DP Physics Questionbank

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

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?

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?

Outline the conditions necessary for simple harmonic motion (SHM) to occur.

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?

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?

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?

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

Outline why the ball will perform simple harmonic oscillations about the equilibrium position.

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

The wave is incident at point Q on the metal–air boundary. The wave makes an angle of 54° with the normal at Q. The speed of sound in the metal is 6010 m s^–1 and the speed of sound in air is 340 m s^–1. Calculate the angle between the normal at Q and the direction of the wave in air.

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. $\frac{3\pi }{2}$

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

The wave is incident at point Q on the metal–air boundary. The wave makes an angle of 54° with the normal at Q. The speed of sound in the metal is 6010 m s^–1 and the speed of sound in air is 340 m s^–1. Calculate the angle between the normal at Q and the direction of the wave in air.

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.  $300 \mathrm{m} {\mathrm{s}}^{-1}$

Outline why the cylinder performs simple harmonic motion when released.

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 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.  $4f x_0$

State the phase difference between the two waves.

State the phase difference between the two waves.

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

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$\pi$

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

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. $2\pi$

A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.

Outline why the beam has to be coherent in order for the fringes to be visible.

A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.

The wavelength of the beam as observed on Earth is 633.0 nm. The separation between a dark and a bright fringe on the screen is 4.50 mm. Calculate D.

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

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

The speed of sound c for longitudinal waves in air is given by

$c=\sqrt{\frac{K}{\rho }}$

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m^–3. Determine, in kg m^–1 s^–2, the value of K for air.

The speed of sound c for longitudinal waves in air is given by

$c=\sqrt{\frac{K}{\rho }}$

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m^–3. Determine the value of K for air. State your answer with the appropriate fundamental (SI) unit.

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

Calculate, in Hz, the frequency for this wave.

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.  $300 \mathrm{m} {\mathrm{s}}^{-1}$

Deduce that a minimum intensity of sound is heard at P.

Deduce that a minimum intensity of sound is heard at P.

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

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.

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

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

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.  $2\lambda$

Calculate the wavelength of the wave.

Calculate the wavelength of the wave.

Determine, for particle P, the magnitude and direction of the acceleration at t = 2.0 m s.

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

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

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

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

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 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

Radio waves are emitted by a straight conducting rod antenna (aerial). The plane of polarization of these waves is parallel to the transmitting antenna.

An identical antenna is used for reception. Suggest why the receiving antenna needs to be be parallel to the transmitting antenna.

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?

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Calculate the wavelength measured by the observer.

The microwaves emitted by the transmitter are horizontally polarized. The microwave receiver contains a polarizing filter. When the receiver is at position W it detects a maximum intensity.

The receiver is then rotated through 180° about the horizontal dotted line passing through the microwave transmitter. Sketch a graph on the axes provided to show the variation of received intensity with rotation angle.

When both loudspeakers are operating, the intensity of sound recorded at Q is $I_0$. Loudspeaker B is now disconnected. Loudspeaker A continues to emit sound with unchanged amplitude and frequency. The intensity of sound recorded at Q changes to $I_{\mathrm{A}}$.

Estimate $\frac{I_{\mathrm{A}}}{I_0}$.

When both loudspeakers are operating, the intensity of sound recorded at Q is $I_0$. Loudspeaker B is now disconnected. Loudspeaker A continues to emit sound with unchanged amplitude and frequency. The intensity of sound recorded at Q changes to $I_{\mathrm{A}}$.

Estimate $\frac{I_{\mathrm{A}}}{I_0}$.

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.  $I_1$

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

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.  $180°$

Show that the intensity of the solar radiation at the location of Titan is 16 W m⁻²

Show that the intensity of the solar radiation at the location of Titan is 16 W m⁻².

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 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 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?

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

Red laser light is incident on a double slit with a slit separation of 0.35 mm.
A double-slit interference pattern is observed on a screen 2.4 m from the slits.
The distance between successive maxima on the screen is 4.7 mm.

Calculate the wavelength of the light. Give your answer to an appropriate number of significant figures.

The slits are separated by 1.5 mm and the laser light has a wavelength of 6.3 x 10^–7 m. The slits are 5.0 m from the train track. Calculate the separation between two adjacent positions of the train when the output voltage is at a maximum.

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. $\frac{29}{15}$

Calculate the speed of light inside the ice cube.

Show that no light emerges from side AB.

The wavelength of the beam as observed on Earth is 633.0 nm. The separation between a dark and a bright fringe on the screen is 4.50 mm. Calculate D.

Calculate the wavelength of the light in water.

State two ways in which the intensity pattern on the screen changes.

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

The wavefronts make an angle θ with the surface of the water. Determine the maximum angle, θ_max, at which the sound can enter water. Give your answer to the correct number of significant figures.

Draw lines on the diagram to complete wavefronts A and B in water for θ < θ_max.

The slits are separated by 1.5 mm and the laser light has a wavelength of 6.3 x 10^–7 m. The slits are 5.0 m from the train track. Calculate the separation between two adjacent positions of the train when the output voltage is at a maximum.

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

The wavefronts make an angle θ with the surface of the water. Determine the maximum angle, θ_max, at which the sound can enter water. Give your answer to the correct number of significant figures.

Draw lines on the diagram to complete wavefronts A and B in water for θ < θ_max.

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

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

Particle P in the metal sheet performs simple harmonic oscillations. When the displacement of P is 3.2 μm the magnitude of its acceleration is 7.9 m s^-2. Calculate the magnitude of the acceleration of P when its displacement is 2.3 μm.

The frequency of the sound wave in the metal is 250 Hz. Determine the wavelength of the wave in air.

P is the first maximum of intensity on one side of M. The following data are available.

d = 0.12 mm

D = 1.5 m

Distance MP = 7.0 mm

Calculate, in nm, the wavelength λ of the light.

Determine the difference between the speed of light corresponding to these two wavelengths in the core glass.

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.

Particle P in the metal sheet performs simple harmonic oscillations. When the displacement of P is 3.2 μm the magnitude of its acceleration is 7.9 m s^-2. Calculate the magnitude of the acceleration of P when its displacement is 2.3 μm.

State the frequency of the wave in air.

Determine the wavelength of the wave in air. 

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. $4y$

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.  $\frac{\sin 60°}{\sin 45°}$

Deduce that a minimum intensity of sound is heard at P.

Deduce that a minimum intensity of sound is heard at P.

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

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 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.  $\frac{7\lambda }{2}$

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

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

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

Outline how the standing wave is formed.

Draw an arrow on the diagram to represent the direction of motion of the molecule at X.

Label a position N that is a node of the standing wave.

The speed of sound is 340 m s^–1 and the length of the pipe is 0.30 m. Calculate, in Hz, the frequency of the sound.

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

Outline how the standing wave is formed.

Draw an arrow on the diagram to represent the direction of motion of the molecule at X.

Label a position N that is a node of the standing wave.

The speed of sound is 340 m s^–1 and the length of the pipe is 0.30 m. Calculate, in Hz, the frequency of the sound.

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

Sketch, on the diagram, the variation of displacement of the air molecules with distance along the pipe when t = $\frac{3}{4f}$.

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. $\frac{3\pi }{2}\text{rad}$

State the frequency of the wave in air.

Determine the wavelength of the wave in air. 

The sound wave in air in (c) enters a pipe that is open at both ends. The diagram shows the displacement, at a particular time T, of the standing wave that is set up in the pipe.

On the diagram, at time T, label with the letter C a point in the pipe that is at the centre of a compression.

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

Calculate the length of the tube.

A particle in the tube has its equilibrium position at the open end of the tube.
State and explain the direction of the velocity of this particle at time $t=\frac{T}{8}$.

Draw on the diagram the standing wave at time $t=\frac{T}{4}$.

Calculate the length of the tube.

A particle in the tube has its equilibrium position at the open end of the tube.
State and explain the direction of the velocity of this particle at time $t=\frac{T}{8}$.

Draw on the diagram the standing wave at time $t=\frac{T}{4}$.

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