AS PHYSICS (9702)

WAVE
THEORY
QUESTIONS
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5 (a) (i) State the conditions required for the formation of a stationary wave.

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

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

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

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

(ii) State the phase difference between any two vibrating particles in a stationary wave
between two adjacent nodes.

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

(b) A motorcycle is travelling at 13.0 m s–1 along a straight road. The rider of the motorcycle sees
a pedestrian standing in the road directly ahead and operates a horn to emit a warning sound.
The pedestrian hears the warning sound from the horn at a frequency of 543 Hz. The speed
of the sound in the air is 334 m s–1.

(i) Calculate the frequency, to three significant figures, of the sound emitted by the horn.

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

(ii) The motorcycle rider passes the stationary pedestrian and then moves directly away from
her. As the rider moves away, he operates the horn for a second time. The pedestrian
now hears sound that is increasing in frequency.

State the variation, if any, in the speed of the motorcycle when the rider operates the
horn for the second time.

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

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(c) A beam of vertically polarised monochromatic light is incident normally on a polarising filter,
as shown in Fig. 5.1.

polarising
filter

vertically polarised 20° transmitted

incident light beam, light beam,

intensity I0 intensity IT

transmission
axis of filter

Fig. 5.1

The filter is positioned with its transmission axis at an angle of 20° to the vertical.
The incident light has intensity I0 and the transmitted light has intensity IT.
IT
(i) By considering the ratio , calculate the ratio
I0

amplitude of transmitted light .

amplitude of incident light

Show your working.

ratio = ......................................................... [3]

(ii) The filter is now rotated, about the direction of the light beam, from its starting position
shown in Fig. 5.1. The direction of rotation is such that the angle of the transmission axis
to the vertical initially increases.

Calculate the minimum angle through which the filter must be rotated so that the intensity
of the transmitted light returns to the value that it had when the filter was at its starting
position.

angle = ....................................................... ° [1]

[Total: 10]
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5 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]

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(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]

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5 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]

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(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]

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5 (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]

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(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

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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]

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4 (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.

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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]

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5 (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]

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(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]

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4 (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]

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(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 ........................................................................................................................................

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

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

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

[Total: 13]

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4 (a) State the principle of superposition.

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

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

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

(b) A transmitter produces microwaves that travel in air towards a metal plate, as shown in
Fig. 4.1.

microwave metal
transmitter microwave plate
receiver

Fig. 4.1

The microwaves have a wavelength of 0.040 m. A stationary wave is formed between the
transmitter and the plate.

(i) Explain the function of the metal plate.

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

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

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

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

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(iii) A microwave receiver is initially placed at position X where it detects an intensity

minimum. The receiver is then slowly moved away from X directly towards the plate.

1. Determine the shortest distance from X of the receiver when it detects another
intensity minimum.

distance = ........................................................... m

2. Determine the number of intensity maxima that are detected by the receiver as it
moves from X to a position that is 9.1 cm away from X.

number = ...............................................................
[2]

[Total: 8]

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5 A source of sound is attached to a rope and then swung at a constant speed in a horizontal circle,
as illustrated in Fig. 5.1.

horizontal circular
path of source,
radius 2.4 m

rope source
of sound
distant
observer

Fig. 5.1 (not to scale)

The source moves with a speed of 12.0 m s−1 and emits sound of frequency 951 Hz. The speed of
the sound in the air is 330 m s−1. An observer, standing a very long distance away from the source,
hears the sound.

(a) Calculate the minimum frequency, to three significant figures, of the sound heard by the
observer.

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

(b) The circular path of the source has a radius of 2.4 m.

Determine the shortest time interval between the observer hearing sound of minimum
frequency and the observer hearing sound of maximum frequency.

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

[Total: 4]

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4 (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

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(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]

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4 (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]

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(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]

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4 (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)

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(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]

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(i) Explain why the frequency of the sound detected by the observer is sometimes above
and sometimes below 1.2 kHz.

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

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

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

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

(ii) State the name of the phenomenon in (b)(i).

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

(iii) On Fig. 4.1, mark with a letter X the position of the vehicle when it emitted the sound that
is detected at time T. [1]

(iv) On Fig. 4.1, mark with a letter Y the position of the vehicle when it emitted the sound that
9T
is detected at time . [1]
4
(c) The speed of the sound in the air is 320 m s–1.

Use Fig. 4.2 to determine the speed of the vehicle in (b).

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

[Total: 9]

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4 A child sits on the ground next to a remote-controlled toy car. At time t = 0, the car begins to move
in a straight line directly away from the child. The variation with time t of the velocity of the car
along this line is shown in Fig. 4.1.

15
velocity / m s–1
10

0
0 1 2 3 4 5 6
t/s

Fig. 4.1

The car’s horn continually emits sound of frequency 925 Hz between time t = 0 and time t = 6.0 s.
The speed of the sound in the air is 338 m s–1.

(a) Describe qualitatively the variation, if any, in the frequency of the sound heard, by the child,
that was emitted from the car horn:

(i) from time t = 0 to time t = 2.0 s

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

(ii) from time t = 4.0 s to time t = 6.0 s.

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

(b) Determine the frequency, to three significant figures, of the sound heard, by the child, that
was emitted from the car horn at time t = 3.0 s.

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

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(c) Determine the time taken for the sound emitted at time t = 4.0 s to travel to the child.

time taken = ...................................................... s [2]

[Total: 6]

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5 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]

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(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]

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5 (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.

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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]

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

(i) the wavelength

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

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

(ii) the amplitude.

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

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

(b) A beam of red laser light is incident normally on a diffraction grating.

(i) Diffraction of the light waves occurs at each slit of the grating. The light waves emerging
from the slits are coherent.

Explain what is meant by:

1. diffraction

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

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

2. coherent.

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

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

(ii) The wavelength of the laser light is 650 nm. The angle between the third order diffraction
maxima is 68°, as illustrated in Fig. 4.1.

third order
diffraction maximum

laser light
68°
wavelength 650 nm

third order
diffraction diffraction maximum
grating

Fig. 4.1 (not to scale)

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Calculate the separation d between the centres of adjacent slits of the grating.

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

(iii) The red laser light is replaced with blue laser light.

State and explain the change, if any, to the angle between the third order diffraction
maxima.

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

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

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

[Total: 9]

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4 (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]

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(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]

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4 (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]

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(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]
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4 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]

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(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]

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5 A progressive wave Y passes a point P. The variation with time t of the displacement x for the
wave at P is shown in Fig. 5.1.

6.0

4.0
x / mm
2.0

0
0 0.1 0.2 0.3 0.4 0.5
t/s
–2.0

–4.0

–6.0

Fig. 5.1

The wave has a wavelength of 8.0 cm.

(a) Determine the speed of the wave.

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

(b) A second wave Z has wavelength 8.0 cm and amplitude 2.0 mm at point P. Waves Y and Z
have the same speed.

For the waves at point P, calculate the ratio

intensity of wave Z
.
intensity of wave Y

ratio = ......................................................... [3]

[Total: 5]

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6 (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]

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5 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]

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(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]

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Waves Answer Key

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