9702/22/F/M/23/Q5

1 (a) A microphone and cathode-ray oscilloscope (CRO) are used to analyse a sound wave of
frequency 5000 Hz. The trace that is displayed on the screen of the CRO is shown in Fig. 5.1.

1.0 cm

1.0 cm

Fig. 5.1

(i) Determine the time-base setting, in s cm–1, of the CRO.

time-base setting = ............................................... s cm–1 [2]

(ii) The intensity of the sound detected by the microphone is now increased from its initial
value of I to a new value of 3I. The frequency of the sound is unchanged. Assume that
the amplitude of the trace on the CRO screen is proportional to the amplitude of the
sound wave.

On Fig. 5.1, sketch the new trace shown on the screen of the CRO. [3]

(b) An arrangement for demonstrating interference using light is shown in Fig. 5.2.

3.6 × 10–4 m P

light from laser,

wavelength 630 nm D

double slit screen

Fig. 5.2 (not to scale)

 The wavelength of the light from the laser is 630 nm. The light is incident normally on the
double slit. The separation of the two slits is 3.6 × 10–4 m. The perpendicular distance between
the double slit and the screen is D.

Coherent light waves from the slits form an interference pattern of bright and dark fringes on
the screen. The distance between the centres of two adjacent bright fringes is 4.0 × 10–3 m.
The central bright fringe is formed at point P.

(i) Explain why a bright fringe is produced by the waves meeting at point P.

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

..................................................................................................................................... [1]

(ii) Calculate distance D.

D = ...................................................... m [3]

(c) The wavelength λ of the light in (b) is now varied. This causes a variation in the distance x
between the centres of two adjacent bright fringes on the screen. The distance D and the
separation of the two slits are unchanged.

On Fig. 5.3, sketch a graph to show the variation of x with λ from λ = 400 nm to λ = 700 nm.
Numerical values of x are not required.

0
400 700
λ / nm

Fig. 5.3
[1]

[Total: 10]
9702/21/M/J/16/Q5

2 The variation with time t of the displacement y of a wave X, as it passes a point P, is shown in
Fig. 5.1.

4.0

3.0
\ / cm
ZDYH;
2.0

1.0

0
0 1.0 2.0 3.0 4.0 5.0
W / ms
–1.0

–2.0

–3.0

–4.0

Fig. 5.1

The intensity of wave X is I.

(a) Use Fig. 5.1 to determine the frequency of wave X.

frequency = .................................................... Hz [2]

(b) A second wave Z with the same frequency as wave X also passes point P.
Wave Z has intensity 2I. The phase difference between the two waves is 90°.

On Fig. 5.1, sketch the variation with time t of the displacement y of wave Z.

Show your working.

[3]
(c) A double-slit interference experiment is used to determine the wavelength of light emitted
from a laser, as shown in Fig. 5.2.

0.45 mm

laser light

double slit ' screen

Fig. 5.2 (not to scale)

The separation of the slits is 0.45 mm. The fringes are viewed on a screen at a distance D
from the double slit.

The fringe width x is measured for different distances D. The variation with D of x is shown in
Fig. 5.3.

5.0

4.0
[ / mm
3.0

2.0

1.0

0
1.5 2.0 2.5 3.0 3.5
'/m

Fig. 5.3

(i) Use the gradient of the line in Fig. 5.3 to determine the wavelength, in nm, of the laser
light.

wavelength = .................................................... nm [4]

(ii) The separation of the slits is increased. State and explain the effects, if any, on the graph
of Fig. 5.3.

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

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

.......................................................................................................................................[2]

[Total: 11]
9702/22/M/J/16/Q5

3 (a) Light of a single wavelength is incident on a diffraction grating. Explain the part played by
diffraction and interference in the production of the first order maximum by the diffraction
grating.

diffraction: .................................................................................................................................

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

interference: ..............................................................................................................................

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

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

...................................................................................................................................................
[3]

(b) The diffraction grating illustrated in Fig. 5.1 is used with light of wavelength 486 nm.

second order

first order
light
wavelength 486 nm
59.4° zero order

diffraction
grating first order

second order screen

Fig. 5.1 (not to scale)

The orders of the maxima produced are shown on the screen in Fig. 5.1. The angle between
the two second order maxima is 59.4°.

Calculate the number of lines per millimetre of the grating.

number of lines per millimetre = ................................................ mm–1 [3]

[Total: 6]
9702/23/M/J/16/Q7

4 (a) Apparatus used to produce stationary waves on a stretched string is shown in Fig. 7.1.

frequency
generator light string

pulley
vibrator wheel

masses

Fig. 7.1

The frequency generator is switched on.

(i) Describe two adjustments that can be made to the apparatus to produce stationary
waves on the string.

1. .......................................................................................................................................

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

2. .......................................................................................................................................

...........................................................................................................................................
[2]

(ii) Describe the features that are seen on the stretched string that indicate stationary waves
have been produced.

...................................................................................................................................... [1]
(b) The variation with time t of the displacement x of a particle caused by a progressive wave R is
shown in Fig. 7.2. For the same particle, the variation with time t of the displacement x caused
by a second wave S is also shown in Fig. 7.2.

4.0
R
3.0

x / cm 2.0
S
1.0

0
0 0.2 0.4 0.6 0.8 1.0
t /s
ï

ï

ï

ï

Fig. 7.2

(i) Determine the phase difference between wave R and wave S. Include an appropriate
unit.

phase difference = .......................................................... [1]

(ii) Calculate the ratio

intensity of wave R
.
intensity of wave S

ratio = .......................................................... [2]

[Total: 6]
9702/21/M/J/17/Q4

5 (a) State the conditions required for the formation of stationary waves.

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

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

...............................................................................................................................................[2]

(b) One end of a string is attached to a vibrator. The string is stretched by passing the other end
over a pulley and attaching a load, as illustrated in Fig. 4.1.

string
pulley
A B
vibrator
support for
pulley
load

Fig. 4.1

The frequency of vibration of the vibrator is adjusted to 250 Hz and a transverse wave travels
along the string with a speed of 12 m s–1. The wave is reflected at the pulley and a stationary
wave forms on the string.

Fig. 4.2 shows the string between points A and B at time t = t1.

string

A B

Fig. 4.2

At time t = t1 the string has maximum displacement.

(i) Calculate the distance AB.

distance = .......................................................m [2]

(ii) On Fig. 4.2, sketch the position of the string between A and B at times

1. t = t1 + 2.0 ms (label this line P),

2. t = t1 + 5.0 ms (label this line Q).

[3]

[Total: 7]
9702/22/M/J/17/Q6

6 (a) Interference fringes may be observed using a light-emitting laser to illuminate a double slit.
The double slit acts as two sources of light.

Explain

(i) the part played by diffraction in the production of the fringes,

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

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

.......................................................................................................................................[2]

(ii) the reason why a double slit is used rather than two separate sources of light.

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

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

.......................................................................................................................................[1]
(b) A laser emitting light of a single wavelength is used to illuminate slits S1 and S2, as shown in
Fig. 6.1.

S1
laser
0.48 mm
light S2
screen

2.4 m

Fig. 6.1 (not to scale)

An interference pattern is observed on the screen AB. The separation of the slits is 0.48 mm.
The slits are 2.4 m from AB. The distance on the screen across 16 fringes is 36 mm, as
illustrated in Fig. 6.2.

16 fringes

36 mm

Fig. 6.2

Calculate the wavelength of the light emitted by the laser.

wavelength = .......................................................m [3]

(c) Two dippers D1 and D2 are used to produce identical waves on the surface of water, as
illustrated in Fig. 6.3.

P
7.2 cm

D1

11.2 cm water

D2

Fig. 6.3 (not to scale)

Point P is 7.2 cm from D1 and 11.2 cm from D2.

The wavelength of the waves is 1.6 cm. The phase difference between the waves produced
at D1 and D2 is zero.

(i) State and explain what is observed at P.

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

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

.......................................................................................................................................[2]

(ii) State and explain the effect on the answer to (c)(i) if the apparatus is changed so that,
separately,

1. the phase difference between the waves at D1 and at D2 is 180°,

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

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

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

2. the intensity of the wave from D1 is less than the intensity of that from D2.

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

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

....................................................................................................................................
[2]

[Total: 10]
9702/23/M/J/17/Q5

7 (a) A diffraction grating is used to determine the wavelength of light.

(i) Describe the diffraction of light at a diffraction grating.

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

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

.......................................................................................................................................[2]

(ii) By reference to interference, explain

1. the zero order maximum,

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

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

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

2. the first order maximum.

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

....................................................................................................................................
[3]

(b) A diffraction grating is used with different wavelengths of light. The angle θ of the second
order maximum is measured for each wavelength. The variation with wavelength λ of sin θ is
shown in Fig. 5.1.

0.60

sin θ

0.50

0.40

0.30

0.20

0.10
300 350 400 450 500 550
λ / nm
Fig. 5.1
 (i) Determine the gradient of the line shown in Fig. 5.1.

gradient = ...........................................................[2]

(ii) Use the gradient determined in (i) to calculate the slit separation d of the diffraction
grating.

d = .......................................................m [2]

(iii) On Fig. 5.1, sketch a line to show the results that would be obtained for the first order
maxima. [1]

[Total: 10]
9702/21/M/J/18/Q5

8 (a) When monochromatic light is incident normally on a diffraction grating, the emergent light
waves have been diffracted and are coherent.

Explain what is meant by

(i) diffracted waves,

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

.......................................................................................................................................[1]

(ii) coherent waves.

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

.......................................................................................................................................[1]

(b) Light consisting of only two wavelengths λ1 and λ2 is incident normally on a diffraction grating.

The third order diffraction maximum of the light of wavelength λ1 and the fourth order
diffraction maximum of the light of wavelength λ2 are at the same angle θ to the direction of
the incident light.

(i)
λ
Show that the ratio 2 is 0.75.
λ1
Explain your working.

[2]

(ii) The difference between the two wavelengths is 170 nm.

Determine wavelength λ1.

λ1 = .................................................... nm [1]

[Total: 5]
9702/22/M/J/18/Q4

9 (a) (i) Define the wavelength of a progressive wave.

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

.......................................................................................................................................[1]

(ii) State what is meant by an antinode of a stationary wave.

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

.......................................................................................................................................[1]

(b) A loudspeaker producing sound of constant frequency is placed near the open end of a pipe,
as shown in Fig. 4.1.

pipe piston
loudspeaker

speed 0.75 cm s–1

Fig. 4.1

A movable piston is at distance x from the open end of the pipe. Distance x is increased from
x = 0 by moving the piston to the left with a constant speed of 0.75 cm s–1.

The speed of the sound in the pipe is 340 m s–1.

(i) A much louder sound is first heard when x = 4.5 cm. Assume that there is an antinode of
a stationary wave at the open end of the pipe.

Determine the frequency of the sound in the pipe.

frequency = ..................................................... Hz [3]

(ii) After a time interval, a second much louder sound is heard. Calculate the time interval
between the first louder sound and the second louder sound being heard.

time interval = ........................................................ s [2]

[Total: 7]
9702/23/M/J/18/Q5

10 (a) State the relationship between the intensity and the amplitude of a wave.

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

...............................................................................................................................................[1]

(b) Microwaves of the same amplitude and wavelength are emitted in phase from two sources P
and Q. The sources are arranged as shown in Fig. 5.1.

P
1.840 m

2.020 m

path of detector
Q

Fig. 5.1

A microwave detector is moved along a path that is parallel to the line joining P and Q. A series
of intensity maxima and intensity minima are detected.

When the detector is at a point X, the distance PX is 1.840 m and the distance QX is 2.020 m.
The microwaves have a wavelength of 6.0 cm.

(i) Calculate the frequency of the microwaves.

frequency = .................................................... Hz [2]

(ii) Describe and explain the intensity of the microwaves detected at X.

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

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

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

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

.......................................................................................................................................[3]
(iii) Describe the effect on the interference pattern along the path of the detector due to each
of the following separate changes.

1. The wavelength of the microwaves decreases.

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

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

2. The phase difference between the microwaves emitted from the sources changes to
180°.

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

....................................................................................................................................
[2]

[Total: 8]
9702/21/M/J/19/Q5

11 (a) A loudspeaker oscillates with frequency f to produce sound waves of wavelength λ. The
loudspeaker makes N oscillations in time t.

(i) State expressions, in terms of some or all of the symbols f, λ and N, for:

1. the distance moved by a wavefront in time t

distance = ...............................................................

2. time t.

time t = ...............................................................
[2]

(ii) Use your answers in (i) to deduce the equation relating the speed v of the sound wave to
f and λ.

[1]

(b) The waveform of a sound wave is displayed on the screen of a cathode-ray oscilloscope
(c.r.o.), as shown in Fig. 5.1.

1.0 cm

1.0 cm

Fig. 5.1

The time-base setting is 0.20 ms cm−1.

Determine the frequency of the sound wave.

frequency = .................................................... Hz [2]

(c) Two sources S1 and S2 of sound waves are positioned as shown in Fig. 5.2.

S1
X
L
Q
S2
L

7.40 m Q
L
Y

Fig. 5.2 (not to scale)

The sources emit coherent sound waves of wavelength 0.85 m. A sound detector is moved
parallel to the line S1S2 from a point X to a point Y. Alternate positions of maximum loudness
L and minimum loudness Q are detected, as illustrated in Fig. 5.2.

Distance S1X is equal to distance S2X. Distance S2Y is 7.40 m.

(i) Explain what is meant by coherent waves.

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

.......................................................................................................................................[1]

(ii) State the phase difference between the two waves arriving at the position of minimum
loudness Q that is closest to point X.

phase difference = ....................................................... ° [1]

(iii) Determine the distance S1Y.

distance = ...................................................... m [2]

[Total: 9]
9702/22/M/J/19/Q4

12 (a) For a progressive water wave, state what is meant by:

(i) displacement

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

.......................................................................................................................................[1]

(ii) amplitude.

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

.......................................................................................................................................[1]

(b) Two coherent waves X and Y meet at a point and superpose. The phase difference between
the waves at the point is 180°. Wave X has an amplitude of 1.2 cm and intensity I. Wave Y
has an amplitude of 3.6 cm.

Calculate, in terms of I, the resultant intensity at the meeting point.

intensity = .......................................................... [2]

(c) (i) Monochromatic light is incident on a diffraction grating. Describe the diffraction of the
light waves as they pass through the grating.

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

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

.......................................................................................................................................[2]
(ii) A parallel beam of light consists of two wavelengths 540 nm and 630 nm. The light is
incident normally on a diffraction grating. Third-order diffraction maxima are produced for
each of the two wavelengths. No higher orders are produced for either wavelength.

Determine the smallest possible line spacing d of the diffraction grating.

d = ...................................................... m [3]

(iii) The beam of light in (c)(ii) is replaced by a beam of blue light incident on the same
diffraction grating.

State and explain whether a third-order diffraction maximum is produced for this blue
light.

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

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

.......................................................................................................................................[2]

[Total: 11]
9702/23/M/J/19/Q5

13 A vertical tube of length 0.60 m is open at both ends, as shown in Fig. 5.1.

tube

N 0.60 m

direction of
incident
sound wave

Fig. 5.1

An incident sinusoidal sound wave of a single frequency travels up the tube. A stationary wave
is then formed in the air column in the tube with antinodes A at both ends and a node N at the
midpoint.

(a) Explain how the stationary wave is formed from the incident sound wave.

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

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

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

...............................................................................................................................................[2]

(b) On Fig. 5.2, sketch a graph to show the variation of the amplitude of the stationary wave with
height h above the bottom of the tube.

amplitude

0
0 0.20 0.40 0.60
h/m

Fig. 5.2
[2]
(c) For the stationary wave, state:

(i) the direction of the oscillations of an air particle at a height of 0.15 m above the bottom of
the tube

.......................................................................................................................................[1]

(ii) the phase difference between the oscillations of a particle at a height of 0.10 m and a
particle at a height of 0.20 m above the bottom of the tube.

phase difference = ........................................................ ° [1]

(d) The speed of the sound wave is 340 m s−1.

Calculate the frequency of the sound wave.

frequency = .................................................... Hz [2]

(e) The frequency of the sound wave is gradually increased.

Determine the frequency of the wave when a stationary wave is next formed.

frequency = .................................................... Hz [1]

[Total: 9]
9702/21/M/J/20/Q4

14 (a) (i) By reference to the direction of propagation of energy, state what is meant by a
longitudinal wave.

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

..................................................................................................................................... [1]

(ii) State the principle of superposition.

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

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

..................................................................................................................................... [2]

(b) The wavelength of light from a laser is determined using the apparatus shown in Fig. 4.1.

double
slit screen
light

3.7 × 10 –4 m

2.3 m

Fig. 4.1 (not to scale)

The light from the laser is incident normally on the plane of the double slit.
The separation of the two slits is 3.7 × 10–4 m. The screen is parallel to the plane of the double
slit. The distance between the screen and the double slit is 2.3 m.

A pattern of bright fringes and dark fringes is seen on the screen. The separation of adjacent
bright fringes on the screen is 4.3 × 10–3 m.

(i) Calculate the wavelength, in nm, of the light.

wavelength = ................................................... nm [3]

(ii) The intensity of the light passing through each slit was initially the same. The intensity of
the light through one of the slits is now reduced.

Compare the appearance of the fringes before and after the change of intensity.

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

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

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

..................................................................................................................................... [2]

[Total: 8]
9702/22/M/J/20/Q4

15 (a) State the difference between progressive waves and stationary waves in terms of the transfer
of energy along the wave.

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

............................................................................................................................................. [1]

(b) A progressive wave travels from left to right along a stretched string. Fig. 4.1 shows part of
the string at one instant.

R direction of
wave travel
Q

P
string
0.48 m

Fig. 4.1

P, Q and R are three different points on the string. The distance between P and R is 0.48 m.
The wave has a period of 0.020 s.

(i) Use Fig. 4.1 to determine the wavelength of the wave.

wavelength = ..................................................... m [1]

(ii) Calculate the speed of the wave.

speed = ................................................ m s–1 [2]

(iii) Determine the phase difference between points Q and R.

phase difference = ........................................................ ° [1]

 (iv) Fig. 4.1 shows the position of the string at time t = 0. Describe how the displacement of
point Q on the string varies with time from t = 0 to t = 0.010 s.

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

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

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

..................................................................................................................................... [2]

(c) A stationary wave is formed on a different string that is stretched between two fixed points
X and Y. Fig. 4.2 shows the position of the string when each point is at its maximum
displacement.

X Y
Z

Fig. 4.2

(i) Explain what is meant by a node of a stationary wave.

..................................................................................................................................... [1]

(ii) State the number of antinodes of the wave shown in Fig. 4.2.

number = ......................................................... [1]

(iii) State the phase difference between points W and Z on the string.

phase difference = ........................................................° [1]

(iv) A new stationary wave is now formed on the string. The new wave has a frequency
that is half of the frequency of the wave shown in Fig. 4.2. The speed of the wave is
unchanged.

On Fig. 4.3, draw a position of the string, for this new wave, when each point is at its
maximum displacement.

X Y

Fig. 4.3
[1]

[Total: 11]
9702/23/M/J/20/Q4

16 Two progressive sound waves Y and Z meet at a fixed point P. The variation with time t of the
displacement x of each wave at point P is shown in Fig. 4.1.

4 wave Y
x / μm
2

0
0 1.0 2.0 3.0 t / ms 4.0
–2
wave Z
–4

–6

Fig. 4.1

(a) Use Fig. 4.1 to state one quantity of waves Y and Z that is:

(i) the same

..................................................................................................................................... [1]

(ii) different.

..................................................................................................................................... [1]

(b) State and explain whether waves Y and Z are coherent.

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

............................................................................................................................................. [1]

(c) Determine the phase difference between the waves.

phase difference = ....................................................... ° [1]

(d) The two waves superpose at P. Use Fig. 4.1 to determine the resultant displacement at time
t = 0.75 ms.

resultant displacement = ................................................... μm [1]

(e) The intensity of wave Y at point P is I.

Determine, in terms of I, the intensity of wave Z.

intensity = ......................................................... [2]

(f) The speed of wave Z is 330 m s–1.

Determine the wavelength of wave Z.

wavelength = ..................................................... m [3]

[Total: 10]
9702/21/M/J/21/Q4

17 (a) For a progressive wave, state what is meant by wavelength.

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

............................................................................................................................................. [1]

(b) A light wave from a laser has a wavelength of 460 nm in a vacuum.

Calculate the period of the wave.

period = ...................................................... s [3]

(c) The light from the laser is incident normally on a diffraction grating.

Describe the diffraction of the light waves at the grating.

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

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

............................................................................................................................................. [2]

(d) A diffraction grating is used with different wavelengths of visible light. The angle θ of the
fourth-order maximum from the zero-order (central) maximum is measured for each
wavelength. The variation with wavelength λ of sin θ is shown in Fig. 4.1.

sin θ

0
0 400 700
λ / nm

Fig. 4.1
(i) The gradient of the graph is G.

Determine an expression, in terms of G, for the distance d between the centres of two
adjacent slits in the diffraction grating.

d = ......................................................... [2]

(ii) On Fig. 4.1, sketch a graph to show the results that would be obtained for the
second-order maxima. [2]

[Total: 10]
9702/22/M/J/21/Q4

18 (a) For a progressive wave, state what is meant by its period.

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

............................................................................................................................................. [1]

(b) State the principle of superposition.

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

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

............................................................................................................................................. [2]

(c) Electromagnetic waves of wavelength 0.040 m are emitted in phase from two sources X and
Y and travel in a vacuum. The arrangement of the sources is shown in Fig. 4.1.

X path of
detector
1.380 m

Y 1.240 m

Fig. 4.1 (not to scale)

A detector moves along a path that is parallel to the line XY. A pattern of intensity maxima and
minima is detected.

Distance XZ is 1.380 m and distance YZ is 1.240 m.

(i) State the name of the region of the electromagnetic spectrum that contains the waves
from X and Y.

..................................................................................................................................... [1]

(ii) Calculate the period, in ps, of the waves.

period = ..................................................... ps [3]

(iii) Show that the path difference at point Z between the waves from X and Y is 3.5 λ, where λ
is the wavelength of the waves.

[1]

(iv) Calculate the phase difference between the waves at point Z.

phase difference = .........................................................° [1]

(v) The waves from X alone have the same amplitude at point Z as the waves from Y alone.

State the intensity of the waves at point Z.

..................................................................................................................................... [1]

(vi) The frequencies of the waves from X and Y are both decreased to the same lower value.
The waves stay within the same region of the electromagnetic spectrum.

Describe the effect of this change on the pattern of intensity maxima and minima along
the path of the detector.

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

..................................................................................................................................... [1]

[Total: 11]
9702/23/M/J/21/Q4

19 (a) State the principle of superposition.

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

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

............................................................................................................................................. [2]

(b) Two waves, with intensities I and 4I, superpose. The waves have the same frequency.

Determine, in terms of I, the maximum possible intensity of the resulting wave.

maximum intensity = ....................................................... I [2]

(c) Coherent light of wavelength 550 nm is incident normally on a double slit of slit separation
0.35 mm. A series of bright and dark fringes forms on a screen placed a distance of 1.2 m
from the double slit, as shown in Fig. 4.1. The screen is parallel to the double slit.

screen

1.2 m
light

0.35 mm

wavelength
550 nm double
slit

Fig. 4.1 (not to scale)

(i) Determine the distance between the centres of adjacent bright fringes on the screen.

distance = ..................................................... m [3]

(ii) The light of wavelength 550 nm is replaced with red light of a single frequency.

State and explain the change, if any, in the distance between the centres of adjacent
bright fringes.

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

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

..................................................................................................................................... [1]

[Total: 8]
9702/21/M/J/22/Q5

20 A horizontal string is stretched between two fixed points A and B. A vibrator is used to oscillate the
string and produce an observable stationary wave.

At one instant, the moving string is straight, as shown in Fig. 5.1.

point P

A B

Fig. 5.1

The dots in the diagram represent the positions of the nodes on the string. Point P on the string is
moving downwards.

The wave on the string has a speed of 35 m s–1 and a period of 0.040 s.

(a) Explain how the stationary wave is formed on the string.

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

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

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

............................................................................................................................................. [2]

(b) On Fig. 5.1, sketch a line to show a possible position of the string a quarter of a cycle later
than the position shown in the diagram. [1]

(c) Determine the horizontal distance from A to B.

distance = ..................................................... m [3]

(d) A particle on the string has zero displacement at time t = 0. From time t = 0 to time t = 0.060 s,
the particle moves through a total distance of 72 mm.

Calculate the amplitude of oscillation of the particle.

amplitude = .................................................. mm [2]

[Total: 8]
9702/22/M/J/22/Q5

21 Light from a laser is used to produce an interference pattern on a screen, as shown in Fig. 5.1.

0.44 mm O central bright fringe

P dark fringe
Q bright fringe
light of R dark fringe
wavelength
660 nm 1.8 m
double screen
slit

Fig. 5.1 (not to scale)

The light of wavelength 660 nm is incident normally on two slits that have a separation of 0.44 mm.
The double slit is parallel to the screen. The perpendicular distance between the double slit and
the screen is 1.8 m.

The central bright fringe on the screen is formed at point O. The next dark fringe below point O
is formed at point P. The next bright fringe and the next dark fringe below point P are formed at
points Q and R respectively.

(a) The light waves from the two slits are coherent.

State what is meant by coherent.

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

............................................................................................................................................. [1]

(b) For the two light waves superposing at R, calculate:

(i) the difference in their path lengths, in nm, from the slits

path difference = ................................................... nm [1]

(ii) their phase difference.

phase difference = ....................................................... ° [1]

(c) Calculate the distance OQ.

distance OQ = ..................................................... m [3]

(d) The intensity of the light incident on the double slit is increased without changing the
frequency.

Describe how the appearance of the fringes after this change is different from, and similar to,
their appearance before the change.

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

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

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

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

............................................................................................................................................. [3]

(e) The light of wavelength 660 nm is now replaced by blue light from a laser.

State and explain the change, if any, that must be made to the separation of the two slits so
that the fringe separation on the screen is the same as it was for light of wavelength 660 nm.

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

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

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

............................................................................................................................................. [2]

[Total: 11]
9702/23/M/J/22/Q5

22 (a) Parallel light rays from the Sun are incident normally on a magnifying glass. The magnifying
glass directs the light to an area A of radius r, as shown in Fig. 5.1.

parallel light rays

from Sun
r

A 5.5 cm

magnifying glass

Fig. 5.1 (not to scale)

The magnifying glass is circular in cross‑section with a radius of 5.5 cm. The intensity of the
light from the Sun incident on the magnifying glass is 1.3 kW m–2.

Assume that all of the light incident on the magnifying glass is transmitted through it.

(i) Calculate the power of the light from the Sun incident on the magnifying glass.

power = ..................................................... W [2]

(ii) The value of r is 1.5 mm.

Calculate the intensity of the light on area A.

intensity = ............................................... W m–2 [1]

(b) A laser emits a beam of electromagnetic waves of frequency 3.7 × 1015 Hz in a vacuum.

(i) Show that the wavelength of the waves is 8.1 × 10–8 m.

[2]

(ii) State the region of the electromagnetic spectrum to which these waves belong.

..................................................................................................................................... [1]

(iii) The beam from the laser now passes through a diffraction grating with 2400 lines per
millimetre. A detector sensitive to the waves emitted by the laser is moved through an
arc of 180° in order to detect the maxima produced by the waves passing through the
grating, as shown in Fig. 5.2.

detector

diffraction grating
laser

beam from
laser detector moves
along this line

Fig. 5.2
 Calculate the number of maxima detected as the detector moves through 180° along the
line shown in Fig. 5.2. Show your working.

number of maxima detected = ......................................................... [4]

(iv) The laser is now replaced with one that emits electromagnetic waves with a wavelength
of 300 nm.

Explain, without calculation, what happens to the number of maxima now detected.
Assume that the detector is also sensitive to this wavelength of electromagnetic waves.

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

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

..................................................................................................................................... [2]

[Total: 12]
9702/21/O/N/16/Q5

23 (a) State what is meant by the diffraction of a wave.

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

...............................................................................................................................................[2]

(b) Laser light of wavelength 500 nm is incident normally on a diffraction grating. The resulting
diffraction pattern has diffraction maxima up to and including the fourth-order maximum.

Calculate, for the diffraction grating, the minimum possible line spacing.

line spacing = ...................................................... m [3]

(c) The light in (b) is now replaced with red light. State and explain whether this is likely to result
in the formation of a fifth-order diffraction maximum.

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

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

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

...............................................................................................................................................[2]

[Total: 7]
9702/22/O/N/16/Q4

24 (a) State what is meant by the diffraction of a wave.

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

...............................................................................................................................................[2]

(b) An arrangement for demonstrating the interference of light is shown in Fig. 4.1.

laser light Y dark fringe

2.0 mm
0.41 mm X central bright fringe
wavelength
580 nm Z dark fringe

'
double slit screen

Fig. 4.1 (not to scale)

The wavelength of the light from the laser is 580 nm. The separation of the slits is 0.41 mm.
The perpendicular distance between the double slit and the screen is D.

Coherent light emerges from the slits and an interference pattern is observed on the screen.
The central bright fringe is produced at point X. The closest dark fringes to point X are
produced at points Y and Z. The distance XY is 2.0 mm.

(i) Explain why a bright fringe is produced at point X.

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

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

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

.......................................................................................................................................[2]

(ii) State the difference in the distances, in nm, from each slit to point Y.

distance = .................................................... nm [1]

(iii) Calculate the distance D.

D = ...................................................... m [3]

(iv) The intensity of the light passing through the two slits was initially the same. The intensity
of the light through one of the slits is now reduced. Compare the appearance of the
fringes before and after the change of intensity.

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

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

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

.......................................................................................................................................[2]

[Total: 10]
9702/21/O/N/17/Q3

25 (a) State the difference between a stationary wave and a progressive wave in terms of

(i) the energy transfer along the wave,

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

.......................................................................................................................................[1]

(ii) the phase of two adjacent vibrating particles.

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

.......................................................................................................................................[1]

(b) A tube is open at both ends. A loudspeaker, emitting sound of a single frequency, is placed
near one end of the tube, as shown in Fig. 3.1.

tube

A A A A

loudspeaker
0.60 m

Fig. 3.1

The speed of the sound in the tube is 340 m s–1. The length of the tube is 0.60 m.
A stationary wave is formed with an antinode A at each end of the tube and two antinodes
inside the tube.

(i) State what is meant by an antinode of the stationary wave.

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

.......................................................................................................................................[1]

(ii) State the distance between a node and an adjacent antinode.

distance = ...................................................... m [1]

(iii) Determine, for the sound in the tube,

1. the wavelength,

wavelength = ...................................................... m [1]

(iv) Determine the speed of a progressive wave along the string.

speed = ..................................................m s–1 [2]

[Total: 8]
9702/21/O/N/18/Q4

26 (a) State the principle of superposition.

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

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

.............................................................................................................................................. [2]

(b) An arrangement for demonstrating the interference of light is shown in Fig. 4.1.

B
P D

Q B
D
light central
wavelength a 22 mm B bright
610 nm fringe
D
B

D
B
2.7 m
screen
double
slit

Fig. 4.1 (not to scale)

The wavelength of the light is 610 nm. The distance between the double slit and the screen
is 2.7 m.

An interference pattern of bright fringes and dark fringes is observed on the screen. The
centres of the bright fringes are labelled B and centres of the dark fringes are labelled D.
Point P is the centre of a particular dark fringe and point Q is the centre of a particular bright
fringe, as shown in Fig. 4.1. The distance across five bright fringes is 22 mm.

(i) The light waves leaving the two slits are coherent.

State what is meant by coherent.

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

...................................................................................................................................... [1]
(ii) 1. State the phase difference between the waves meeting at Q.

phase difference = .............................................................. °

2. Calculate the path difference, in nm, of the waves meeting at P.

path difference = ......................................................... nm

[2]

(iii) Determine the distance a between the two slits.

a = ...................................................... m [3]

(iv) A higher frequency of visible light is now used. State and explain the change to the
separation of the fringes.

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

...................................................................................................................................... [1]

(v) The intensity of the light incident on the double slit is now increased without altering
its frequency. Compare the appearance of the fringes after this change with their
appearance before this change.

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

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

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

...................................................................................................................................... [2]

[Total: 11]
9702/22/O/N/18/Q5

27 Red light of wavelength 640 nm is incident normally on a diffraction grating having a line spacing
of 1.7 × 10–6 m, as shown in Fig. 5.1.

diffraction second order

grating
first order
θ
zero order
incident light first order
wavelength 640 nm

second order

Fig. 5.1 (not to scale)

The second order diffraction maximum of the light is at an angle θ to the direction of the incident
light.

(a) Show that angle θ is 49°.

[3]

(b) Determine a different wavelength of visible light that will also produce a diffraction maximum
at an angle of 49°.

wavelength = ...................................................... m [2]

[Total: 5]
9702/23/O/N/18/Q4

28 (a) On Fig. 4.1, complete the two graphs to illustrate what is meant by the amplitude A, the
wavelength λ and the period T of a progressive wave.

Ensure that you label the axes of each graph.

0 0

Fig. 4.1
[3]

(b) A horizontal string is stretched between two fixed points X and Y. A vibrator is used to oscillate
the string and produce a stationary wave. Fig. 4.2 shows the string at one instant in time.

string

X Y

Fig. 4.2

The speed of a progressive wave along the string is 30 m s–1. The stationary wave has a
period of 40 ms.

(i) Explain how the stationary wave is formed on the string.

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

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

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

.......................................................................................................................................[2]
(ii) A particle on the string oscillates with an amplitude of 13 mm. At time t, the particle has
zero displacement.

Calculate

1. the displacement of the particle at time (t + 100 ms),

displacement = ........................................................ mm

2. the total distance moved by the particle from time t to time (t + 100 ms).

distance = ........................................................ mm
[3]

(iii) Determine

1. the frequency of the wave,

frequency = ..................................................... Hz [1]

2. the horizontal distance from X to Y.

distance = ...................................................... m [3]

[Total: 12]
9702/21/O/N/19/Q5

29 A ripple tank is used to demonstrate the interference of water waves.

Two dippers D1 and D2 produce coherent waves that have circular wavefronts, as illustrated in
Fig. 5.1.

D1 D2

Fig. 5.1

The lines in the diagram represent crests. The waves have a wavelength of 6.0 cm.

(a) One condition that is required for an observable interference pattern is that the waves must
be coherent.

(i) Describe how the apparatus is arranged to ensure that the waves from the dippers are
coherent.

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

..................................................................................................................................... [1]

(ii) State one other condition that must be satisfied by the waves in order for the interference
pattern to be observable.

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

..................................................................................................................................... [1]

(b) Light from a lamp above the ripple tank shines through the water onto a screen below the
tank. Describe one way of seeing the illuminated pattern more clearly.

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

............................................................................................................................................. [1]
(c) The speed of the waves is 0.40 m s–1. Calculate the period of the waves.

period = ...................................................... s [2]

(d) Fig. 5.1 shows a point X that lies on a crest of the wave from D1 and midway between two
adjacent crests of the wave from D2.

For the waves at point X, state:

(i) the path difference, in cm

path difference = ................................................... cm [1]

(ii) the phase difference.

phase difference = ....................................................... ° [1]

(e) On Fig. 5.1, draw one line, at least 4 cm long, which joins points where only maxima of the
interference pattern are observed. [1]

[Total: 8]
9702/22/O/N/19/Q5

30 (a) State what is meant by the wavelength of a progressive wave.

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

............................................................................................................................................. [1]

(b) A cathode-ray oscilloscope (CRO) is used to analyse a sound wave. The screen of the CRO
is shown in Fig. 5.1.

1 cm

1 cm

Fig. 5.1

The time-base setting of the CRO is 2.5 ms cm–1.

Determine the frequency of the sound wave.

frequency = .................................................... Hz [2]

(c) The source emitting the sound in (b) is at point A. Waves travel from the source to point C
along two different paths, AC and ABC, as shown in Fig. 5.2.

20.8 m C
A

8.0 m
reflecting
B surface

Fig. 5.2 (not to scale)

Distance AB is 8.0 m and distance AC is 20.8 m. Angle ABC is 90°. Assume that there is no
phase change of the sound wave due to the reflection at point B. The wavelength of the
waves is 1.6 m.

(i) Show that the waves meeting at C have a path difference of 6.4 m.

[1]

(ii) Explain why an intensity maximum is detected at point C.

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

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

..................................................................................................................................... [2]

(iii) Determine the difference between the times taken for the sound to travel from the source
to point C along the two different paths.

time difference = ....................................................... s [2]

(iv) The wavelength of the sound is gradually increased. Calculate the wavelength of the
sound when an intensity maximum is next detected at point C.

wavelength = ...................................................... m [1]

[Total: 9]
9702/23/O/N/19/Q5

31 (a) Light waves emerging from the slits of a diffraction grating are coherent and produce an
interference pattern.

Explain what is meant by:

(i) coherence

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

..................................................................................................................................... [1]

(ii) interference.

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

..................................................................................................................................... [1]

(b) A narrow beam of light from a laser is incident normally on a diffraction grating, as shown in
Fig. 5.1.

second order
maximum spot

51° zero order

laser 51° maximum spot
light
diffraction
grating second order
maximum spot
screen

Fig. 5.1 (not to scale)

Spots of light are seen on a screen positioned parallel to the grating. The angle corresponding
to each of the second order maxima is 51°. The number of lines per unit length on the
diffraction grating is 6.7 × 105 m–1.

(i) Determine the wavelength of the light.

wavelength = ..................................................... m [2]

(ii) State and explain the change, if any, to the distance between the second order maximum
spots on the screen when the light from the laser is replaced by light of a shorter
wavelength.

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

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

.......................................................................................................................................[1]

[Total: 5]
9702/21/O/N/20/Q6

32 (a) Describe the conditions required for two waves to be able to form a stationary wave.

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

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

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

............................................................................................................................................. [2]

(b) A stationary wave on a string has nodes and antinodes. The distance between a node and an
adjacent antinode is 6.0 cm.

(i) State what is meant by a node.

..................................................................................................................................... [1]

(ii) Calculate the wavelength of the two waves forming the stationary wave.

wavelength = ................................................... cm [1]

(iii) State the phase difference between the particles at two adjacent antinodes of the
stationary wave.

phase difference = ....................................................... ° [1]

[Total: 5]
9702/22/O/N/20/Q5

33 Microwaves with the same wavelength and amplitude are emitted in phase from two sources X
and Y, as shown in Fig. 5.1.

path of detector
X

A position of central maximum

B position of adjacent minimum
Y

Fig. 5.1 (not to scale)

A microwave detector is moved along a path parallel to the line joining X and Y. An interference
pattern is detected. A central intensity maximum is located at point A and there is an adjacent
intensity minimum at point B. The microwaves have a wavelength of 0.040 m.

(a) Calculate the frequency, in GHz, of the microwaves.

frequency = ................................................. GHz [3]

(b) For the waves arriving at point B, determine:

(i) the path difference

path difference = ..................................................... m [1]

(ii) the phase difference.

phase difference = ........................................................° [1]

(c) The amplitudes of the waves from the sources are changed. This causes a change in the
amplitude of the waves arriving at point A. At this point, the amplitude of the wave arriving from
source X is doubled and the amplitude of the wave arriving from source Y is also doubled.

Describe the effect, if any, on the intensity of the central maximum at point A.

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

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

............................................................................................................................................. [2]

(d) Describe the effect, if any, on the positions of the central intensity maximum and the adjacent
intensity minimum due to the following separate changes.

(i) The separation of the sources X and Y is increased.

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

..................................................................................................................................... [1]

(ii) The phase difference between the microwaves emitted by the sources X and Y changes
to 180°.

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

..................................................................................................................................... [1]

[Total: 9]
9702/23/O/N/20/Q5

34 (a) A sound wave is detected by a microphone that is connected to a cathode-ray oscilloscope

(CRO). The trace on the screen of the CRO is shown in Fig. 5.1.

1.0 cm

1.0 cm

Fig. 5.1

The time-base setting of the CRO is 2.0 × 10–5 s cm–1.

(i) Determine the frequency of the sound wave.

frequency = .................................................... Hz [2]

(ii) The intensity of the sound wave is now doubled. The frequency is unchanged. Assume
that the amplitude of the trace is proportional to the amplitude of the sound wave.

On Fig. 5.1, sketch the new trace shown on the screen. [2]

(iii) The time-base is now switched off.

Describe the trace seen on the screen.

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

..................................................................................................................................... [1]
(b) A beam of light of a single wavelength is incident normally on a diffraction grating, as illustrated
in Fig. 5.2.

diffraction second order

grating

16°
zero order
light beam 16°

second order

Fig. 5.2 (not to scale)

Fig. 5.2 does not show all of the emerging beams from the grating. The angle between the
second-order emerging beam and the central zero-order beam is 16°. The grating has a line
spacing of 3.4 × 10–6 m.

(i) Calculate the wavelength of the light.

wavelength = ..................................................... m [2]

(ii) Determine the highest order of emerging beam from the grating.

highest order = ......................................................... [2]

[Total: 9]
9702/22/O/N/21/Q5

35 A tube is initially fully submerged in water. The axis of the tube is kept vertical as the tube is slowly
raised out of the water, as shown in Fig. 5.1.

loudspeaker

surface of water
air column

water
wall of
tube

Fig. 5.1

A loudspeaker producing sound of frequency 530 Hz is positioned at the open top end of the tube
as it is raised. The water surface inside the tube is always level with the water surface outside the
tube. The speed of the sound in the air column in the tube is 340 m s–1.

(a) Describe a simple way that a student, without requiring any additional equipment, can detect
when a stationary wave is formed in the air column as the tube is being raised.

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

............................................................................................................................................. [1]

(b) Determine the height of the top end of the tube above the surface of the water when a
stationary wave is first produced in the tube. Assume that an antinode is formed level with the
top of the tube.

height = ..................................................... m [3]

(c) Determine the distance moved by the tube between the positions at which the first and
second stationary waves are formed.

distance = ..................................................... m [1]

[Total: 5]
9702/23/O/N/21/Q5

36 (a) For a progressive wave on a stretched string, state what is meant by amplitude.

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

............................................................................................................................................. [1]

(b) Light from a laser has a wavelength of 690 nm in a vacuum.

Calculate the period of the light wave.

period = ...................................................... s [3]

(c) A two-source interference experiment uses the arrangement shown in Fig. 5.1.

D
light from laser,
wavelength λ double slit screen

Fig. 5.1 (not to scale)

Light from a laser is incident normally on a double slit. A screen is parallel to the double slit.

Interference fringes are seen on the screen at distance D from the double slit. The separation
of the centres of the slits is a. The light has wavelength λ.

The separation x of the centres of adjacent bright fringes is measured for different values of
distance D.
The variation with D of x is shown in Fig. 5.2.

0
0 D

Fig. 5.2

The gradient of the graph is G.

(i) Determine an expression, in terms of G and λ, for the separation a of the slits.

a = ......................................................... [2]

(ii) The experiment is repeated with slits of separation 2a. The wavelength of the light is
unchanged.

On Fig. 5.2, sketch a graph to show the results of this experiment. [2]

[Total: 8]
9702/21/O/N/22/Q4

37 (a) Polarisation is a phenomenon associated with light waves but not with sound waves.

(i) State the meaning of polarisation.

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

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

..................................................................................................................................... [1]

(ii) State why light waves can be plane polarised but sound waves cannot.

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

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

..................................................................................................................................... [1]

(b) Two polarising filters A and B are positioned so that their planes are parallel to each other and
perpendicular to a central axis line XY, as shown in Fig. 4.1.

filter filter
A B
direction of
rotation

I0
X Y
unpolarised
light

vertical horizontal
transmission axis transmission axis

Fig. 4.1

The transmission axis of filter A is vertical and the transmission axis of filter B is horizontal.

Unpolarised light of a single frequency is directed along the line XY from a source positioned
at X. The light emerging from filter A is vertically plane polarised and has intensity I0.
 Filter B is rotated from its starting position about the line XY, as shown in Fig. 4.1.
1
After rotation, the intensity of the light emerging from filter B is I0.
4
Calculate the angle of rotation of filter B from its starting position.

angle of rotation = ....................................................... ° [3]

(c) A microwave of intensity I0 and amplitude A0 meets another microwave of the same frequency
1
and of intensity I0 travelling in the opposite direction. Both microwaves are vertically plane
4
polarised and superpose where they meet.

(i) Explain, without calculation, why these two waves cannot form a stationary wave with
zero amplitude at its nodes.

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

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

..................................................................................................................................... [2]

(ii) Determine, in terms of A0, the maximum amplitude of the wave formed.

maximum amplitude = .................................................... A0 [3]

[Total: 10]
9702/22/O/N/22/Q5

38 (a) Two progressive sound waves meet to form a stationary wave. The two waves have the
same amplitude, wavelength, frequency and speed.

State the other condition that must be fulfilled by the two waves in order for them to produce
the stationary wave.

............................................................................................................................................. [1]

(b) A stationary wave is formed on a string that is stretched between two fixed points A and B.
Fig. 5.1 shows the string at time t = 0 when each point is at its maximum displacement.

A B

Fig. 5.1

Distance AB is 0.80 m. The period of the stationary wave is 0.016 s.

(i) On Fig. 5.1, sketch a solid line to show the position of the string:

● at time t = 0.004 s (label this line P)

● at time t = 0.024 s (label this line Q).

[2]

(ii) Determine the speed of a progressive wave along the string.

speed = ................................................ m s–1 [3]

(c) A beam of vertically polarised light of intensity I0 is incident normally on a polarising filter that
has its transmission axis at 30° to the vertical, as shown in Fig. 5.2.

vertically polarised
incident light 30° transmitted transmitted
beam, beam, beam,
intensity I0 intensity I1 intensity I2

polarising filter with second polarising filter

transmission axis at with transmission axis at
30° to the vertical 90° to the vertical

Fig. 5.2

The transmitted light from the first polarising filter has intensity I1. This light is then incident
normally on a second polarising filter that has its transmission axis at 90° to the vertical. The
transmitted light from the second filter has intensity I2.

Calculate:
I1
(i) the ratio
I0

I1
= ......................................................... [2]
I0
I2
(ii) the ratio .
I0

I2
= ......................................................... [2]
I0
[Total: 10]
9702/23/O/N/22/Q4

39 (a) A progressive longitudinal wave travels through a medium from left to right. Fig. 4.1 shows
the positions of some of the particles of the medium at time t0 and a graph showing the
particle displacements at the same time t0.

direction of wave travel

X Y Z

displacement

0
distance

Fig. 4.1

Particle displacements to the right of their equilibrium positions are shown as positive on the
graph and particle displacements to the left are shown as negative on the graph.

The period of the wave is T.

(i) On Fig. 4.1, draw circles around two particles which are exactly one wavelength apart.
[1]

(ii) On Fig. 4.1, sketch a line on the graph to represent the displacements of the particles for
T
the longitudinal wave at time t0 + . [3]
4

T
(iii) State the direction of motion of particle Z at time t0 + .
4
..................................................................................................................................... [1]

(b) The frequency of the wave in (a) is 16 kHz. The distance between particles X and Y is 0.19 m.

Calculate the speed of the wave as it travels through the medium.

speed = ................................................ m s–1 [3]

(c) A longitudinal sound wave is travelling through a solid. The initial intensity of the wave is I0.
The frequency of the wave remains constant and the amplitude falls to half of its original
value.

Determine, in terms of I0, the final intensity of the wave.

intensity = ..................................................... I0 [2]

(d) The sound wave in (c) now meets another sound wave travelling in the opposite direction.

(i) State a condition necessary for these two waves to form a stationary wave.

..................................................................................................................................... [1]

(ii) State two ways in which a stationary wave differs from a progressive wave.

1 ........................................................................................................................................

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2 ........................................................................................................................................

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[2]

[Total: 13]