Water is draining from a vertical tube that was initially full. A vibrating tuning fork is held near the top of the tube. For two positions of the water surface only, the sound is at its maximum loudness.

The distance between the two positions of maximum loudness is x.

What is the wavelength of the sound emitted by the tuning fork?

A.  $\frac{x}{2}$

B.  x

C.  $\frac{3x}{2}$

D.  2x

D

Light is incident at the boundary between air and diamond. The speed of light in diamond is less than the speed of light in air. The angle of incidence i of the light is greater than the critical angle. Which diagram is correct for this situation?

A

A standing wave is formed on a string. P and Q are adjacent antinodes on the wave. Three statements are made by a student:

I.   The distance between P and Q is half a wavelength.
II.  P and Q have a phase difference of π rad.
III. Energy is transferred between P and Q.

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A

This question was generally well answered by HL candidates. Given the number of candidates who (incorrectly) chose statement III "Energy is transferred between P and Q" as true, this question might be a useful review to identify the properties of standing waves.

A point source of light of amplitude A₀ gives rise to a particular light intensity when viewed at a distance from the source. When the amplitude is increased and the viewing distance is doubled, the light intensity is doubled. What is the new amplitude of the source? 

A. 2A₀

B. 2$\sqrt{2}$ A₀

C. 4A₀

D. 8A₀

B

The diagram shows an interference pattern observed on a screen in a double-slit experiment with monochromatic light of wavelength 600 nm. The screen is 1.0 m from the slits.

What is the separation of the slits?

A.  6.0 × 10⁻⁷ m

B.  6.0 × 10⁻⁶ m

C.  6.0 × 10⁻⁵ m

D.  6.0 × 10⁻⁴ m

D

In two different experiments, white light is passed through a single slit and then is either refracted through a prism or diffracted with a diffraction grating. The prism produces a band of colours from M to N. The diffraction grating produces a first order spectrum P to Q.

What are the colours observed at M and P?

A

This has low discrimination and the difficulty index suggests candidates found it hard with the incorrect option C being the most popular. The spreading of colours and formation of a spectrum (or rainbow) is something that is covered during an introductory course in physics and then developed in refraction and diffraction.

A particle undergoes simple harmonic motion. Which quantities of the motion can be simultaneously zero?

A.  Displacement and velocity

B.  Displacement and acceleration

C.  Velocity and acceleration

D.  Displacement, velocity and acceleration

B

A metal rod of length 45 cm is clamped at its mid point. The speed of sound in the metal rod is 1500 m s⁻¹ and the speed of sound in air is 300 m s⁻¹. The metal rod vibrates at its first harmonic. What is the wavelength in air of the sound wave produced by the metal rod?

A. 4.5 cm

B. 9.0 cm

C. 18 cm

D. 90 cm

C

X and Y are two coherent sources of waves. The phase difference between X and Y is zero. The intensity at P due to X and Y separately is I. The wavelength of each wave is 0.20 m.

What is the resultant intensity at P?

A.   0

B.   I

C.   2I

D.   4I

D

The diagram shows a second harmonic standing wave on a string fixed at both ends.

What is the phase difference, in rad, between the particle at X and the particle at Y?

A. 0

B. $\frac{\pi }{4}$

C. $\frac{\pi }{2}$

D. $\frac{3\pi }{4}$

A

Monochromatic light of wavelength $\lambda$ is incident on two slits S₁ and S₂. An interference pattern is observed on the screen.

O is equidistant from S₁ and S₂. A bright fringe is observed at O and a dark fringe at X.

There are two dark fringes between O and X. What is the path difference between the light arriving at X from the two slits?

A.  $\frac{\lambda }{2}$

B.  $\frac{3\lambda }{2}$

C.  $\frac{5\lambda }{2}$

D.  $\frac{7\lambda }{2}$

C

With a relatively high discrimination index, this question was well answered by stronger HL candidates. Some students had difficulty recognising that there would be 2.5λ rather than 1.5λ, and as a result option B was a significant distractor.

A travelling wave of period 5.0 ms travels along a stretched string at a speed of 40 m s^–1. Two points on the string are 0.050 m apart.

What is the phase difference between the two points?

A.  0

B.  $\frac{\pi }{2}$

C.  $\pi$

D.  2$\pi$

B

In an experiment to determine the speed of sound in air, a tube that is open at the top is filled with water and a vibrating tuning fork is held over the tube as the water is released through a valve.

An increase in intensity in the sound is heard for the first time when the air column length is $x$. The next increase is heard when the air column length is $y$.

Which expressions are approximately correct for the wavelength of the sound?

I. 4$x$

II. 4$y$

III. $\frac{4y}{3}$

A. I and II

B. I and III

C. II and III

D. I, II and III

B

The question was well answered by students.

Properties of waves are

I.    polarization
II.   diffraction
III.  refraction

Which of these properties apply to sound waves?

A.  I and II
B.  I and III
C.  II and III
D.  I, II and III

C

Monochromatic light of wavelength λ is incident on a double slit. The resulting interference pattern is observed on a screen a distance y from the slits. The distance between consecutive fringes in the pattern is 55 mm when the slit separation is a.

λ, y and a are all doubled. What is the new distance between consecutive fringes?

A. 55 mm

B. 110 mm

C. 220 mm

D. 440 mm

B

L is a point source of light. The intensity of the light at a distance 2$x$ from L is I. What is the intensity at a distance 3$x$ from L?

A.   $\frac{4}{9}$I

B.   $\frac{2}{3}$I

C.   $\frac{3}{2}$I

D.   $\frac{9}{4}$I

A

The graph shows the variation with position s of the displacement x of a wave undergoing simple harmonic motion (SHM).

What is the magnitude of the velocity at the displacements X, Y and Z?

B

Wavefronts travel from air to medium Q as shown.

What is the refractive index of Q?

A.  $\frac{\sin 30°}{\sin 45°}$

B.  $\frac{\sin 45°}{\sin 30°}$

C.  $\frac{\sin 45°}{\sin 60°}$

D.  $\frac{\sin 60°}{\sin 45°}$

B

This has a negative discrimination index and the majority of candidates chose option C which would be correct if we were considering rays but the question asks about wavefronts. It must be stressed that it is important to read the question carefully and not skim over the introductory stem. In this type of question students are advised to draw the rays on the diagram perpendicular to the wavefronts to make it easier to work out which angles to use.

A glass block of refractive index 1.5 is immersed in a tank filled with a liquid of higher refractive index. Light is incident on the base of the glass block. Which is the correct diagram for rays incident on the glass block at an angle greater than the critical angle?

D

Response D was the most common response, with response A providing a significant distractor for roughly a third of candidates unsure about refraction beyond the critical angle.

The graph shows the variation with time for the displacement of a particle in a travelling wave.

What are the frequency and amplitude for the oscillation of the particle?

C

A pipe of length 0.6 m is filled with a gas and closed at one end. The speed of sound in the gas is 300 m s^–1. What are the frequencies of the first two harmonics in the tube?

A.  125 Hz and 250 Hz

B.  125 Hz and 375 Hz

C.  250 Hz and 500 Hz

D.  250 Hz and 750 Hz

B

A third-harmonic standing wave of wavelength 0.80 m is set up on a string fixed at both ends. Two points on the wave are separated by a distance of 0.60 m. What is a possible phase difference between the two points on the wave?

A. $\frac{\pi }{4}\text{rad}$

B. $\frac{\pi }{2}\text{rad}$

C. $\pi \text{rad}$

D. $\frac{3\pi }{2}\text{rad}$

C

This question had a low discrimination index with response D the most popular and an even spread between the other 3 answers. A third-harmonic standing wave of wavelength 0.8m must be on a string of length 1.2m giving 3 loops of 0.4m each. Depending on where the initial point is chosen, two points separated by 0.6m will either be in adjacent loops e.g. at 0.1m and 0.7 m with a phase difference of π or in the two end loops e.g at 0.3 m and 0.9m with a phase difference of 0. So for a standing wave there are only two possible answers, π (response C) or 0 (not included in these responses).

Which graph shows the variation of amplitude with intensity for a wave?

B

A string stretched between two fixed points sounds its second harmonic at frequency f.

Which expression, where n is an integer, gives the frequencies of harmonics that have a node at the centre of the string?

A.     $\frac{n+1}{2}f$

B.     nf

C.     2nf

D.     (2n + 1)f

B

Which diagram shows the shape of the wavefront as a result of the diffraction of plane waves by an object?

A

A ray of light passes from the air into a long glass plate of refractive index n at an angle θ to the edge of the plate.

The ray is incident on the internal surface of the glass plate and the refracted ray travels along the external surface of the plate.

What change to n and what change to θ will cause the ray to travel entirely within the plate after incidence?

A