C. Wave behaviour

The four pendulums shown have been cut from the same uniform sheet of board. They are attached to the ceiling with strings of equal length.

Which pendulum has the shortest period?

A simple pendulum has a time period $T$ on the Earth. The pendulum is taken to the Moon where the gravitational field strength is $\frac{1}{6}$ that of the Earth.

What is the time period of the pendulum on the Moon?

A.  $T\sqrt{6}$

B.  $T$

C.  $\frac{\sqrt{6}}{6}T$

D.  $\frac{T}{6}$

Calculate the period of oscillations of q.

An object undergoes simple harmonic motion (shm) of amplitude $x$₀. When the displacement of the object is $\frac{x_0}{3}$, the speed of the object is $v$. What is the speed when the displacement is $x$₀?

A. 0

B. $\frac{v}{3}$

C. $\frac{\sqrt{2}}{3}v$

D. $3v$

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

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

An object at the end of a spring oscillates vertically with simple harmonic motion (shm). The graph shows the variation with time $t$ of the displacement $x$ of the object.

What is the velocity of the object?

A. $-\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

B. $\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

C. $-\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$

D. $\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$ 

A plate performs simple harmonic oscillations with a frequency of 39 Hz and an amplitude of 8.0 cm.

Show that the maximum speed of the oscillating plate is about 20 m s⁻¹.

Outline why the cylinder performs simple harmonic motion when released.

The mass of the cylinder is $118 \mathrm{kg}$ and the cross-sectional area of the cylinder is $2.29\times {10}^{-1} {\mathrm{m}}^2$. The density of water is $1.03\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. Show that the angular frequency of oscillation of the cylinder is about $4.4 \mathrm{rad} {\mathrm{s}}^{-1}$.

Determine the maximum kinetic energy $E_{\mathrm{kmax}}$ of the cylinder.

Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during one period of oscillation $T$.

Outline two reasons why both models predict that the motion is simple harmonic when $a$ is small.

Determine the time period of the system when $a$ is small.

Outline, without calculation, the change to the time period of the system for the model represented by graph B when $a$ is large.

The graph shows for model A the variation with $x$ of elastic potential energy E_p stored in the spring.

Describe the graph for model B.

A simple pendulum and a mass–spring system oscillate with the same time period. The mass of the pendulum bob and the mass on the spring are initially identical. The masses are halved.

What is $\frac{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{pendulum}}{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{mass}–\mathrm{spring} \mathrm{system}}$ when the masses have been changed?

A.  $\frac{\sqrt{2}}{2}$

B.  $1$

C.  $\sqrt{2}$

D.  $2$

Calculate, in m s⁻¹, the maximum velocity of vibration of point P when it is vibrating with a frequency of 195 Hz.

Calculate, in terms of g, the maximum acceleration of P.

Estimate the displacement needed to double the energy of the string.

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?

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?

A mass–spring system oscillates vertically with a period of $T$ at the surface of the Earth. The gravitational field strength at the surface of Mars is $0.3 \text{g}$. What is the period of the same mass–spring system on the surface of Mars?

A.  $0.9T$

B.  $0.3T$

C.  $T$

D.  $3T$

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. $\frac{3\pi }{2}$

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.  $4f x_0$

A particle undergoes simple harmonic motion of period $T$. At time $t=0$ the particle is at its equilibrium position.

What is $t$ when the particle is at its greatest distance from the equilibrium position?

A.  $\frac{T}{8}$

B.  $\frac{T}{2}$

C.  $\frac{3T}{4}$

D.  $T$

A particle undergoes simple harmonic motion of period $T$. At time $t=0$ the particle is at its equilibrium position.

What is $t$ when the particle is at its greatest distance from the equilibrium position?

A.  $\frac{T}{8}$

B.  $\frac{T}{2}$

C.  $\frac{3T}{4}$

D.  $T$

Explain why the magnitude of the emf is related to the amplitude of the ground movement.

Show that the phase difference between the oscillations of the two corks is $\pi$ radians.

The magnitude of the net force on q is given by $\frac{32kQq}{D^3}x$. Explain why the charge q will execute simple harmonic oscillations about C.

The mass of the charge q is 0.025 kg.

Calculate the angular frequency of the oscillations using the data in (a)(ii) and the expression in (b)(i).

The charges Q are replaced by neutral masses M and the charge q by a neutral mass m. The mass m is displaced away from C by a small distance $x$ and released. Discuss whether the motion of m will be the same as that of q.

Sketch the phase difference between the oscillations of the two corks is $\pi$ radians.

Which graph represents the variation with displacement of the potential energy P and the total energy T of a system undergoing simple harmonic motion (SHM)?

A simple pendulum oscillates with frequency $f$. The length of the pendulum is halved. What is the new frequency of the pendulum?

A.  $2f$

B.  $\sqrt{2}f$

C.  $\frac{f}{\sqrt{2}}$

D.  $\frac{f}{2}$

A mass oscillating in simple harmonic motion on the end of a spring has an amplitude $x$₀ and a total energy E_T. The mass on the spring is doubled and made to oscillate with the same amplitude $x$₀.

What is the total energy of the oscillating system after the change?

A.  E_T

B.  $\sqrt{2}$E_T

C.  2E_T

D.  4E_T

A particle undergoes simple harmonic motion of period $T$. At time $t=0$ the particle is at its equilibrium position.

What is $t$ when the particle is at its greatest distance from the equilibrium position?

A.  $\frac{T}{8}$

B.  $\frac{T}{2}$

C.  $\frac{3T}{4}$

D.  $T$

A particle undergoes simple harmonic motion of period $T$. At time $t=0$ the particle is at its equilibrium position.

What is $t$ when the particle is at its greatest distance from the equilibrium position?

A.  $\frac{T}{8}$

B.  $\frac{T}{2}$

C.  $\frac{3T}{4}$

D.  $T$

A particle undergoes simple harmonic motion of period $T$. At time $t=0$ the particle is at its equilibrium position.

What is $t$ when the particle is at its greatest distance from the equilibrium position?

A.  $\frac{T}{8}$

B.  $\frac{T}{2}$

C.  $\frac{3T}{4}$

D.  $T$

The four pendulums shown have been cut from the same uniform sheet of board. They are attached to the ceiling with strings of equal length.

Which pendulum has the shortest period?

A simple pendulum has a time period $T$ on the Earth. The pendulum is taken to the Moon where the gravitational field strength is $\frac{1}{6}$ that of the Earth.

What is the time period of the pendulum on the Moon?

A.  $T\sqrt{6}$

B.  $T$

C.  $\frac{\sqrt{6}}{6}T$

D.  $\frac{T}{6}$

Calculate the period of oscillations of q.

Calculate the period of oscillations of q.

An object undergoes simple harmonic motion (shm) of amplitude $x$₀. When the displacement of the object is $\frac{x_0}{3}$, the speed of the object is $v$. What is the speed when the displacement is $x$₀?

A. 0

B. $\frac{v}{3}$

C. $\frac{\sqrt{2}}{3}v$

D. $3v$

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

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

An object at the end of a spring oscillates vertically with simple harmonic motion (shm). The graph shows the variation with time $t$ of the displacement $x$ of the object.

What is the velocity of the object?

A. $-\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

B. $\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

C. $-\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$

D. $\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$ 

A plate performs simple harmonic oscillations with a frequency of 39 Hz and an amplitude of 8.0 cm.

Show that the maximum speed of the oscillating plate is about 20 m s⁻¹.

A plate performs simple harmonic oscillations with a frequency of 39 Hz and an amplitude of 8.0 cm.

Show that the maximum speed of the oscillating plate is about 20 m s⁻¹.

Outline why the cylinder performs simple harmonic motion when released.

The mass of the cylinder is $118 \mathrm{kg}$ and the cross-sectional area of the cylinder is $2.29\times {10}^{-1} {\mathrm{m}}^2$. The density of water is $1.03\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. Show that the angular frequency of oscillation of the cylinder is about $4.4 \mathrm{rad} {\mathrm{s}}^{-1}$.

Determine the maximum kinetic energy $E_{\mathrm{kmax}}$ of the cylinder.

Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during one period of oscillation $T$.

Outline why the cylinder performs simple harmonic motion when released.

The mass of the cylinder is $118 \mathrm{kg}$ and the cross-sectional area of the cylinder is $2.29\times {10}^{-1} {\mathrm{m}}^2$. The density of water is $1.03\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. Show that the angular frequency of oscillation of the cylinder is about $4.4 \mathrm{rad} {\mathrm{s}}^{-1}$.

Determine the maximum kinetic energy $E_{\mathrm{kmax}}$ of the cylinder.

Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during one period of oscillation $T$.

Outline two reasons why both models predict that the motion is simple harmonic when $a$ is small.

Determine the time period of the system when $a$ is small.

Outline, without calculation, the change to the time period of the system for the model represented by graph B when $a$ is large.

The graph shows for model A the variation with $x$ of elastic potential energy E_p stored in the spring.

Describe the graph for model B.

Outline two reasons why both models predict that the motion is simple harmonic when $a$ is small.

Determine the time period of the system when $a$ is small.

Outline, without calculation, the change to the time period of the system for the model represented by graph B when $a$ is large.

The graph shows for model A the variation with $x$ of elastic potential energy E_p stored in the spring.

Describe the graph for model B.

A simple pendulum and a mass–spring system oscillate with the same time period. The mass of the pendulum bob and the mass on the spring are initially identical. The masses are halved.

What is $\frac{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{pendulum}}{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{mass}–\mathrm{spring} \mathrm{system}}$ when the masses have been changed?

A.  $\frac{\sqrt{2}}{2}$

B.  $1$

C.  $\sqrt{2}$

D.  $2$

Calculate, in m s⁻¹, the maximum velocity of vibration of point P when it is vibrating with a frequency of 195 Hz.

Calculate, in terms of g, the maximum acceleration of P.

Estimate the displacement needed to double the energy of the string.

Calculate, in m s⁻¹, the maximum velocity of vibration of point P when it is vibrating with a frequency of 195 Hz.

Calculate, in terms of g, the maximum acceleration of P.

Estimate the displacement needed to double the energy of the string.

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?

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?

A mass–spring system oscillates vertically with a period of $T$ at the surface of the Earth. The gravitational field strength at the surface of Mars is $0.3 \text{g}$. What is the period of the same mass–spring system on the surface of Mars?

A.  $0.9T$

B.  $0.3T$

C.  $T$

D.  $3T$

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. $\frac{3\pi }{2}$

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.  $4f x_0$

A particle undergoes simple harmonic motion of period $T$. At time $t=0$ the particle is at its equilibrium position.

What is $t$ when the particle is at its greatest distance from the equilibrium position?

A.  $\frac{T}{8}$

B.  $\frac{T}{2}$

C.  $\frac{3T}{4}$

D.  $T$

A particle undergoes simple harmonic motion of period $T$. At time $t=0$ the particle is at its equilibrium position.

What is $t$ when the particle is at its greatest distance from the equilibrium position?

A.  $\frac{T}{8}$

B.  $\frac{T}{2}$

C.  $\frac{3T}{4}$

D.  $T$

Explain why the magnitude of the emf is related to the amplitude of the ground movement.

Explain why the magnitude of the emf is related to the amplitude of the ground movement.

Show that the phase difference between the oscillations of the two corks is $\pi$ radians.

Show that the phase difference between the oscillations of the two corks is $\pi$ radians.

The magnitude of the net force on q is given by $\frac{32kQq}{D^3}x$. Explain why the charge q will execute simple harmonic oscillations about C.

The mass of the charge q is 0.025 kg.

Calculate the angular frequency of the oscillations using the data in (a)(ii) and the expression in (b)(i).

The charges Q are replaced by neutral masses M and the charge q by a neutral mass m. The mass m is displaced away from C by a small distance $x$ and released. Discuss whether the motion of m will be the same as that of q.

The magnitude of the net force on q is given by $\frac{32kQq}{D^3}x$. Explain why the charge q will execute simple harmonic oscillations about C.

The mass of the charge q is 0.025 kg.

Calculate the angular frequency of the oscillations using the data in (a)(ii) and the expression in (b)(i).

The charges Q are replaced by neutral masses M and the charge q by a neutral mass m. The mass m is displaced away from C by a small distance $x$ and released. Discuss whether the motion of m will be the same as that of q.

Sketch the phase difference between the oscillations of the two corks is $\pi$ radians.

Sketch the phase difference between the oscillations of the two corks is $\pi$ radians.

Which graph represents the variation with displacement of the potential energy P and the total energy T of a system undergoing simple harmonic motion (SHM)?

A simple pendulum oscillates with frequency $f$. The length of the pendulum is halved. What is the new frequency of the pendulum?

A.  $2f$

B.  $\sqrt{2}f$

C.  $\frac{f}{\sqrt{2}}$

D.  $\frac{f}{2}$

A mass oscillating in simple harmonic motion on the end of a spring has an amplitude $x$₀ and a total energy E_T. The mass on the spring is doubled and made to oscillate with the same amplitude $x$₀.

What is the total energy of the oscillating system after the change?

A.  E_T

B.  $\sqrt{2}$E_T

C.  2E_T

D.  4E_T

A particle undergoes simple harmonic motion of period $T$. At time $t=0$ the particle is at its equilibrium position.

What is $t$ when the particle is at its greatest distance from the equilibrium position?

A.  $\frac{T}{8}$

B.  $\frac{T}{2}$

C.  $\frac{3T}{4}$

D.  $T$

A particle undergoes simple harmonic motion of period $T$. At time $t=0$ the particle is at its equilibrium position.

What is $t$ when the particle is at its greatest distance from the equilibrium position?

A.  $\frac{T}{8}$

B.  $\frac{T}{2}$

C.  $\frac{3T}{4}$

D.  $T$

A particle undergoes simple harmonic motion of period $T$. At time $t=0$ the particle is at its equilibrium position.

What is $t$ when the particle is at its greatest distance from the equilibrium position?

A.  $\frac{T}{8}$

B.  $\frac{T}{2}$

C.  $\frac{3T}{4}$

D.  $T$

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

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

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

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

Calculate, in m s^–1, the speed for this wave.

Calculate, in Hz, the frequency for this wave.

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.  $2\lambda$

Show that the speed of the wave on the string is about 240 m s⁻¹.

Show that the speed of the wave on the string is about 240 m s⁻¹.

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.  $300 \mathrm{m} {\mathrm{s}}^{-1}$

The graph shows the variation with distance $x$ of the displacement of the particles in a wave. The frequency of the wave is 600 Hz.

What is the speed of the wave?

A.  0.012 m s⁻¹

B.  0.024 m s⁻¹

C.  1.2 m s⁻¹

D.  2.4 m s⁻¹

Calculate the speed of waves on the string.

Calculate the speed of waves on the string.

Sketch on the diagram the position of P at time t = 0.50 s.

Plot on the diagram the position of P at time t = 0.50 s.

A longitudinal wave is travelling through a medium. The variation with distance d of the displacement $x$ of the particles in the medium at time t is shown.

Which point is at the centre of a compression?

A longitudinal wave is travelling through a medium. The variation with distance d of the displacement $x$ of the particles in the medium at time t is shown.

Which point is at the centre of a compression?

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

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

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

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

Calculate, in m s^–1, the speed for this wave.

Calculate, in Hz, the frequency for this wave.

Calculate, in m s^–1, the speed for this wave.

Calculate, in Hz, the frequency for this wave.

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.  $2\lambda$

Show that the speed of the wave on the string is about 240 m s⁻¹.

Show that the speed of the wave on the string is about 240 m s⁻¹.

Show that the speed of the wave on the string is about 240 m s⁻¹.

Show that the speed of the wave on the string is about 240 m s⁻¹.

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.  $300 \mathrm{m} {\mathrm{s}}^{-1}$

The graph shows the variation with distance $x$ of the displacement of the particles in a wave. The frequency of the wave is 600 Hz.

What is the speed of the wave?

A.  0.012 m s⁻¹

B.  0.024 m s⁻¹

C.  1.2 m s⁻¹

D.  2.4 m s⁻¹

Calculate the speed of waves on the string.

Calculate the speed of waves on the string.

Calculate the speed of waves on the string.

Calculate the speed of waves on the string.

Sketch on the diagram the position of P at time t = 0.50 s.

Sketch on the diagram the position of P at time t = 0.50 s.

Plot on the diagram the position of P at time t = 0.50 s.

Plot on the diagram the position of P at time t = 0.50 s.

A longitudinal wave is travelling through a medium. The variation with distance d of the displacement $x$ of the particles in the medium at time t is shown.

Which point is at the centre of a compression?

A longitudinal wave is travelling through a medium. The variation with distance d of the displacement $x$ of the particles in the medium at time t is shown.

Which point is at the centre of a compression?

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?

Explain why the received intensity varies between maximum and minimum values.

B is placed at the first minimum. The frequency is then changed until the received intensity is again at a maximum.

Show that the lowest frequency at which the intensity maximum can occur is about 3 kHz.

Speed of sound = 340 m s⁻¹

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

Explain why the received intensity varies between maximum and minimum values.

B is placed at the first minimum. The frequency is then changed until the received intensity is again at a maximum.

Show that the lowest frequency at which the intensity maximum can occur is about 3 kHz.

Speed of sound = 340 m s⁻¹

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.  $\sin \theta =\frac{1}{n_2}$

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.  $\frac{7\lambda }{2}$

Light of wavelength $\lambda$ is diffracted after passing through a very narrow single slit of width $x$. The intensity of the central maximum of the diffracted light is $I_0$. The slit width is doubled.

What is the intensity of central maximum and the angular position of the first minimum?

Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.

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. $4y$

Estimate, using the graph, the radius of a carbon-12 nucleus.

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

Light of wavelength λ is normally incident on a diffraction grating of spacing 3λ. What is the angle between the two second-order maxima?

A.  ${\sin }^{-1}\frac{2}{3}$

B.  ${\sin }^{-1}\frac{4}{3}$

C.  $2{\sin }^{-1}\frac{2}{3}$

D.  >90° so no second orders appear

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

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.  $\frac{\sin 60°}{\sin 45°}$

The separation of adjacent slits is d. Show that for the second-order diffraction maximum $2\lambda =d\sin \theta$.

Monochromatic light of wavelength 633 nm is normally incident on a diffraction grating. The diffraction maxima incident on a screen are detected and their angle θ to the central beam is determined. The graph shows the variation of sinθ with the order n of the maximum. The central order corresponds to n = 0.

Determine a mean value for the number of slits per millimetre of the grating.

The diagram shows the diffraction pattern for light passing through a single slit.

What is

                                      $\frac{\text{wavelength of light}}{\text{width of slit}}$

A. 0.01

B. 0.02

C. 1

D. 2

Monochromatic light of wavelength $\lambda$ passes through a single-slit of width $b$ and produces a diffraction pattern on a screen. Which combination of changes to $b$ and $\lambda$ will cause the greatest decrease in the width of the central maximum?

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

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.  $3$

The speed of sound in air is 340 m s⁻¹ and in water it is 1500 m s⁻¹.

Discuss whether the sound wave can enter the water.

The intensity of light at point O is $I_0$. The distance OP is $x$.

Sketch, on the axes, a graph to show the variation of the intensity of light with distance from point O on the screen. Your graph should cover the distance range from 0 to 2$x$.

A ray of light enters from air into a water droplet of radius $r$ at point S. S is a vertical distance $h$ from the centre of the droplet. The droplet has a refractive index $n$ and the angle of refraction is θ.

What is sin θ?

A.  $\frac{nh}{r}$

B.  $\frac{r}{nh}$

C.  $\frac{h}{nr}$

D.  $\frac{nr}{h}$

Show that, when sound travels from clay to sandstone, the critical angle is approximately 40°.

The angle between the clay–air surface and path 1 is 80°.

Draw, on the diagram, the subsequent path of a sound wave that travels initially in the clay along path 1.

Monochromatic light is incident on two very narrow slits. The light that passes through the slits is observed on a screen. M is directly opposite the midpoint of the slits. $x$ represents the displacement from M in the direction shown.

A student argues that what will be observed on the screen will be a total of two bright spots opposite the slits. Explain why the student’s argument is incorrect.

The graph shows the actual variation with displacement $x$ from M of the intensity of the light on the screen. $I_0$ is the intensity of light at the screen from one slit only.

Explain why the intensity of light at $x$ = 0 is 4 $I_0$.

The slits are separated by a distance of 0.18 mm and the distance to the screen is 2.2 m. Determine, in m, the wavelength of light.

The two slits are replaced by many slits of the same separation. State one feature of the intensity pattern that will remain the same and one that will change.

Stays the same:

Changes:

Monochromatic light is incident on two very narrow slits. The light that passes through the slits is observed on a screen. M is directly opposite the midpoint of the slits. $x$ represents the displacement from M in the direction shown.

A student argues that what will be observed on the screen will be a total of two bright spots opposite the slits. Explain why the student’s argument is incorrect.

The graph shows the actual variation with displacement $x$ from M of the intensity of the light on the screen. $I_0$ is the intensity of light at the screen from one slit only.

The slits are separated by a distance of 0.18 mm and the distance to the screen is 2.2 m. Determine, in m, the wavelength of light.

Explain the pattern seen on the screen.

Calculate, in nm, $\lambda$.

The student changes the light source to one that emits two colours:
• blue light of wavelength $\lambda$, and
• red light of wavelength 1.5$\lambda$.

Predict the pattern that the student will see on the screen.

Explain the pattern seen on the screen.

Calculate, in nm, $\lambda$.

The student changes the light source to one that emits two colours:
• blue light of wavelength $\lambda$, and
• red light of wavelength 1.5$\lambda$.

Predict the pattern that the student will see on the screen.

A group of students perform an experiment to find the refractive index of a glass block. They measure various values of the angle of incidence i and angle of refraction r for a ray entering the glass from air. They plot a graph of the sin r against sin i.

They determine the gradient of the graph to be m.

Which of the following gives the critical angle of the glass?

A.  sin⁻¹(m)

B.  sin⁻¹$\left(\frac{1}{m}\right)$

C.  m

D.  $\frac{1}{m}$

Two identical sources oscillate in phase and produce constructive interference at a point P. The intensity recorded at P is I.

What is the intensity at P from one source?

A.  $\sqrt{2}$I
B.  I

C.  $\frac{I}{2}$

D.  $\frac{I}{4}$

A group of students perform an experiment to find the refractive index of a glass block. They measure various values of the angle of incidence i and angle of refraction r for a ray entering the glass from air. They plot a graph of the sin r against sin i.

They determine the gradient of the graph to be m.

Which of the following gives the critical angle of the glass?

A.  sin⁻¹(m)

B.  sin⁻¹$\left(\frac{1}{m}\right)$

C.  m

D.  $\frac{1}{m}$

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?

Explain why the received intensity varies between maximum and minimum values.

B is placed at the first minimum. The frequency is then changed until the received intensity is again at a maximum.

Show that the lowest frequency at which the intensity maximum can occur is about 3 kHz.

Speed of sound = 340 m s⁻¹

Explain why the received intensity varies between maximum and minimum values.

B is placed at the first minimum. The frequency is then changed until the received intensity is again at a maximum.

Show that the lowest frequency at which the intensity maximum can occur is about 3 kHz.

Speed of sound = 340 m s⁻¹

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

Explain why the received intensity varies between maximum and minimum values.

B is placed at the first minimum. The frequency is then changed until the received intensity is again at a maximum.

Show that the lowest frequency at which the intensity maximum can occur is about 3 kHz.

Speed of sound = 340 m s⁻¹

Explain why the received intensity varies between maximum and minimum values.

B is placed at the first minimum. The frequency is then changed until the received intensity is again at a maximum.

Show that the lowest frequency at which the intensity maximum can occur is about 3 kHz.

Speed of sound = 340 m s⁻¹

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.  $\sin \theta =\frac{1}{n_2}$

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.  $\frac{7\lambda }{2}$

Light of wavelength $\lambda$ is diffracted after passing through a very narrow single slit of width $x$. The intensity of the central maximum of the diffracted light is $I_0$. The slit width is doubled.

What is the intensity of central maximum and the angular position of the first minimum?

Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.

Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.

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. $4y$

Estimate, using the graph, the radius of a carbon-12 nucleus.

Estimate, using the graph, the radius of a carbon-12 nucleus.

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

Light of wavelength λ is normally incident on a diffraction grating of spacing 3λ. What is the angle between the two second-order maxima?

A.  ${\sin }^{-1}\frac{2}{3}$

B.  ${\sin }^{-1}\frac{4}{3}$

C.  $2{\sin }^{-1}\frac{2}{3}$

D.  >90° so no second orders appear

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

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.  $\frac{\sin 60°}{\sin 45°}$

The separation of adjacent slits is d. Show that for the second-order diffraction maximum $2\lambda =d\sin \theta$.

Monochromatic light of wavelength 633 nm is normally incident on a diffraction grating. The diffraction maxima incident on a screen are detected and their angle θ to the central beam is determined. The graph shows the variation of sinθ with the order n of the maximum. The central order corresponds to n = 0.

Determine a mean value for the number of slits per millimetre of the grating.

The separation of adjacent slits is d. Show that for the second-order diffraction maximum $2\lambda =d\sin \theta$.

Monochromatic light of wavelength 633 nm is normally incident on a diffraction grating. The diffraction maxima incident on a screen are detected and their angle θ to the central beam is determined. The graph shows the variation of sinθ with the order n of the maximum. The central order corresponds to n = 0.

Determine a mean value for the number of slits per millimetre of the grating.

The diagram shows the diffraction pattern for light passing through a single slit.

What is

                                      $\frac{\text{wavelength of light}}{\text{width of slit}}$

A. 0.01

B. 0.02

C. 1

D. 2

Monochromatic light of wavelength $\lambda$ passes through a single-slit of width $b$ and produces a diffraction pattern on a screen. Which combination of changes to $b$ and $\lambda$ will cause the greatest decrease in the width of the central maximum?

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

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.  $3$

The speed of sound in air is 340 m s⁻¹ and in water it is 1500 m s⁻¹.

Discuss whether the sound wave can enter the water.

The speed of sound in air is 340 m s⁻¹ and in water it is 1500 m s⁻¹.

Discuss whether the sound wave can enter the water.

The intensity of light at point O is $I_0$. The distance OP is $x$.

Sketch, on the axes, a graph to show the variation of the intensity of light with distance from point O on the screen. Your graph should cover the distance range from 0 to 2$x$.

The intensity of light at point O is $I_0$. The distance OP is $x$.

Sketch, on the axes, a graph to show the variation of the intensity of light with distance from point O on the screen. Your graph should cover the distance range from 0 to 2$x$.

A ray of light enters from air into a water droplet of radius $r$ at point S. S is a vertical distance $h$ from the centre of the droplet. The droplet has a refractive index $n$ and the angle of refraction is θ.

What is sin θ?

A.  $\frac{nh}{r}$

B.  $\frac{r}{nh}$

C.  $\frac{h}{nr}$

D.  $\frac{nr}{h}$

Show that, when sound travels from clay to sandstone, the critical angle is approximately 40°.

The angle between the clay–air surface and path 1 is 80°.

Draw, on the diagram, the subsequent path of a sound wave that travels initially in the clay along path 1.

Show that, when sound travels from clay to sandstone, the critical angle is approximately 40°.

The angle between the clay–air surface and path 1 is 80°.

Draw, on the diagram, the subsequent path of a sound wave that travels initially in the clay along path 1.

Monochromatic light is incident on two very narrow slits. The light that passes through the slits is observed on a screen. M is directly opposite the midpoint of the slits. $x$ represents the displacement from M in the direction shown.

A student argues that what will be observed on the screen will be a total of two bright spots opposite the slits. Explain why the student’s argument is incorrect.

The graph shows the actual variation with displacement $x$ from M of the intensity of the light on the screen. $I_0$ is the intensity of light at the screen from one slit only.

Explain why the intensity of light at $x$ = 0 is 4 $I_0$.

The slits are separated by a distance of 0.18 mm and the distance to the screen is 2.2 m. Determine, in m, the wavelength of light.

The two slits are replaced by many slits of the same separation. State one feature of the intensity pattern that will remain the same and one that will change.

Stays the same:

Changes:

Monochromatic light is incident on two very narrow slits. The light that passes through the slits is observed on a screen. M is directly opposite the midpoint of the slits. $x$ represents the displacement from M in the direction shown.

A student argues that what will be observed on the screen will be a total of two bright spots opposite the slits. Explain why the student’s argument is incorrect.

The graph shows the actual variation with displacement $x$ from M of the intensity of the light on the screen. $I_0$ is the intensity of light at the screen from one slit only.

Explain why the intensity of light at $x$ = 0 is 4 $I_0$.

The slits are separated by a distance of 0.18 mm and the distance to the screen is 2.2 m. Determine, in m, the wavelength of light.

The two slits are replaced by many slits of the same separation. State one feature of the intensity pattern that will remain the same and one that will change.

Stays the same:

Changes:

Explain why the intensity of light at $x$ = 0 is 4 $I_0$.

The slits are separated by a distance of 0.18 mm and the distance to the screen is 2.2 m. Determine, in m, the wavelength of light.

The two slits are replaced by many slits of the same separation. State one feature of the intensity pattern that will remain the same and one that will change.

Stays the same:

Changes:

Monochromatic light is incident on two very narrow slits. The light that passes through the slits is observed on a screen. M is directly opposite the midpoint of the slits. $x$ represents the displacement from M in the direction shown.

A student argues that what will be observed on the screen will be a total of two bright spots opposite the slits. Explain why the student’s argument is incorrect.

The graph shows the actual variation with displacement $x$ from M of the intensity of the light on the screen. $I_0$ is the intensity of light at the screen from one slit only.

The slits are separated by a distance of 0.18 mm and the distance to the screen is 2.2 m. Determine, in m, the wavelength of light.

Monochromatic light is incident on two very narrow slits. The light that passes through the slits is observed on a screen. M is directly opposite the midpoint of the slits. $x$ represents the displacement from M in the direction shown.

A student argues that what will be observed on the screen will be a total of two bright spots opposite the slits. Explain why the student’s argument is incorrect.

The graph shows the actual variation with displacement $x$ from M of the intensity of the light on the screen. $I_0$ is the intensity of light at the screen from one slit only.

The slits are separated by a distance of 0.18 mm and the distance to the screen is 2.2 m. Determine, in m, the wavelength of light.

Explain the pattern seen on the screen.

Calculate, in nm, $\lambda$.

The student changes the light source to one that emits two colours:
• blue light of wavelength $\lambda$, and
• red light of wavelength 1.5$\lambda$.

Predict the pattern that the student will see on the screen.

Explain the pattern seen on the screen.

Calculate, in nm, $\lambda$.

The student changes the light source to one that emits two colours:
• blue light of wavelength $\lambda$, and
• red light of wavelength 1.5$\lambda$.

Predict the pattern that the student will see on the screen.

Explain the pattern seen on the screen.

Calculate, in nm, $\lambda$.

The student changes the light source to one that emits two colours:
• blue light of wavelength $\lambda$, and
• red light of wavelength 1.5$\lambda$.

Predict the pattern that the student will see on the screen.

Explain the pattern seen on the screen.

Calculate, in nm, $\lambda$.

The student changes the light source to one that emits two colours:
• blue light of wavelength $\lambda$, and
• red light of wavelength 1.5$\lambda$.

Predict the pattern that the student will see on the screen.

A group of students perform an experiment to find the refractive index of a glass block. They measure various values of the angle of incidence i and angle of refraction r for a ray entering the glass from air. They plot a graph of the sin r against sin i.

They determine the gradient of the graph to be m.

Which of the following gives the critical angle of the glass?

A.  sin⁻¹(m)

B.  sin⁻¹$\left(\frac{1}{m}\right)$

C.  m

D.  $\frac{1}{m}$

Two identical sources oscillate in phase and produce constructive interference at a point P. The intensity recorded at P is I.

What is the intensity at P from one source?

A.  $\sqrt{2}$I
B.  I

C.  $\frac{I}{2}$

D.  $\frac{I}{4}$

A group of students perform an experiment to find the refractive index of a glass block. They measure various values of the angle of incidence i and angle of refraction r for a ray entering the glass from air. They plot a graph of the sin r against sin i.

They determine the gradient of the graph to be m.

Which of the following gives the critical angle of the glass?

A.  sin⁻¹(m)

B.  sin⁻¹$\left(\frac{1}{m}\right)$

C.  m

D.  $\frac{1}{m}$

Adjacent minima are separated by a distance of 0.12 m. Calculate $f$.

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

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 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. $\frac{3\pi }{2}\text{rad}$

Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.

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

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.  $2\mathrm{\pi }$

The string is made to vibrate in its third harmonic. State the distance between consecutive nodes. 

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

The tube is raised until the loudness of the sound reaches a maximum for a second time.

Draw, on the following diagram, the position of the nodes in the tube when the second maximum is heard.

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⁻¹. Determine the frequency of the sound emitted by the loudspeaker.

A standing wave is formed in a pipe closed at one end. The third harmonic has a frequency of 400 Hz when the speed of sound is 300 m s⁻¹. What is the length of the pipe?

A.  $\frac{3}{16}$ m

B.  $\frac{9}{16}$ m

C.  $\frac{3}{4}$ m

D.  $\frac{14}{16}$ m

The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.

The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.

A standing wave is formed in a pipe open at one end and closed at the other. The length of the pipe is L and the speed of sound in the pipe is V.

n is a positive integer.

What expression is correct about the frequencies of the harmonics in the pipe?

A.  $\frac{(2n-1)V}{2L}$

B.  $\frac{(2n-1)V}{4L}$

C.  $\frac{nV}{2L}$

D.  $\frac{nV}{4L}$

A standing wave with a first harmonic of frequency $f_1$ is formed on a string fixed at both ends.

The frequency of the third harmonic is $f_3$.

What is $\frac{f_1}{f_3}$?

A.  3

B.  $\frac{3}{2}$

C.  $\frac{2}{3}$

D.  $\frac{1}{3}$

A standing wave is formed between two loudspeakers that emit sound waves of frequency $f$.

A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is 1.5 m. The speed of sound is 300 m s⁻¹.

What is $f$?

A.  400 Hz

B.  200 Hz

C.  100 Hz

D.  50 Hz

Adjacent minima are separated by a distance of 0.12 m. Calculate $f$.

Adjacent minima are separated by a distance of 0.12 m. Calculate $f$.

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

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 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. $\frac{3\pi }{2}\text{rad}$

Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.

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

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.  $2\mathrm{\pi }$

The string is made to vibrate in its third harmonic. State the distance between consecutive nodes. 

The string is made to vibrate in its third harmonic. State the distance between consecutive nodes. 

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

The tube is raised until the loudness of the sound reaches a maximum for a second time.

Draw, on the following diagram, the position of the nodes in the tube when the second maximum is heard.

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⁻¹. Determine the frequency of the sound emitted by the loudspeaker.

The tube is raised until the loudness of the sound reaches a maximum for a second time.

Draw, on the following diagram, the position of the nodes in the tube when the second maximum is heard.

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⁻¹. Determine the frequency of the sound emitted by the loudspeaker.

A standing wave is formed in a pipe closed at one end. The third harmonic has a frequency of 400 Hz when the speed of sound is 300 m s⁻¹. What is the length of the pipe?

A.  $\frac{3}{16}$ m

B.  $\frac{9}{16}$ m

C.  $\frac{3}{4}$ m

D.  $\frac{14}{16}$ m

The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.

The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.

The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.

The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.

A standing wave is formed in a pipe open at one end and closed at the other. The length of the pipe is L and the speed of sound in the pipe is V.

n is a positive integer.

What expression is correct about the frequencies of the harmonics in the pipe?

A.  $\frac{(2n-1)V}{2L}$

B.  $\frac{(2n-1)V}{4L}$

C.  $\frac{nV}{2L}$

D.  $\frac{nV}{4L}$

A standing wave with a first harmonic of frequency $f_1$ is formed on a string fixed at both ends.

The frequency of the third harmonic is $f_3$.

What is $\frac{f_1}{f_3}$?

A.  3

B.  $\frac{3}{2}$

C.  $\frac{2}{3}$

D.  $\frac{1}{3}$

A standing wave is formed between two loudspeakers that emit sound waves of frequency $f$.

A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is 1.5 m. The speed of sound is 300 m s⁻¹.

What is $f$?

A.  400 Hz

B.  200 Hz

C.  100 Hz

D.  50 Hz

Loudspeaker A is switched off. Loudspeaker B moves away from M at a speed of 1.5 m s⁻¹ while emitting a frequency of 3.0 kHz.

Determine the difference between the frequency detected at M and that emitted by B.

Sound of frequency 2400 Hz is emitted from a stationary source towards the oscillating plate in (b). The speed of sound is 340 m s⁻¹.

Determine the maximum frequency of the sound that is received back at the source after reflection at the plate.

A train is moving in a straight line away from a stationary observer when the train horn emits a sound of frequency $f_0$. The speed of the train is $0.10v$ where $v$ is the speed of sound. What is the frequency of the horn as heard by the observer?

A.  $\frac{0.9}{1}{f}_0$

B.  $\frac{1}{1.1}{f}_0$

C.  $\frac{1.1}{1}{f}_0$

D.  $\frac{1}{0.9}{f}_0$

Source S produces sound waves of speed v and frequency $f$. S moves with constant velocity $\frac{v}{5}$ away from a stationary observer.

What is the frequency measured by the observer?

A.  $\frac{4}{5}f$

B.  $\frac{5}{6}f$

C.  $\frac{6}{5}f$

D.  $\frac{5}{4}f$

The speed of the tram is measured by detecting a beam of microwaves of wavelength 2.8 cm reflected from the rear of the tram as it moves away from the station. Predict the change in wavelength of the microwaves at the stationary microwave detector in the station.

Loudspeaker A is switched off. Loudspeaker B moves away from M at a speed of 1.5 m s⁻¹ while emitting a frequency of 3.0 kHz.

Determine the difference between the frequency detected at M and that emitted by B.

Loudspeaker A is switched off. Loudspeaker B moves away from M at a speed of 1.5 m s⁻¹ while emitting a frequency of 3.0 kHz.

Determine the difference between the frequency detected at M and that emitted by B.

Sound of frequency 2400 Hz is emitted from a stationary source towards the oscillating plate in (b). The speed of sound is 340 m s⁻¹.

Determine the maximum frequency of the sound that is received back at the source after reflection at the plate.

Sound of frequency 2400 Hz is emitted from a stationary source towards the oscillating plate in (b). The speed of sound is 340 m s⁻¹.

Determine the maximum frequency of the sound that is received back at the source after reflection at the plate.

A train is moving in a straight line away from a stationary observer when the train horn emits a sound of frequency $f_0$. The speed of the train is $0.10v$ where $v$ is the speed of sound. What is the frequency of the horn as heard by the observer?

A.  $\frac{0.9}{1}{f}_0$

B.  $\frac{1}{1.1}{f}_0$

C.  $\frac{1.1}{1}{f}_0$

D.  $\frac{1}{0.9}{f}_0$

Source S produces sound waves of speed v and frequency $f$. S moves with constant velocity $\frac{v}{5}$ away from a stationary observer.

What is the frequency measured by the observer?

A.  $\frac{4}{5}f$

B.  $\frac{5}{6}f$

C.  $\frac{6}{5}f$

D.  $\frac{5}{4}f$

The speed of the tram is measured by detecting a beam of microwaves of wavelength 2.8 cm reflected from the rear of the tram as it moves away from the station. Predict the change in wavelength of the microwaves at the stationary microwave detector in the station.

The speed of the tram is measured by detecting a beam of microwaves of wavelength 2.8 cm reflected from the rear of the tram as it moves away from the station. Predict the change in wavelength of the microwaves at the stationary microwave detector in the station.