A spring XY lies on a frictionless table with the end Y free.

A horizontal pulse travels along the spring from X to Y.  What happens when the pulse reaches Y? 

A. The pulse will be reflected towards X and inverted. 
B. The pulse will be reflected towards X and not be inverted. 
C. Y will move and the pulse will disappear. 
D. Y will not move and the pulse will disappear.

B

The graphs show the variation of the displacement y of a medium with distance $x$ and with time t for a travelling wave.

What is the speed of the wave?

A.   0.6 m s^–1

B.   0.8 m s^–1

C.   600 m s^–1

D.   800 m s^–1

D

Two pulses are travelling towards each other.

What is a possible pulse shape when the pulses overlap?

A

A sound wave has a frequency of 1.0 kHz and a wavelength of 0.33 m. What is the distance travelled by the wave in 2.0 ms and the nature of the wave?

C

What is the phase difference, in rad, between the centre of a compression and the centre of a rarefaction for a longitudinal travelling wave?

A. 0

B. $\frac{\pi }{2}$

C. $\pi$

D. $2\pi$

C

Unpolarized light of intensity I₀ is incident on the first of two polarizing sheets. Initially the planes of polarization of the sheets are perpendicular.

Which sheet must be rotated and by what angle so that light of intensity $\frac{I_0}{4}$ can emerge from the second sheet?

C

A wave travels along a string. Graph M shows the variation with time of the displacement of a point X on the string. Graph N shows the variation with distance of the displacement of the string. PQ and RS are marked on the graphs.

What is the speed of the wave?

A.  $\frac{\text{PQ}}{\text{RS}}$

B.  $\text{PQ}\times \text{RS}$

C.  $\frac{\text{RS}}{\text{PQ}}$

D.  $\frac{1}{\text{PQ}\times \text{RS}}$

C

A system that is subject to a restoring force oscillates about an equilibrium position.

For the motion to be simple harmonic, the restoring force must be proportional to

A.     the amplitude of the oscillation.

B.     the displacement from the equilibrium position.

C.     the potential energy of the system.

D.     the period of the oscillation.

B

Two identical waves, each with amplitude X₀ and intensity I, interfere constructively. What are the amplitude and intensity of the resultant wave?

D

When a sound wave travels from a region of hot air to a region of cold air, it refracts as shown.

What changes occur in the frequency and wavelength of the sound as it passes from the hot air to the cold air?

B

Unpolarized light with an intensity of 320 W m⁻² goes through a polarizer and an analyser, originally aligned parallel.

The analyser is rotated through an angle θ = 30°. Cos 30° = $\frac{\sqrt{3}}{2}$.

What is the intensity of the light emerging from the analyser? 

A.  120 W m⁻²

B.  $80\sqrt{3}$ W m⁻²

C.  240 W m⁻²

D.  $160\sqrt{3}$ W m⁻²

A

This question proved a little challenging for SL candidates with many choosing incorrect answers especially C or D instead of correct A. At HL option C also was a popular option although a high discrimination index shows that the question discriminated well between the candidates. It appears that candidates are forgetting that 50% of the intensity is lost when unpolarised light passes through a polarizer, and then more is lost at the analyser according to Malus' Law.

Unpolarized light is incident on two polarizing filters X and Y. They are arranged so that light emerging from Y has a maximum intensity. X is fixed and Y is rotated through θ about the direction of the incident beam in its own plane.

What are the first three successive values of θ for which the final transmitted intensity is a maximum?

A.  90°, 180°, 270°

B.  90°, 270°, 450°

C.  180°, 360°, 540°

D.  180°, 540°, 720°

C

The diagram shows an interference pattern produced by two sources that oscillate on the surface of a liquid.

Which of the distances shown in the diagram corresponds to one fringe width of the interference pattern?

C

A string is fixed at both ends. P and Q are two particles on the string.

The first harmonic standing wave is formed in the string. What is correct about the motion of P and Q?

A.  P is a node and Q is an antinode.

B.  P is an antinode and Q is a node.

C.  P and Q oscillate with the same amplitude.

D.  P and Q oscillate with the same frequency.

D

In a double-slit experiment, a source of monochromatic red light is incident on slits S₁ and S₂ separated by a distance $d$. A screen is located at distance $x$ from the slits. A pattern with fringe spacing $y$ is observed on the screen.

Three changes are possible for this arrangement

I.    increasing $x$

II.   increasing $d$

III.  using green monochromatic light instead of red.

Which changes will cause a decrease in fringe spacing $y$?

A.   I and II only

B.   I and III only

C.   II and III only

D.   I, II, and III

C

A pipe of length L is closed at one end. Another pipe is open at both ends and has length 2L. What is the lowest common frequency for the standing waves in the pipes?

A. $\frac{\text{speed of sound in air}}{8\text{L}}$

B. $\frac{\text{speed of sound in air}}{4\text{L}}$

C. $\frac{\text{speed of sound in air}}{2\text{L}}$

D. $\frac{\text{speed of sound in air}}{\text{L}}$

B

A particle is displaced from rest and released at time t = 0. It performs simple harmonic motion (SHM). Which graph shows the variation with time of the kinetic energy E_k of the particle?

D

What changes occur to the frequency and wavelength of monochromatic light when it travels from glass to air?

B

What statement about X-rays and ultraviolet radiation is correct?

A.  X-rays travel faster in a vacuum than ultraviolet waves.

B.  X-rays have a higher frequency than ultraviolet waves.

C.  X-rays cannot be diffracted unlike ultraviolet waves.

D.  Microwaves lie between X-rays and ultraviolet in the electromagnetic spectrum.

B

Two strings of lengths L₁ and L₂ are fixed at both ends. The wavespeed is the same for both strings. They both vibrate at the same frequency. L₁ vibrates at its first harmonic. L₂ vibrates at its third harmonic.

What is $\frac{L_1}{L_2}$?

A.   $\frac{1}{3}$

B.   1

C.   2

D.   3

D

A body undergoes one oscillation of simple harmonic motion (shm). What is correct for the direction of the acceleration of the body and the direction of its velocity? 

A. Always opposite 
B. Opposite for half a period 
C. Opposite for a quarter of a period 
D. Never opposite

B

A longitudinal wave moves through a medium. Relative to the direction of energy transfer through the medium, what are the displacement of the medium and the direction of propagation of the wave?

B

A student blows across the top of a cylinder that contains water. A first-harmonic standing sound wave is produced in the air of the cylinder. More water is then added to the cylinder. The student blows so that a first-harmonic standing wave is produced with a different frequency.

What is the nature of the displacement in the air at the water surface and the change in frequency when the water is added?

D

The graph shows the variation with time t of the velocity v of an object undergoing simple harmonic motion (SHM). At which velocity does the displacement from the mean position take a maximum positive value?

D

A string fixed at both ends vibrates in the first harmonic with frequency 400 Hz. The speed of sound in the string is 480 m s^–1. What is the length of the string?

A. 0.42 m

B. 0.60 m

C. 0.84 m

D. 1.2 m

B

Response D was the most common option selected, perhaps by students equating the wavelength of the sound with the length of the string, or incorrectly taking the first harmonic to be the fundamental frequency.

A beam of unpolarized light of intensity $I_0$ is incident on a polarizing filter. The polarizing filter is rotated through an angle θ. What is the variation in the intensity $I$ of the beam with angle θ after passing through the polarizing filter?

D

Option B was chosen most frequently among both HL and SL candidates. It seems likely that students selecting this answer were anticipating a question with two polarising filters where the second filter was rotated. Again, careful reading of the questions by candidates is necessary. A high discrimination index was observed for this question. This is a good conceptual question and would be useful in the teaching and/or revision of polarisation.

Three quantities used to describe a light wave are

          I.   frequency
          II.  wavelength
          III. speed.

Which quantities increase when the light wave passes from water to air?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

C

Two travelling waves are moving through a medium. The diagram shows, for a point in the medium, the variation with time t of the displacement d of each of the waves.

For the instant when t = 2.0 ms, what is the phase difference between the waves and what is the resultant displacement of the waves?

D

Two wave generators, placed at position P and position Q, produce water waves with a wavelength of$4.0 \text{cm}$. Each generator, operating alone, will produce a wave oscillating with an amplitude of $3.0 \text{cm}$ at position R. PR is$42 \text{cm}$ and RQ is $60 \text{cm}$.

Both wave generators now operate together in phase. What is the amplitude of the resulting wave at R?

A.  $9 \text{cm}$

B.  $6 \text{cm}$

C.  $3 \text{cm}$

D.  zero

D

A standing wave is formed on a rope. The distance between the first and fifth antinode on the standing wave is 60 cm. What is the wavelength of the wave?

A.  12 cm

B.  15 cm

C.  24 cm

D.  30 cm

D

Option D was the most common (correct) answer, however answers A and B proved to be significant distractors. This would be a useful practice question when reviewing standing waves, nodes/antinodes and wavelengths.

Two sound waves from a point source on the ground travel through the ground to a detector. The speed of one wave is 7.5 km s^–1, the speed of the other wave is 5.0 km s^–1. The waves arrive at the detector 15 s apart. What is the distance from the point source to the detector?

A.     38 km

B.     45 km

C.     113 km

D.     225 km

D

A girl in a stationary boat observes that 10 wave crests pass the boat every minute. What is the period of the water waves?

A.  $\frac{1}{10}$ min

B.  $\frac{1}{10}$ min^–1

C.  10 min

D.  10 min^–1

A

The bob of a pendulum has an initial displacement $x_0$ to the right. The bob is released and allowed to oscillate. The graph shows how the displacement varies with time. At which point is the velocity of the bob at its maximum magnitude directed towards the left?

C

Horizontally polarized light is incident on a pair of polarizers X and Y. The axis of polarization of X makes an angle θ with the horizontal. The axis of polarization of Y is vertical.

What is θ so that the intensity of the light transmitted through Y is a maximum?

A.  $0°$

B.  $45°$

C.  $90°$

D.  $180°$

B

A ray of light is incident on the flat side of a semi-circular glass block placed in paraffin. The ray is totally internally reflected inside the glass block as shown.

The refractive index of glass is $n_1$ and the refractive index of paraffin is $n_2$.

What is correct?

A.  $\sin \theta =\frac{n_1}{n_2}$

B.  $\sin \theta =\frac{n_2}{n_1}$

C.  $\sin \theta =\frac{1}{n_1}$

D.  $\sin \theta =\frac{1}{n_2}$

B

While option A (correct) was the most frequent response from candidates, options B and D were significant distractors. Very few candidates selected option A, recognizing that different frequency and amplitude could not lead to zero intensity through interference.

A glass block has a refractive index in air of n_g. The glass block is placed in two different liquids: liquid X with a refractive index of n_X and liquid Y with a refractive index of n_Y.

In liquid X $\frac{n_{\text{g}}}{n_{\text{X}}}=2$ and in liquid Y $\frac{n_{\text{g}}}{n_{\text{Y}}}=1.5.$ What is $\frac{\text{speed of light in liquid X}}{\text{speed of light in liquid Y}}$?

A.  $\frac{2}{4}$

B.  $\frac{3}{4}$

C.  $\frac{4}{3}$

D.  $3$

C

A beam of unpolarized light is incident on the first of two parallel polarizers. The transmission axes of the two polarizers are initially parallel.

The first polarizer is now rotated about the direction of the incident beam by an angle smaller than 90°. Which gives the changes, if any, in the intensity and polarization of the transmitted light?

A

A ray of monochromatic light is incident on the parallel interfaces between three media. The speeds of light in the media are v₁, v₂ and v₃.

What is correct about the speeds of light in the media?

A.  v₃ < v₁ < v₂

B.  v₃ < v₂ < v₁

C.  v₂ < v₃ < v₁

D.  v₂ < v₁ < v₃

D

An object moves with simple harmonic motion. The acceleration of the object is

A.  constant.

B.  always directed away from the centre of the oscillation.

C.  a maximum at the centre of the oscillation.

D.  a maximum at the extremes of the oscillation.

D

Which graph shows the variation with time t of the kinetic energy (KE) of an object undergoing simple harmonic motion (shm) of period T?

D

A travelling wave has a frequency of $500 \mathrm{Hz}$. The closest distance between two points on the wave that have a phase difference of $60°\left(\frac{\mathrm{\pi }}{3}\mathrm{rad}\right)$ is $0.050 \mathrm{m}$. What is the speed of the wave?

A.  $25 \mathrm{m} {\mathrm{s}}^{-1}$

B.  $75 \mathrm{m} {\mathrm{s}}^{-1}$

C.  $150 \mathrm{m} {\mathrm{s}}^{-1}$

D.  $300 \mathrm{m} {\mathrm{s}}^{-1}$

C

A first-harmonic standing wave is formed on a vertical string of length 3.0 m using a vibration generator. The boundary conditions for this string are that it is fixed at one boundary and free at the other boundary.

The generator vibrates at a frequency of 300 Hz.

What is the speed of the wave on the string?

A.     0.90 km s^–1

B.     1.2 km s^–1

C.     1.8 km s^–1

D.     3.6 km s^–1 

D

Unpolarized light is incident on two polarizers. The axes of polarization of both polarizers are initially parallel. The second polarizer is then rotated through 360° as shown.

Which graph shows the variation of intensity with angle θ for the light leaving the second polarizer?

B

A particle oscillates with simple harmonic motion (shm) of period T. Which graph shows the variation with time of the kinetic energy of the particle?

D

A pipe of fixed length is closed at one end. What is $\frac{\text{third harmonic frequency of pipe}}{\text{first harmonic frequency of pipe}}$?

A. $\frac{1}{5}$

B. $\frac{1}{3}$

C. 3

D. 5

C

A pair of slits in a double slit experiment are illuminated with monochromatic light of wavelength 480 nm. The slits are separated by 1.0 mm. What is the separation of the fringes when observed at a distance of 2.0 m from the slits?

A.     2.4 × 10^–4 mm

B.     9.6 × 10^–4 mm

C.     2.4 × 10^–1 mm

D.     9.6 × 10^–1 mm

D

The frequency of the first harmonic in a pipe is measured. An adjustment is then made which causes the speed of sound in the pipe to increase. What is true for the frequency and the wavelength of the first harmonic when the speed of sound has increased?

A

Which of these waves cannot be polarized?

A. microwaves

B. ultrasound

C. ultraviolet

D. X rays

B

This question was very well answered by candidates, with a high difficulty index.

A travelling wave on the surface of a lake has wavelength $\lambda$. Two points along the wave oscillate with the phase difference of $\mathrm{\pi }$. What is the smallest possible distance between these two points?

A.  $\frac{\lambda }{4}$

B.  $\frac{\lambda }{2}$

C.  $\lambda$

D.  $2\lambda$

B

The orbital radius of the Earth around the Sun is 1.5 times that of Venus. What is the intensity of solar radiation at the orbital radius of Venus?

A. 0.6 kW m^-2

B. 0.9 kW m^-2

C. 2 kW m^-2

D. 3 kW m^-2

D

This had a low discrimination index at both SL and HL and although the correct answer was the most popular, all options gained high support. Candidates should be reminded that they have a data booklet and become familiar with its contents before the exam.

A sound wave has a wavelength of 0.20 m. What is the phase difference between two points along the wave which are 0.85 m apart?

A.     zero

B.     45°

C.     90°

D.     180°

C

A particle performs simple harmonic motion (shm). What is the phase difference between the displacement and the acceleration of the particle?

A. 0

B. $\frac{\pi }{2}$

C. $\pi$

D. $\frac{3\pi }{2}$

C

A particle undergoes simple harmonic motion (SHM). The graph shows the variation of velocity v of the particle with time t.

What is the variation with time of the acceleration a of the particle?

A

The refractive index of glass is $\frac{3}{2}$ and the refractive index of water is $\frac{4}{3}$. What is the critical angle for light travelling from glass to water?

A.  ${\sin }^{-1}\left(\frac{1}{2}\right)$

B.  ${\sin }^{-1}\left(\frac{2}{3}\right)$

C.  ${\sin }^{-1}\left(\frac{3}{4}\right)$

D.  ${\sin }^{-1}\left(\frac{8}{9}\right)$

D

The motion of an object is described by the equation

acceleration ∝ − displacement.

What is the direction of the acceleration relative to that of the displacement and what is the displacement when the speed is a maximum?

D

What is true about the acceleration of a particle that is oscillating with simple harmonic motion (SHM)?

A.     It is in the opposite direction to its velocity

B.     It is decreasing when the potential energy is increasing

C.     It is proportional to the frequency of the oscillation

D.     It is at a minimum when the velocity is at a maximum

D

Three statements about electromagnetic waves are:

I.   They can be polarized.
II.  They can be produced by accelerating electric charges.
III. They must travel at the same velocity in all media.

Which combination of statements is true?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A

What are the changes in speed, frequency and wavelength of light as it travels from a material of low refractive index to a material of high refractive index?

D

This question was well answered by the majority of candidates.

An interference pattern with minima of zero intensity is observed between light waves. What must be true about the frequency and amplitude of the light waves?

C

This question was generally well answered by SL candidates with both a high difficulty and discrimination index. Candidates who selected an incorrect answer seems more certain about the correct amplitude than the resulting intensity.

Unpolarized light of intensity $I_1$ is incident on a polarizer. The light that passes through this polarizer then passes through a second polarizer.

The second polarizer can be rotated to vary the intensity of the emergent light. What is the maximum value of the intensity emerging from the second polarizer?

A.  $\frac{I_1}{4}$

B.  $\frac{I_1}{2}$

C.  $\frac{2I_1}{3}$

D.  $I_1$

B

Monochromatic light travelling upwards in glass is incident on a boundary with air. The path of the refracted light is shown.

A layer of liquid is then placed on the glass without changing the angle of incidence on the glass. The refractive index of the glass is greater than the refractive index of the liquid and the refractive index of the liquid is greater than that of air.

What is the path of the refracted light when the liquid is placed on the glass?

D

A low discrimination index with most candidates choosing C. They have deduced, correctly, that the ray moves away from the normal on entering the denser medium but have apparently forgotten that the stem of the question has shown them that it reaches the glass-air boundary at an angle greater than the critical angle.

A student stands a distance L from a wall and claps her hands. Immediately on hearing the reflection from the wall she claps her hands again. She continues to do this, so that successive claps and the sound of reflected claps coincide. The frequency at which she claps her hands is f. What is the speed of sound in air?

A. $\frac{L}{2f}$

B. $\frac{L}{f}$

C. Lf 

D. 2Lf

D

In simple harmonic oscillations which two quantities always have opposite directions?

A.  Kinetic energy and potential energy

B.  Velocity and acceleration

C.  Velocity and displacement

D.  Acceleration and displacement

D

The frequency of the first harmonic standing wave in a pipe that is open at both ends is 200 Hz. What is the frequency of the first harmonic in a pipe of the same length that is open at one end and closed at the other?

A.  50 Hz

B.  75 Hz

C.  100 Hz

D.  400 Hz

C

An object performs simple harmonic motion (shm). The graph shows how the velocity v of the object varies with time t.

The displacement of the object is x and its acceleration is a. What is the variation of x with t and the variation of a with t?

A

Two wave pulses, each of amplitude A, approach each other. They then superpose before continuing in their original directions. What is the total amplitude during superposition and the amplitudes of the individual pulses after superposition?

D

The air in a pipe, open at both ends, vibrates in the second harmonic mode.

What is the phase difference between the motion of a particle at P and the motion of a particle at Q?

A.  $0$

B.  $\frac{\mathrm{\pi }}{2}$

C.  $\mathrm{\pi }$

D.  $2\mathrm{\pi }$

C

A pipe is open at both ends. What is correct about a standing wave formed in the air of the pipe?

A. The sum of the number of nodes plus the number of antinodes is an odd number.

B. The sum of the number of nodes plus the number of antinodes is an even number.

C. There is always a central node.

D. There is always a central antinode.

A

A particle is moving in a straight line with an acceleration proportional to its displacement and opposite to its direction. What are the velocity and the acceleration of the particle when it is at its maximum displacement?

D

A particle undergoes simple harmonic motion of amplitude $x_0$ and frequency $f$. What is the average speed of the particle during one oscillation?

A.  $0$

B.  $f x_0$

C.  $2f x_0$

D.  $4f x_0$

D

The refractive index for light travelling from medium X to medium Y is $\frac{4}{3}$. The refractive index for light travelling from medium Y to medium Z is $\frac{3}{5}$. What is the refractive index for light travelling from medium X to medium Z?

A. $\frac{4}{5}$

B. $\frac{15}{12}$

C. $\frac{5}{4}$

D. $\frac{29}{15}$

A

The graph shows the variation with distance x of the displacement of the particles of a medium in which a longitudinal wave is travelling from left to right. Displacements to the right of equilibrium positions are positive.

Which point is at the centre of a compression?

A.  x = 0

B.  x = 1 m

C.  x = 2 m

D.  x = 3 m

B

A light source of power P is observed from a distance $d$. The power of the source is then halved.

At what distance from the source will the intensity be the same as before?

A.  $\frac{d}{\sqrt{2}}$

B.  $\frac{d}{2}$

C.  $\frac{d}{4}$

D.  $\frac{d}{8}$

A

SL candidate responses were divided across options A, B and C, and so this question would be a useful teaching tool for exploring the relationship between power, intensity and distance.

The graph shows the variation of the displacement of a wave with distance along the wave.

The wave speed is 0.50 m s^-1.

What is the period of the wave?

A. 0.33 s

B. 1.5 s

C. 3.0 s

D. 6.0 s

C

Object P moves vertically with simple harmonic motion (shm). Object Q moves in a vertical circle with a uniform speed. P and Q have the same time period T. When P is at the top of its motion, Q is at the bottom of its motion.

What is the interval between successive times when the acceleration of P is equal and opposite to the acceleration of Q?

A. $\frac{T}{4}$

B. $\frac{T}{2}$

C. $\frac{3T}{4}$

D. T

B

A wave of period 10 ms travels through a medium. The graph shows the variation of particle displacement with distance for the wave.

What is the average speed of a particle in the medium during one cycle?

A.  4.0 m s⁻¹

B.  8.0 m s⁻¹

C.  16 m s⁻¹

D.  20 m s⁻¹

C

Option D was a very efficient distractor as the most common (incorrect) selection by both HL and SL candidates. The difficulty index was low for this question, suggesting that HL and SL candidates found this question quite challenging. Candidates are again encouraged to read the questions carefully; it is likely that candidates selecting option D were providing the wave speed rather than particle speed.

A particle moving in a circle completes 5 revolutions in 3 s. What is the frequency?

A.   $\frac{3}{5}$Hz

B.   $\frac{5}{3}$Hz

C.   $\frac{3\pi }{5}$Hz

D.   $\frac{5\pi }{3}$Hz

B

Monochromatic light is used to produce double-slit interference fringes on a screen. The fringe separation on the screen is $y$. The distance from the slits to the screen and the separation of the slits are both doubled, and the light source is unchanged. What is the new fringe separation on the screen?

A. $\frac{y}{4}$

B. $y$

C. $2y$

D. $4y$

B

What are the changes in the speed and in the wavelength of monochromatic light when the light passes from water to air?

A

A light ray is incident on an air–diamond boundary. The refractive index of diamond is greater than 1. Which diagram shows the correct path of the light ray?

A

A transverse travelling wave is moving through a medium. The graph shows, for one instant, the variation with distance of the displacement of particles in the medium.

The frequency of the wave is 25 Hz and the speed of the wave is 100 m s^–1. What is correct for this wave?

A. The particles at X and Y are in phase.

B. The velocity of the particle at X is a maximum.

C. The horizontal distance between X and Z is 3.0 m.

D. The velocity of the particle at Y is 100 m s^–1.

C