1.

This question is about waves and wave properties. (a)

By making reference to waves, distinguish between a ray and a wavefront. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3)

The diagram below shows three wavefronts incident on a boundary between medium I and medium R. Wavefront CD is shown crossing the boundary. Wavefront EF is incomplete. A

C

E

F medium I medium R

B

(b)

(i)

D

On the diagram above, draw a line to complete the wavefront EF. (1)

(ii)

Explain in which medium, I or R, the wave has the higher speed. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3)

1

(iii)

By taking appropriate measurements from the diagram, determine the ratio of the speeds of the wave travelling from medium I to medium R. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2)

The graph below shows the variation with time t of the velocity v of one particle of the medium through which the wave is travelling. 8 6 4 v / ms–1

2 0

0

1

2

3

4

–2

5

6

7 t / ms

–4 –6 –8

(c)

(i)

Explain how it can be deduced from the graph that the particle is oscillating. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2)

(ii)

Determine the frequency of oscillation of the particle. ........................................................................................................................... ........................................................................................................................... (2)

(iii)

Mark on the graph with the letter M one time at which the particle is at maximum displacement. (1)

(iv)

Estimate the area between the curve and the x-axis from the time t = 0 to the time 2

t = 1.5 ms. ........................................................................................................................... ........................................................................................................................... (2)

(v)

Suggest what the area in c (iv) represents. ........................................................................................................................... (1) (Total 17 marks)

2.

This question is about waves and wave motion. (a)

(i)

Define what is meant by the speed of a wave. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2)

(ii)

Light is emitted from a candle flame. Explain why, in this situation, it is correct to refer to the “speed of the emitted light”, rather than its velocity. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2)

(b)

(i)

Define, by reference to wave motion, what is meant by displacement. ........................................................................................................................... ........................................................................................................................... (2)

3

(ii)

By reference to displacement, describe the difference between a longitudinal wave and a transverse wave. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3)

The centre of an earthquake produces both longitudinal waves (P waves) and transverse waves (S waves). The graph below shows the variation with time t of the distance d moved by the two types of wave. d / km

S wave

P wave

1200

800

400

0 0

25

50

75

100

125

150

175

200

225 t/s

(c)

Use the graph to determine the speed of (i)

the P waves. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (1)

4

(ii)

the S waves. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (1)

The waves from an earthquake close to the Earth’s surface are detected at three laboratories L1, L2 and L3. The laboratories are at the corners of a triangle so that each is separated from the others by a distance of 900 km, as shown in the diagram below. 900 km L1

L2

L3

The records of the variation with time of the vibrations produced by the earthquake as detected at the three laboratories are shown below. All three records were started at the same time.

L1 L2

start of trace

L3 time

On each record, one pulse is made by the S wave and the other by the P wave. The separation of the two pulses is referred to as the S-P interval.

5

(d)

(i)

On the trace produced by laboratory L2, identify, by reference to your answers in (c), the pulse due to the P wave (label the pulse P). (1)

(ii)

Using evidence from the records of the earthquake, state which laboratory was closest to the site of the earthquake. ........................................................................................................................... (1)

(iii)

State three separate pieces of evidence for your statement in (d)(ii). (3)

1.

................................................................................................................. .................................................................................................................

2.

................................................................................................................. .................................................................................................................

3.

................................................................................................................. .................................................................................................................

(iv)

The S-P intervals are 68 s, 42 s and 27 s for laboratories L1, L2 and L3 respectively. Use the graph, or otherwise, to determine the distance of the earthquake from each laboratory. Explain your working. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... Distance from L1 = ......................km ........................................................................................................................... Distance from L2 = ......................km ........................................................................................................................... Distance from L3 = ......................km ........................................................................................................................... (4)

6

(v)

Mark on the diagram a possible site of the earthquake. (1)

There is a tall building near to the site of the earthquake, as illustrated below.

building

ground direction of vibrations The base of the building vibrates horizontally due to the earthquake.

(e)

(i)

On the diagram above, draw the fundamental mode of vibration of the building caused by these vibrations. (1)

The building is of height 280 m and the mean speed of waves in the structure of the building is 3.4 × 103 ms–1. (ii)

Explain quantitatively why earthquake waves of frequency about 6 Hz are likely to be very destructive. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (Total 25 marks)

7

3.

This question is about waves and wave motion. (a)

Describe, by reference to the propagation of energy, what is meant by a transverse wave. Transverse wave

(2)

..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................

(b)

State one example, other than a wave on a string, of a transverse wave. ..................................................................................................................................... (1)

A transverse wave is travelling along a string that is under tension. The diagram below shows the displacement of part of the string at time t = 0. The dotted line shows the position of the string when there is no wave travelling along it. displacement / cm

5.0

15

25

35

distance along string / cm 45

8

(c)

On the diagram above, draw lines to identify for this wave (i)

the amplitude (label this A); (1)

(ii)

the wavelength (label this λ). (1)

(d)

The period of the wave is 1.2 × 10–3 s. Deduce that the speed of the wave is 250 m s–1. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2)

(e)

Using the axes below, draw the displacement of the string when t = 3.0 × 10–4 s. (The displacement of the string at t = 0 is shown as a dotted line.)

displacement / cm

5.0

15

25

35

distance along string / cm 45

(3) (Total 10 marks)

9

4.

This question is about waves and wave properties. Travelling and standing (stationary) waves (a)

State two differences between a travelling wave and a standing (stationary) wave. 1.

......................................................................................................................... .........................................................................................................................

2.

......................................................................................................................... ......................................................................................................................... (2)

(b)

In the scale diagram below, plane wavefronts travel from medium 1 to medium 2 across the boundary AB. direction of travel

medium 1 A

B medium 2

State and explain in which medium the wavefronts have the greater speed. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (3)

10

(c)

By taking measurements from the diagram, determine the ratio

speed of wave in medium 1 . speed of wave in medium 2 ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (3)

(d)

To demonstrate the production of a standing wave, Samantha attaches the end B of a length AB of rubber tubing to a rigid support. She holds the other end A of the tubing, pulls on it slightly and then shakes the end A in a direction at right angles to AB. At a certain frequency of shaking, the tubing is seen to form the standing wave pattern shown below.

A

B

Explain how this pattern is formed. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (5)

11

(e)

The speed v with which energy is propagated in the tubing by a travelling wave depends on the tension T in the tubing. The relationship between these quantities is vk T

where k is a constant. In an experiment to verify this relationship, the fundamental (first harmonic) frequency f was measured for different values of tension T. (i)

Explain how the results of this experiment, represented graphically, can be used to verify the relationship v  k T . ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (4)

(ii)

In the experiment, the length of the tubing was kept constant at 2.4 m. The fundamental frequency for a tension of 9.0 N in the tubing was 1.8 Hz. Calculate the numerical value of the constant k. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (3)

12

The Doppler effect (f)

A source S emits sound waves at constant frequency. In the diagram below, S is moving at constant speed in the direction shown, along a straight-line between two stationary observers A and B.

B

A S

(i)

Draw, on the above diagram, three wavefronts representing the waves emitted by S. (2)

(ii)

Use your sketch to explain any difference in the frequency of the sound as heard by observer A and by observer B. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (Total 24 marks)

5.

This question is about sound waves. A sound wave of frequency 660 Hz passes through air. The variation of particle displacement with distance along the wave at one instant of time is shown below.

0.5

displacement / mm

00

1.0

2.0

distance / m

–0.5

13

(a)

State whether this wave is an example of a longitudinal or a transverse wave. ..................................................................................................................................... (1)

(b)

Using data from the above graph, deduce for this sound wave, (i)

the wavelength. ........................................................................................................................... (1)

(ii)

the amplitude. ........................................................................................................................... (1)

(iii)

the speed. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (Total 5 marks)

6.

This question is about wave properties and interference. The diagram below represents the direction of oscillation of a disturbance that gives rise to a wave.

14

(a)

By redrawing the diagram in the spaces below, add arrows to show the direction of wave energy transfer to illustrate the difference between (i)

a transverse wave and

(1)

(ii)

a longitudinal wave.

(1)

15

A wave travels along a stretched string. The diagram below shows the variation with distance along the string of the displacement of the string at a particular instant in time. A small marker is attached to the string at the point labelled M. The undisturbed position of the string is shown as a dotted line. Directions of wave travel

M

(b)

On the diagram above (i)

draw an arrow to indicate the direction in which the marker is moving. (1)

(ii)

indicate, with the letter A, the amplitude of the wave. (1)

(iii)

indicate, with the letter λ, the wavelength of the wave. (1)

(iv)

T later, where T is the period of 4 oscillation of the wave. Indicate, with the letter N, the new position of the marker. draw the displacement of the string a time

(2)

The wavelength of the wave is 5.0 cm and its speed is 10 cm s–1. (c)

Determine (i)

the frequency of the wave. ........................................................................................................................... (1)

16

(ii)

how far the wave has moved in

T s. 4 (2)

Interference of waves (d)

By reference to the principle of superposition, explain what is meant by constructive interference.

..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (4) (Total 14 marks)

7.

Waves (a)

Distinguish, in terms of the propagation of energy, the difference between a transverse travelling wave and a longitudinal travelling wave. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (3)

17

(b)

The diagram below shows an aluminium rod AB of length 1.50 m hanging horizontally from two strings.

string

string

A

B aluminium rod 1.50 m

hammer

End A of the rod is hit gently with a hammer. As a result, a wave pulse travels down the rod and is reflected from end B. The hammer remains in contact with the rod until the pulse reflected from end B reaches A. This pulse causes the hammer to rebound from the end of the rod.

(i)

Suggest, giving a reason , whether the wave pulse is longitudinal or transverse. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2)

(ii)

The hammer is in contact with end A of the rod for 6.00  10–4 s. Calculate the speed of the pulse in the rod. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2)

18

(iii)

As a result of the rod being hit with the hammer, a sound is heard. Suggest how this sound arises. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (3) (Total 10 marks)

19

8.

Waves on a string A travelling wave is created on a string. The graph below shows the variation with time t of the displacement y of a particular point on the string. Graph 1 y / mm

2.0 1.0 t / ms

0.0 0.0

0.1

0.2

0.3

0.4

0.5

–1.0 –2.0

The variation with distance x of the displacement y of the string at t = 0 is shown below. Graph 2 y / mm

2.0 1.0 x / cm

0.0 0.0

0.1

0.2

0.3

0.4

0.5

–1.0 –2.0

(a)

Use information from the graphs to calculate, for this wave, (i)

the wavelength; ......................................................................................................................... (1)

(ii)

the frequency; ......................................................................................................................... (2)

(iii)

the speed of the wave. ......................................................................................................................... (1)

20

(b)

The wave is moving from left to right and has period T. (i)

On graph 1, draw a labelled line to indicate the amplitude of the wave. (1)

(ii)

T On graph 2, draw the displacement of the string at t  . 4 (2) (Total 7 marks)

9.

This question is about waves. (a)

With reference to the direction of energy transfer through a medium, distinguish between a transverse wave and a longitudinal wave. ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... (3)

21

(b)

A wave is travelling along the surface of some shallow water in the x-direction. The graph shows the variation with time t of the displacement d of a particle of water.

d / mm 10 8 6 4 2 0 0

0.05

0.1

–2

0.15

0.2

0.25

0.3 t/s

–4 –6 –8 –10

Use the graph to determine for the wave (i)

the frequency, ........................................................................................................................... ........................................................................................................................... (2)

(ii)

the amplitude. ........................................................................................................................... (1)

22

(c)

The speed of the wave in (b) is 15 cm s–1. Deduce that the wavelength of this wave is 2.0 cm. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2)

(d)

The graph in (b) shows the displacement of a particle at the position x = 0. On the axes below, draw a graph to show the variation with distance x along the water surface of the displacement d of the water surface at time t = 0.070 s.

d / mm 10 8 6 4 2 0 0

1

2

3

4

x/cm

–2 –4 –6 –8 –10 (3)

23

(e)

The wave encounters a shelf that divides the water into two separate depths. The water to the right of the shelf is deeper than that to the left of the shelf. wave fronts shelf direction of travel of wave 30 

shallow water

deep water

The angle between the wavefronts in the shallow water and the shelf is 30°. The speed of the wave in the shallow water is 15 cm s–1 and in the deeper water is 20 cm s–1. For the wave in the deeper water, determine the angle between the normal to the wavefronts and the shelf. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (Total 14 marks)

24

10.

This question is about wave phenomena. (a)

The graph below shows the variation with time t of the displacement x of one particle in a sound wave. x/mm

0.3 0.2 0.1

0.0 0.0

0.1

0.2

0.3

0.4

0.5

–0.1

0.6 t/ms

–0.2 –0.3

The speed of the wave is 380 m s–1.

(i)

Suggest, by marking the letter C on the t-axis of the graph above, one time at which the particle could be at the centre of a compression. (1)

(ii)

Deduce the wavelength of the wave. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3)

(b)

(i)

Outline the conditions necessary for the formation of a standing (stationary) wave. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2)

25

(ii)

A horizontal tube, closed at one end, has some fine powder sprinkled along its length. A source S of sound is placed at the open end of the tube, as shown below.

heap of powder source S The frequency of the source S is varied. Explain why, at a particular frequency, the powder is seen to form small equally-spaced heaps in the tube. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2)

(iii)

The mean separation of the heaps of powder in (b)(ii) is 9.3 cm when the frequency of the source S is 1800 Hz. Calculate the speed of sound in the tube. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2)

(c)

The experiment in (b)(ii) is repeated on a day when the temperature of the air in the tube is higher. The mean separation of the heaps is observed to have increased for the same frequency of the source S. Deduce qualitatively the effect, if any, of temperature rise on the speed of the sound in the tube. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2)

26

(d)

The diagram below shows wavefronts produced by two sources S1 and S2 of sound that are vibrating in phase.

B

A

S1

B

S2

The waves interfere constructively along the lines labelled A and B.

(i)

State what is meant by constructive interference. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3)

(ii)

On the diagram above, draw another line, labelled C, along which the waves interfere constructively. (1)

(iii)

On the diagram above, draw another line, labelled D, along which the waves interfere destructively. (1) (Total 17 marks)

27