iRIzIeJGb8ZkEAAQQQQGAsBQgwxlI3ico2Hn++devWUIvWrFkzfh6HnkRjQFMQQACB8SRAgDFORnv//v3au3dvqLfGk0qN1ywIIIAAAgiMlQB3kYyVbBKVe/bsWd10002DWmQ872M83ZI7CIANCIwTAe4iGScDnWTdJMBIsgEZi+YY/7jt4MGDoaKNyyTGw8SM5Vvf+pZKSkrGokrKRACBJBIgwEiiwRhHTSHASOHBHslBYyR5UpiIpiOAgBR6GB7PweCtcLUFmINxtcWpDwEEEEAAgXEgQIAxDgaZLiKAAAIIIHC1BQgwwuLGPAXjVk4WBBBAAAEEELhyAQKMsGFxcbF++MMf6ujRo1euSgkIIIAAAgiMcwEmeYbfAMbkx8hi3GXxyCOPaPr06ZFNSfl7JBM2R5InKTtPoxBAYNgCfO6HTUXCURQgwAhjRgcYEd8dO3aovLxcEydOjGxKqt8jOWiMJE9SdZrGIIDAZQvwub9sMjKMgkDCAGOoL91RqDPli4jc7hXrE9ludDDevtjtRtpIvth9ke3xyotNH4GN5Ivdb2w3tkV+R9JHtyFeXUNtj843VF3GfmOJty92u5E2Udv7Srt65aVy2820TbZxxKLvkxP5bEU+R/xGYKwFEgYYY115MpUfexB64IEHQg+kyszMTKZmDmiL0ebLPWiMJM+ASnmBAAIpJ8DnPuWGzBINvsYSvRjFTtx2223avn275s6dO4qlUhQCCCCAAALjS4AAI2q833nnHS1cuDBp51xENZVVBBBAAAEEklqAACM8PPzjr6R+n9I4BBBAAIEUE2AORooNWHRzR3JddSR5outkHQEEUk+Az33qjZkVWsyDtqwwivQBAQQQQACBJBPgEkmSDchYNOfkyZM6f/58f9Ferze0fv311yf9w8T6G80KAggggEBKCXAGI6WGa2Bjh3uLaktLi7KyskI/RgmRdWM7CwIIIIAAAmMhwByMsVBNwjKXLFmivXv39rds8eLF2rNnT/9rVhBAwLoCzMGw7tgmc88IMJJ5dEaxbcY/cbv11lv7S/z973+v2bNn979mBQEErCtAgGHdsU3mnnGJJJlHZxTbZgQTxj9xMxbjN8HFKOJSFAIIIIDAIAHOYAwise6Gs2fP6qabbtKf//xnJndad5jpGQKDBDiDMYiEDVdBgADjKiAnUxXGHSTJ/P9VksmKtiBgFQECDKuMZGr1gwAjtcaL1iKAAAKXLUCAcdlkZBgFAeZghBGNZ0WwIIAAAggggMDoCBBghB1vvvlmVVVVyZinwIIAAggggAACVybAJZKwn3EK0ViMf9f+2GOP8V9Vr+x9RW4EEEgiAS6RJNFgjKOmEGCEBzsSYETG3ngQlXE759y5cyOb+I0AAgikpAABRkoOW8o3OmGAEfulm/K9HUEH6urqdO+9944g59hn4aAx9sbUgIAVBDhWWGEUU68PCf/Z2XD/10XqdXtwi2ODqcilkpKSksGJ2YIAAggggAACCQUSBhgJc1p4544dO7Rs2TJNnjzZwr2kawgggAACCIydAAFGlK0x5+KBBx7gQVRRJqwigAACCCAwEgECjLDae++9x4TOkbyDyIMAAggggMAQAgkneQ6Rnk1JJMDErSQaDJqCQBILcKxI4sGxcNN40JaFB5euIYAAAgggYJYAAYZZ8tSLAAIIIICAhQUIMCw8uHQNAQQQQAABswQIMMySp14EEEAAAQQsLECAYeHBpWsIIIAAAgiYJUCAYZY89SKAAAIIIGBhAQIMCw8uXUMAAQQQQMAsAQIMs+SpFwEEEEAAAQsLEGBYeHDpGgIIIIAAAmYJEGCYJU+9CCCAAAIIWFiAAMPCg0vXEEAAAQQQMEuAAMMseepFAAEEEEDAwgIEGBYeXLqGAAIIIICAWQIEGGbJUy8CCCCAAAIWFiDAsPDg0jUEEEAAAQTMEiDAMEueehFAAAEEELCwAAGGhQeXriGAAAIIIGCWAAGGWfLUiwACCCCAgIUFCDAsPLh0DQEEEEAAAbMECDDMkqdeBBBAAAEELCxAgGHhwaVrCCCAAAIImCVAgGGWPPUigAACCCBgYQECDAsPLl1DAAEEEEDALAECDLPkqRcBBBBAAAELCxBgWHhw6RoCCCCAAAJmCRBgmCVPvQgggAACCFhYgADDwoNL1xBAAAEEEDBLgADDLHnqRQABBBBAwMICBBgWHly6hgACCCCAgFkCBBhmyVMvAggggAACFhYgwLDw4NI1BBBAAAEEzBIgwDBLnnoRQAABBBCwsAABhoUHl64hgAACCCBglgABhlny1IsAAggggICFBQgwLDy4dA0BBBBAAAGzBAgwzJKnXgQQQAABBCwsQIBh4cGlawgggAACCJglQIBhljz1IoAAAgggYGEBAowUHtxgMJjCrafpAwT8XnncLhXYbLKFfnJUWtMorz8wIFniFxd0qmGVnM5KeXouJ1/iUtmLAAIIjESAAGMkauRBYDQFAh+qoeIuLT/8t6ru/kJG4Njb/aJmt69VfsUenRpmrBA49a6eXPW8fKPZNspCAAEERihAgDFCOLIhMFoCga5Desl9rVaU3qM8x4RQsXbHXFVsWKMcd5WebT5z6ar8x/Ra5U91PCv30mlJgQACCFwFAQKMq4BMFQgkErBnlqkx2KrqwilDJOvW0RNnlPgkxjm1vfiYNl7zj6pcNnOIMsKbejxyOZ0qrnlbjTWlcoYuxThV4KpXm++MvAe2q9TZd4nGWfq8WnwX4pfFHgQQQOASAgQYlwBiNwLmCszTPfNmKP4HNSB/26tau22Gnntqsb6SdqnW+tS07hV5Zj4ub+hSTJ2+3eLSHGeBnj6Wp2dOBhX8tF2b9aKWbHx32JdnLlUr+xFAYPwJxD9ujT8LeoxA8ggEPtSe6u1qL/uBimddF79d/la9uPY/dOe+zSqZ1nd5JX7ivj2O9S5tKMlWuiS741bdkeeUitZoQ8VcOYwjQvoszZt/i3z7W9V5WZNML1Uz+xFAYDwJXDOeOktfEUgNgR51vPaUVh3/vna98T1Ni/dnQGhy6D/rl3f+TPtyb5T0eWp0j1YigMC4ECDAGBfDTCdTR6BHHe41KtwobfasUWF40ufg9l/QqT1bter4P2hf7ZzQ2YjBaYba4lBOlvMy0g9VBtsQQACBSwsQYFzaiBQIXB2BgE8ttY9pydZrtNmzXWXZGfHrDRxX40sN8jX7NGfSo4PSLbjhNRXt9Gh/WXaC+RuDsrEBAQQQGDWBeCdfR60CCkIAgUsLBHwHVLkgV7f/Ypqea75EcGEUZ89WWWN36JkZxnMz+n4+U+fOuyXH4zr0yUk1ElxcGp4UCCAwZgIEGGNGa17BXq9XZ8+eNa8B1Hx5Av4WbVtWqp90luidXf9DJZkJzlxcXsmkHkcCxmfe+OyzIJAsAgQYyTISo9AO4wCzfv16ZWVl6cyZYTycaRTqpIgrFfhc3rdqtK7ZJ/me113Trw0/KjzyyHCbnC6PeiQFvG4V2y6+vtKayW8tAeMzb3z2jWMAf2BYa2xTtTe2IP/QIlXHrr/dn332mXbv3q3S0tL+bZ2dncrMzOx/zQoCCFhbwDh7YQQYkaWurk533323Jk6cGApaOdRHZPh9tQQ4g3G1pMeoniNHjmj+/PkDgosxqopiEUAghQSMPziMY4NxjGBBwAwBzmCYoT5KdRoHjnnz5o1SaRSDAAJWFuAMhpVHNzn7xhmM5ByXYbVq7ty5+vjjj7Vu3bpB6Y1LJH13FkTuMOA3HrwHrPweMD7zsYtxbDCOESwImCFAgGGG+ijWOXnyZG3ZskXGwWXx4sWjWDJFIYBAqgoYxwLjmGAcG4xjBAsCZggQYJihPgZ1GhM69+zZo8bGRt12221jUANFIoBAsgsYn33jGGAcC5jkneyjZf32MQfDgmNs3FViLMbscRYEEBgfAok+9zabLXTJdHxI0MtkESDASJaRoB0IIIDAGAkQYIwRLMUmFOASSUIediKAAAIIIIDASAQIMEaiRh4EEEAAAQQQSChAgJGQh50IIIAAAgggMBIBAoyRqJEHAQQQQAABBBIKEGAk5GEnAggggAACCIxEgABjJGrkQQABBFJIgMeEp9BgWaipBBgWGky6ggACCCCAQLIIEGAky0jQDgQQQAABBCwkQIBhocGkKwgggAACCCSLAAFGsowE7UAAAQQQQMBCAgQYFhpMuoIAAggggECyCBBgJMtI0A4EEEAAAQQsJECAYaHBpCsIIIDA+BYIyN/2rEprWuQfbQi/Vwdqnlad9/MEJffIe+BZVdZ1KJAgVTLtCnjdKrYtlTthv2Ja7G9RTfG/qOHUhZgdA18SYAz04BUCCCCAQKoK9DRr0z1eLf7hbKWPah8C6ml5TaXr/qDeROX2tGpn6TNqS5goUQEpsi99jh5yXa/1T76rUwkiKQKMFBlPmokAAgggkEjgnNpe3qGjlau0ZNqERAnZd8UCdmXk36vKkz/Vs81n4pZGgBGXhh0IIIAAAqkiEDjl0c+2/QEkRwMAAAfBSURBVDfdM2+G+r7YAurxVMppW6pXPM2qcxXLZrPJZstRaU2jvP7oP7175PW45SpwhtMUy+X2hNMY5WxU9oKfyKfdKs+aKKfLo55YmB6PXNkLtMXnU1P5LUpzVsrTY9QRkN/rkbu/fqcKXG55vINKGFii3yuP26WCUJuNdke3KZw04FNb3cU0ztLtOhBdrrG/oUalTiO/8TO8ugO+liivOHnsM1W88lbVV/9C3mjKqF4QYERhsIoAAgggkIoCn6ur8edy53xX82ZdF9OB3XpoU5Mmle+W8cj03u5tmvbLh7XyxdbwPI0edbjXKH/5YU2tblNvKM2Tmnq4QlmLatXmlzIKN6vj0ONy6G7t7PxM3dWFyoipRRmFqu44pPUOh4p2fqDe7ioVZkj+jno9nF+hw1OfVHdvUMHeNlVPPazlWctU03YutpTw63Nqe/FRLT/8Vb3waW+43WuVVv+QVr/l7ZvfEfhQDQ8Wac5raVrd+YmCwU/kmX9MpfmV4bkR59S27UEt2jtRD7d9ESoj2Pu+nkh7UwtW7lTbgADrYjMCpxr0YG65PJH2Bjv0QtYRLe8vN5J2ghxf+6Zymv5d73UNPS+FACNixW8EEEAAgRQV8Otk53E5Zs/Q1EHfarla/8SjKsnsCwnsjlt1R96Naj5wTN3GX949rXp1Y4sWPveUKvIcobMfdsdcrdlRq/WdW1UZ+UIfkcxZtby6QwcW/k9VVcyVw2ib3aG8NT/VrvWnta6yYei//gOn9YcDHcqZf7sy0/s6ZHd8R1W/6lJjWXaojYGuQ3rJfW1U3zKU/f1/0Ao16KXG4wr0/E5vbTutFaX3KM8RvmRkn6b8++5RUfNv9IfuoSZonlHzs1Vy56zRhkh7laHssmrtWvGfWvXsewPO3NinztBsx3t6870TQ05qHTQUIzIkEwIIIIAAAmYJBM7oxNFzyslyDmNyZ7qmZ82U2rt00v9X9bQeVL3vFs392t+EL62EO5HuVFaO1N7ZPfI7Unr+qMb6buXM/WpfcNHvE92GIa4v2KfqG9/JVtPGV7WnxaMGjzemDZ+r671/V5NmKmt61HRW4yxKd3dfEBJab1V13ll5GhrUYPy4XVqQVa6m/nbErITa2zZEoNbXXl/9QbWGLvsMz4gAI8aXlwgggAACKSbg71Zn+/kRNPqCTp/oki9BTt/REzo9RAyQIEv/rsDpEzqasPAunTg91JmEG5W79g117rpd596p1l0LsjRpmPMn+iuXcemnXM5JWVqw47cKXYy5caFeaH1ZRTquzpPxb+T1bVmgG/rnfhhzNyYqq3z3xaKHuUaAMUwokiGAAAIIJKlA6GzD9SNo3ARNnTFLjgQ5h77skiBD1K6+SwhRG2JXHbM0Y2q8O14ylFlYorLqRgWDX6i79TndeXq7FuQ/E548GlvYwNcB79uqKG/RwndOqPdX1SorKVFJyd/J+cl/qX1g0phX4TkkwWDfvI3o36F5JcMPG4afMqYJvEQAAQQQQCApBOxTNGP2jSO4nGFXxpw7tMLxgY4c+8vAeQShsyIa5mWXOAoZX1fxCqfaj/xJvgFnQfrmjChnlqaH51jEKSG8eYIcuUv0UOkiOXzGWQ+7Zs377uAzEYEOuYudshW/rNYPu9Su2Es/f9Wn5xLcvRK3vefUVvM92YrdA+eMXMKIACPxqLIXAQQQQCDpBcJzBEZyOSNjju7fnKf9q55UbYuvL8jwH5N7dYW2ZK1T1dJM2WVX+vRZygk5BHTef35gMBLxiT6Tct4vf2Cy8u5fre/s/7Eqa4+Egwzj0oVLy7dM1daqEmUO9S0cChRmqcDVcPF2Wr9XBxvbpLIfqHjWdbLPKpbr8Zu0ZdPz8viMyywX5Gt+U/VN39TWqqXKu90InN5T/Wu/Dtd7Qb6WV1S56vkEl4SmKP+RSi2Maa+3YYvWrtOg9vZdApoXdWtwBKLv91BdG5iCVwgggAACCCS1wHXK/P4/an17/Fsm4zffuEtiu5p3zddpV67SjLkHk36kzvm16txXodzIXRyhL/RPVJ71JX3prp+ra8AZiXDp9pla6FqhC8ZzML5Upre6Lig9e4Web67V/NNPyZlmzGfI1j91ztWuzje0NvfGoZtlz9Z9r72p1V/eq/xJaX3PsJh0t/Z+eaX2bf6ephnf3PZpKtz8mlrvO69Nzmtls10r56bzuq/1FT1qlJsxT/+yr1p5vykN15urx/5jikr37Nb6BNeE7NOWqHZAe29Q/t7JWh0pt7/F4YmmRUPdGtyXyBY0bgxmQQABBBBAIKUFjNP492utHte+tXnDuJskpTtrfuONsywLy9Xp2qvqwilDtoczGEOysBEBBBBAILUEblTuQ6uV9+LrarrEP+FKrX4lY2sD6ml+XVXTf6RH8ocOLoxWE2Ak49jRJgQQQACByxcwLgu87NDe/3U05rkRl18UORII+Fv1cvV5bXkqfLkmTlIukcSBYTMCCCCAAAIIjFyAMxgjtyMnAggggAACCMQRIMCIA8NmBBBAAAEEEBi5AAHGyO3IiQACCCCAAAJxBAgw4sCwGQEEEEAAAQRGLkCAMXI7ciKAAAIIIIBAHAECjDgwbEYAAQQQQACBkQsQYIzcjpwIIIAAAgggEEeAACMODJsRQAABBBBAYOQC/x/vnCkzfiMqegAAAABJRU5ErkJggg=="></p>
<p>Calculate the wavelength of the light. Give your answer to an appropriate number of significant figures.</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>Explain the change to the appearance of the interference pattern when the red-light laser is replaced by one that emits green light.</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>One of the slits is now covered.</p>
<p>Describe the appearance of the pattern on the screen.</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>when 2 waves meet the resultant displacement</p>
<p>is the «vector» sum of their individual displacements</p>
<p> </p>
<p><em>Displacement should be mentioned at least once in MP 1 or 2.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>λ = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4.7 \times {{10}^{ - 3}} \times 0.35 \times {{10}^{ - 3}}}}{{2.4}}">
<mfrac>
<mrow>
<mn>4.7</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>0.35</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>2.4</mn>
</mrow>
</mfrac>
</math></span></p>
<p>= 6.9 x 10<sup>–7</sup> «m»</p>
<p>answer to 2 SF</p>
<p> </p>
<p><em>Allow missed powers of 10 for MP1.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>green wavelength smaller than red</p>
<p>fringe separation / distance between maxima decreases</p>
<p> </p>
<p><em>Allow ECF from MP1.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>bright central maximum</p>
<p>subsidiary maxima «on either side»</p>
<p> </p>
<p>the width of the central fringe is twice / larger than the width of the subsidiary/secondary fringes/maxima</p>
<p><em><strong>OR</strong></em></p>
<p>intensity of pattern is decreased</p>
<p> </p>
<p><em>Allow marks from a suitably labelled intensity graph for single slit diffraction.</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;">
[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>
<br><hr><br><div class="specification">
<p>The ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{distance of Mars from the Sun}}}}{{{\text{distance of Earth from the Sun}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>distance of Mars from the Sun</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>distance of Earth from the Sun</mtext>
</mrow>
</mrow>
</mfrac>
</math></span> = 1.5.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the intensity of solar radiation at the orbit of Mars is about 600 W m<sup>–2</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>Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.</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>The atmosphere of Mars is composed mainly of carbon dioxide and has a pressure less than 1 % of that on the Earth. Outline why the greenhouse effect is not significant on Mars.</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>use of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="I \propto \frac{1}{{{r^2}}}">
<mi>I</mi>
<mo>∝</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> «1.36 × 10<sup>3</sup> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{{{1.5}^2}}}">
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mrow>
<mn>1.5</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>» ✔</p>
<p>604 «W m<sup>–2</sup>» ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{600}}{4}">
<mfrac>
<mrow>
<mn>600</mn>
</mrow>
<mn>4</mn>
</mfrac>
</math></span> for mean intensity ✔</p>
<p>temperature/K = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt[4]{{\frac{{600}}{{4 \times 5.67 \times {{10}^{ - 8}}}}}} = ">
<mroot>
<mrow>
<mfrac>
<mrow>
<mn>600</mn>
</mrow>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mn>5.67</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>8</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mn>4</mn>
</mroot>
<mo>=</mo>
</math></span>» 230 ✔</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognize the link between molecular density/concentration and pressure ✔</p>
<p>low pressure means too few molecules to produce a significant heating effect</p>
<p><em><strong>OR</strong></em></p>
<p>low pressure means too little radiation re-radiated back to Mars ✔</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>A longitudinal wave travels in a medium with speed 340 m s<sup>−1</sup>. The graph shows the variation with time <em>t</em> of the displacement <em>x</em> of a particle P in the medium. Positive displacements on the graph correspond to displacements to the right for particle P.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Another wave travels in the medium. The graph shows the variation with time <em>t</em> of the displacement of each wave at the position of P.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>
<div class="specification">
<p>A standing sound wave is established in a tube that is closed at one end and open at the other end. The period of the wave is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>. The diagram represents the standing wave at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math> and at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>T</mi><mn>8</mn></mfrac></math>. The wavelength of the wave is 1.20 m. Positive displacements mean displacements to the right.</p>
<p style="text-align: left;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the wavelength of the wave.</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>State the phase difference between the two waves.</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>Identify a time at which the displacement of P is zero.</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>Estimate the amplitude of the resultant wave.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of the tube.</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>A particle in the tube has its equilibrium position at the open end of the tube.<br>State and explain the direction of the velocity of this particle at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>T</mi><mn>8</mn></mfrac></math>.</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>Draw on the diagram the standing wave at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>T</mi><mn>4</mn></mfrac></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</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"><mi>T</mi><mo>=</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo></math>«s» or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>250</mn><mo> </mo></math>«Hz» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mn>340</mn><mo>×</mo><mn>4</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>.</mo><mn>36</mn><mo>≈</mo><mn>1</mn><mo>.</mo><mn>4</mn><mo> </mo></math>«m» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.<br>Award <strong>[2]</strong> for a bald correct answer.</em></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"><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac><mo>/</mo><mn>90</mn><mo>°</mo></math> <em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi mathvariant="normal">π</mi></mrow><mn>2</mn></mfrac><mo>/</mo><mn>270</mn><mo>°</mo></math> ✓</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.5 «ms» ✓</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>8.0 <em><strong>OR</strong> </em>8.5 «μm» ✓</p>
<p><em><br>From the graph on the paper, value is 8.0. From the calculated correct trig functions, value is 8.49.</em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>L</em> = «<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mn>3</mn><mn>4</mn></mfrac><mi>λ</mi><mo>=</mo></mstyle></math>» 0.90 «m» ✓</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>to the right ✓<br><br></p>
<p>displacement is getting less negative</p>
<p><em><strong>OR</strong></em></p>
<p>change of displacement is positive ✓</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontal line drawn at the equilibrium position ✓</p>
<div class="question_part_label">c.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.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">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the Earth-Sun distance.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the intensity of the solar radiation at the location of Titan is 16 W m<sup>−2</sup></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>Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the <strong>average </strong>intensity of solar radiation <strong>absorbed</strong> by the whole surface of Titan is 3.1 W m<sup>−2</sup></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the equilibrium surface temperature of Titan is about 90 K.</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>The orbital radius of Titan around Saturn is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> and the period of revolution is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>T</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant="normal">π</mi><mn>2</mn></msup><msup><mi>R</mi><mrow><mo> </mo><mn>3</mn></mrow></msup></mrow><mrow><mi>G</mi><mi>M</mi></mrow></mfrac></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math> is the mass of Saturn.</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>The orbital radius of Titan around Saturn is 1.2 × 10<sup>9 </sup>m and the orbital period is 15.9 days. Estimate the mass of Saturn.</p>
<div class="marks">[2]</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>incident intensity <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1360</mn><mrow><mn>9</mn><mo>.</mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfrac></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>7</mn><mo>≈</mo><mn>16</mn></math> «W m<sup>−2</sup>» ✓</p>
<p> </p>
<p><em>Allow the use of 1400 for the solar constant.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>exposed surface is ¼ of the total surface ✓</p>
<p>absorbed intensity = (1−0.22) × incident intensity ✓</p>
<p>0.78 × 0.25 × 15.7 <em><strong>OR </strong> </em>3.07 «W m<sup>−2</sup>» ✓</p>
<p> </p>
<p><em>Allow 3.06 from rounding and 3.12 if they use 16</em> W m<sup>−2</sup>.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>σT </em><sup>4</sup> = 3.07</p>
<p><em><strong>OR</strong></em></p>
<p><em>T</em> = 86 «K» ✓</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct equating of gravitational force / acceleration to centripetal force / acceleration ✓</p>
<p>correct rearrangement to reach the expression given ✓</p>
<p> </p>
<p><em>Allow use of <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mi>G</mi><mi>M</mi></mrow><mi>R</mi></mfrac></msqrt><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mi>R</mi></mrow><mi>T</mi></mfrac></math> for <strong>MP1</strong>.</em></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"><mi>T</mi><mo>=</mo><mn>15</mn><mo>.</mo><mn>9</mn><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></math> «s» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant="normal">π</mi><mn>2</mn></msup><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfenced><mn>3</mn></msup></mrow><mrow><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>×</mo><msup><mfenced><mrow><mn>15</mn><mo>.</mo><mn>9</mn><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></mrow></mfenced><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mn>5</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>26</mn></msup><mo> </mo></math>«kg» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></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="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two microwave transmitters, X and Y, are placed 12 cm apart and are connected to the same source. A single receiver is placed 54 cm away and moves along a line AB that is parallel to the line joining X and Y.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>Maxima and minima of intensity are detected at several points along AB.</p>
<p>(i) Explain the formation of the intensity <strong>minima</strong>.</p>
<p>(ii) The distance between the central maximum and the first minimum is 7.2 cm. Calculate the wavelength of the microwaves.</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>Radio waves are emitted by a straight conducting rod antenna (aerial). The plane of polarization of these waves is parallel to the transmitting antenna.</p>
<p><img 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"></p>
<p>An identical antenna is used for reception. Suggest why the receiving antenna needs to be be parallel to the transmitting antenna.</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>The receiving antenna becomes misaligned by 30° to its original position.</p>
<p><img 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" alt></p>
<p>The power of the received signal in this new position is 12 μW.</p>
<p>(i) Calculate the power that was received in the original position.</p>
<p>(ii) Calculate the minimum time between the wave leaving the transmitting antenna and its reception.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>i<br>minima = destructive interference<br><em>Allow “crest meets trough”, but not “waves cancel”.</em><br><em>Allow “destructive superposition” but not bald “superposition”.</em><br><br>at minima waves meet 180° <em><strong>or</strong></em> π out of phase<br><em>Allow similar argument in terms of effective path difference of </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{2}">
<mfrac>
<mi>λ</mi>
<mn>2</mn>
</mfrac>
</math></span><em>.</em><br><em>Allow “antiphase”, allow “completely out of phase”</em><br><em>Do not allow “out of phase” without angle. Do not allow <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{n\lambda }}{2}">
<mfrac>
<mrow>
<mi>n</mi>
<mi>λ</mi>
</mrow>
<mn>2</mn>
</mfrac>
</math></span> unless qualified to odd integers but accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {n + \frac{1}{2}} \right)\lambda ">
<mrow>
<mo>(</mo>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mi>λ</mi>
</math></span></em><br><br>ii<br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda = \frac{{sd}}{D}">
<mi>λ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>s</mi>
<mi>d</mi>
</mrow>
<mi>D</mi>
</mfrac>
</math></span> <em><strong>or</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda = \frac{{12 \times 2 \times 7.2}}{{54}} = ">
<mi>λ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>12</mn>
<mo>×</mo>
<mn>2</mn>
<mo>×</mo>
<mn>7.2</mn>
</mrow>
<mrow>
<mn>54</mn>
</mrow>
</mfrac>
<mo>=</mo>
</math></span> <em><strong>or</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda = \frac{{12 \times 7.2}}{{54}} = ">
<mi>λ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>12</mn>
<mo>×</mo>
<mn>7.2</mn>
</mrow>
<mrow>
<mn>54</mn>
</mrow>
</mfrac>
<mo>=</mo>
</math></span> seen<br><em>Award <strong>[2]</strong> for a bald correct answer.</em><br><br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda = ">
<mi>λ</mi>
<mo>=</mo>
</math></span> «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12 \times 2 \times 7.2}}{{54}} = ">
<mfrac>
<mrow>
<mn>12</mn>
<mo>×</mo>
<mn>2</mn>
<mo>×</mo>
<mn>7.2</mn>
</mrow>
<mrow>
<mn>54</mn>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 3.2 «cm»<br><em>Award <strong>[1 max]</strong> for 1.6 «cm»</em><br><em>Award <strong>[2 max]</strong> to a trigonometric solution in which candidate works out individual path lengths and equates to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{2}">
<mfrac>
<mi>λ</mi>
<mn>2</mn>
</mfrac>
</math></span>.</em></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>the component of the polarized signal in the direction of the receiving antenna</p>
<p>is a maximum «when both are parallel»</p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p>receiving antenna must be parallel to plane of polarisation<br>for power/intensity to be maximum</p>
<p><em>Do not accept “receiving antenna must be parallel to transmitting antenna”</em></p>
<p><em><strong>ALTERNATIVE 3: </strong></em></p>
<p>refers to Malus’ law <em><strong>or</strong></em> <em>I = I<sub>0</sub> </em>cos<sup>2</sup><em>θ</em></p>
<p>explains that <em>I</em> is max when<em> θ</em> = 0</p>
<p><em><strong>ALTERNATIVE 4:</strong></em></p>
<p>an electric current is established in the receiving antenna which is proportional to the electric field</p>
<p>maximum current in receiving antenna requires maximum field <strong>«</strong>and so must be parallel<strong>»</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i<br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{I_0} = \frac{I}{{{{\cos }^2}\theta }}">
<mrow>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mi>I</mi>
<mrow>
<mrow>
<msup>
<mrow>
<mi>cos</mi>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mi>θ</mi>
</mrow>
</mfrac>
</math></span> <em><strong>or</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12}}{{{{\cos }^2}30}}">
<mfrac>
<mrow>
<mn>12</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mi>cos</mi>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mn>30</mn>
</mrow>
</mfrac>
</math></span> seen<br><em>Award <strong>[2]</strong> for bald correct answer.</em><br><em>Award <strong>[1 max]</strong> for MP1 if 9 x 10<sup>-6</sup>W is the final answer (I and I<sub>0</sub> reversed).</em><br><em>Award<strong> [1 max]</strong> if cos not squared (14 μW).</em></p>
<p>1.6 × 10<sup>-5</sup>«W»<br><em>Units not required but if absent assume W.</em><br><br>ii<br>1.9 × 10<sup>–4 </sup>«s»</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>