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

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

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

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$\pi$

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

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

Calculate, in Hz, the frequency for this wave.

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

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.

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 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.  $2\lambda$

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

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

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

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.

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.

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

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

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 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.

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

Calculate the wavelength of the wave.

Calculate the wavelength of the wave.

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