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– 19 –
M06/4/PHYSI/HP2/ENG/TZ2/XX+
(Question B2 continued)
The Doppler effect
(f)
A source S emits sound waves at constant frequency. In the diagram below, S is moving
at constant speed in the direction shown, along a straight-line between two stationary
observers A and B.
B
A
S
(i)
(ii)
Draw, on the above diagram, three wavefronts representing the waves emitted
by S.
[2]
Use your sketch to explain any difference in the frequency of the sound as heard by
observer A and by observer B.
[2]
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1933
– 20 –
M06/4/PHYSI/HP2/ENG/TZ2/XX+
(Question B2 continued)
(g)
Some speed detectors make use of the Doppler effect and the beat frequency between a
transmitted wave and a reflected wave.
(i)
Explain, with reference to sound waves, the term beat frequency.
[2]
..................................................................
..................................................................
..................................................................
..................................................................
(ii)
Some speed detectors transmit microwaves rather than sound. In this situation, the
Doppler equations that apply to sound can also be assumed to apply to microwaves.
In the diagram below, a speed detector in a stationary police car emits microwaves
of frequency 10.6 GHz. The waves are reflected off an approaching car.
reflected wave
transmitted radar
wave
radar transmitter
18.0 m s–1
Police
stationary
moving car
The car is travelling in a direct line towards the police car with a speed 18.0 m s–1.
The reflected waves are Doppler shifted and interfere with the transmitted waves to
produce beats. The speed of the microwaves is 3.00 % 108 m s!1.
Calculate the beat frequency measured at the speed detector.
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
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– 31 –
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(Question B4, part 1 continued)
Doppler effect
(d)
(i)
State what is meant by the Doppler effect.
[2]
..................................................................
..................................................................
..................................................................
..................................................................
(ii)
A source of sound has frequency f and is moving with constant speed v
directly towards a stationary observer. The speed of sound in still air is c.
Derive an expression for the frequency fo of the sound heard by the observer.
Explain your working.
[3]
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
(iii) A moving police car produces sound from its engine and from its siren. The car
passes a stationary person. The person notices a Doppler shift as the car passes.
When the police car, travelling at the same speed, next passes the person, its siren
is not sounding. The Doppler shift is not as noticeable. Suggest one reason for this
observation.
[2]
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(Question B2 continued)
Part 2
(a)
The Doppler effect
State what is meant by the Doppler effect.
[2]
.......................................................................
.......................................................................
.......................................................................
(b)
The frequency of a sound emitted by a source is f and its wavelength is !. The speed of
sound in air is v.
An observer is moving at constant speed u towards a stationary sound source.
observer
u
source
State, in terms of f, u and v, the
(i)
speed of the sound relative to the observer.
[1]
..................................................................
(ii)
frequency of the sound as measured by the observer.
[1]
..................................................................
(c)
Deduce that the wavelength of the sound as measured by the observer is equal to !.
[2]
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(Question B2, part 2 continued)
(d)
The frequency of the source is 1200 Hz. The sound is reflected from the moving observer
and is received back at the source. The frequency of the received sound back at the
source is 1400 Hz. The speed of sound v in air is 340 m s–1.
Determine the speed u of the moving observer.
[4]
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.......................................................................
.......................................................................
.......................................................................
.......................................................................
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±±
M10/4/PHYSI/HP2/ENG/TZ1/XX+
(Question B3 continued)
Part 2
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[1]
(This question continues on the following page)
2210-6508
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