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DOPPLER EFFECT
MCQ
1) A railway engine, travelling at a constant speed on a straight level track is sounding its
whistle. The whistle emits a sound of constant frequency. The engine approaches a station
platform and passes an observer O standing on the platform at time t = T.
Which of the following sketch graphs best shows the variation with time t of the frequency f
of the sound heard by O?
2) A stationary source of sound emits waves of wavelength λ, period T and speed V. The
source now moves with speed v in a straight line away from a stationary observer.
What are the wavelength and the speed of the wave as detected by the observer?
Wavelength Speed
A 𝑉+𝑣
B − 𝑣𝑇 𝑉
C 𝑉−𝑣
D + 𝑣𝑇 𝑉
3) A police car, sounding its siren, is travelling at constant speed towards a stationary
observer. The sound emitted by the siren is of constant frequency. The frequency of the
sound as heard by the observer is higher than that heard by the driver of the police car. The
reason for this is that
A. the wavefronts received by the observer are closer together than the wavefronts received
by the driver.
B. the speed of the wavefronts is greater as measured by the observer than by the driver.
C. the speed of the wavefronts is less as measured by the observer than by the driver.
D. the wavefronts received by the observer are further apart than the wavefronts received by
the driver.
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4) Which of the following is a correct description of the Doppler effect?
A. Change in frequency of light due to motion of the source of light.
B. Change in frequency of light due to relative motion between the source of light and the
observer.
C. Change in observed frequency of light due to relative motion between the source of
light and the observer.
D. Change in observed frequency of light due to change in velocity of the source of light.
5) A source S, moving at constant speed, emits a sound of constant frequency. The source
passes by a stationary observer O, as shown below.
Which one of the following shows the variation with time t of the frequency f observed at O
as the source S approaches and passes by the observer.
6) A sample of hydrogen on Earth emits a spectral line that is measured by an Earth observer
to have wavelength 500 nm. The same spectral line is emitted by a galactic source that is
moving away from Earth at speed of 0.1c. What is the wavelength of the galactic spectral line
that will be measured by the Earth observer?
A. 50 nm B. 450 nm C. 550 nm D. 5000 nm
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7) A point source is moving at a constant speed in a straight-line towards the right and emits
sound waves of constant frequency. The speed of the source is less than the speed of sound.
Which of the diagrams correctly shows the wavefronts emitted by the source?
8) When a train travels towards you sounding its whistle, the pitch of the sound you hear is
different from when the train is at rest. This is because
A. the sound waves are travelling faster toward you.
B. the wavefronts of the sound reaching you are spaced closer together.
C. the wavefronts of the sound reaching you are spaced further apart.
D. the sound frequency emitted by the whistle changes with the speed of the train.
9) A sound emitting source moves along a straight line with speed v relative to an observer at
rest.
The speed of sound relative to the medium is c. The observer measures the speed of sound
emitted by the source as
A. c. B. c + v.
C. c – v. D. v – c.
10) The diagram below represents the wavefronts spreading
out from a moving source of sound S. The positions of four
observers are also shown. If the frequency of the source is f,
which observer hears a sound closest in value to this
frequency when the source is at the position shown?
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11) A train approaches, and passes through, a station. During this period the velocity of the
train is constant and the engine is continuously sounding its whistle. Which one of the
following correctly describes what an observer on the platform will hear?
Sound heard as the train is Sound heard as the train is
approaching the station passing through the station
A Constant frequency Increasing frequency
B Increasing frequency Decreasing frequency
C Decreasing frequency Increasing frequency
D Constant frequency Decreasing frequency
12) A source S produces sound waves of frequency 𝑓 and is moving along a straight line as
shown below.
Which observer I, II, III or IV could hear a sound of frequency f when the source is in the
position shown?
A. I B. II C. III D. IV
13) A source of sound moves directly towards a stationary observer. The frequency of the
sound detected by the observer is different from the source frequency because
A. the loudness of the sound increases as the source moves towards the observer.
B. the apparent wavelength of the sound is longer.
C. the speed of sound relative to the observer is increased.
D. the apparent wavelength of the sound is shorter.
14) A strong wind is blowing in the direction P to Q as shown, at less than the speed of
sound.
A whistle at Q emits sound of frequency f. Which of the following will be true for a
listener at point P?
A. No sound will be heard.
B. The sound heard will have frequency less than f.
C. The sound heard will have frequency f.
D. The sound heard will have frequency greater than f.
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15) A stationary source emits sound of frequency𝑓0 . An observer is moving towards the
source at constant speed along the path indicated by the dotted line. The observer
passes very close to the source at time 𝑇.
Which one of the following graphs best shows the variation with time t of the
frequency f heard by the observer?
Structured Questions
Take speed of sound in air as 330 ms-1 when not given.
1) (a) Describe the Doppler effect.
(b) An observer stands on a bridge above a railway track as a train approaches at a constant
speed of 44 ms-1. The train continuously sounds a whistle which has a frequency of 880 Hz.
Calculate the frequency heard by the observer as the train (i) approaches, (ii) recedes.
(ans: 1015 Hz, 776 Hz)
2) (a) A source approaches a stationary observer at 40 ms -1 emitting sound of frequency 500
Hz. What frequency does the observer hear? (ans: 570 Hz)
(b) A source is moving away from a stationary observer at 32 ms -1 emitting sound of
frequency 480 Hz. What frequency does the observer hear? (ans: 440 Hz)
3) A trumpeter plays her trumpet while in a car. The note she plays has a frequency of 300
Hz but you hear a note with a frequency of 280 Hz. (a) is she moving towards or away from
you? (b) how fast is she moving? (ans: 23.6 ms-1)
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4) A galaxy is moving away from the Earth at 26000 kms-1. Calculate the wavelength and
frequency change of a 650 nm line in its spectrum. (ans: 56.3 nm, 3.7 1013 Hz)
5) An ambulance with a 500 Hz siren approaches and then passes a stationary observer at a
steady speed of 20 ms-1. Calculate the change in frequency of the sound heard by the
observer. (ans: 60.8 Hz)
6) (a) A source emits a sound of frequency 440 Hz. It moves in a straight line towards a
stationary observer with a speed of 30 m s -1. The observer hears a sound of frequency 484
Hz. Calculate the speed of sound in air. (ans: 330 ms-1)
(b) Find the change in the frequency of a siren from a train that is moving towards you at 50
ms-1. Assume that the emitted frequency is 400 Hz and speed of sound in air is 330 ms-1.
(ans: 71.4 Hz)
7) The highest frequency you can hear is 20 000 Hz. If a plane making a sound of frequency
500 Hz went fast enough, you would not be able to hear it. How fast would the plane have to
go? (ans: 321.8 m s-1)
8) A car travelling at 30 ms-1 emits a sound of frequency 500 Hz. Calculate the frequency of
the sound measured by an observer in front of the car. (ans: 550 Hz)
9) Paul is standing on the platform of a station. A high speed train is approaching the station
in a straight line at constant speed and is sounding its whistle.
As the train passes by Paul, the frequency of the sound emitted by the whistle as heard by
Paul, changes from 640 Hz to 430 Hz.
Determine (a) the speed of the train, (b) the frequency of the sound emitted by the whistle as
heard by a person on the train.
–1
(ans: (a) 64.8 m s (b) 514 Hz)
10) A star emits light of wavelength 650 nm. If the light received at the Earth from this star
has a wavelength of 690 nm, how fast is the star moving away from the Earth?
(ans: 0.06 c)
11) An atom of hydrogen travelling towards the Earth at 2 106 m s-1 emits light of
wavelength 658 nm. What is the change in wavelength experienced by an observer on the
Earth? (ans: 4.39 nm)
12) Consider a source moving away from a stationary observer with speed𝑣. The source
emits waves of speed 𝑐 and wavelength𝑠 . Explain why the observer will measure a longer
wavelength for the waves received and show that the shift in wavelength ∆ = 𝑂 − 𝑠 obeys
∆ 𝑣
=𝑐
𝑠
13) A star in another galaxy is traveling away from us at a speed of 5.6106 ms-1. It has a
known absorption spectrum line that should be located at 520 nm on an identical stationary
star. Where is this line located on the moving star? (ans: 530 nm)
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14) A train with a 500 Hz siren on is moving at a constant speed of 8 ms -1 in a straight line.
An observer is in front of the train and off its line of motion. Sketch a graph to show how the
frequency of sound heard by the observer changes with distance travelled by the train
15) Hydrogen atoms in a distant galaxy emit light of wavelength 658 nm. The light received
on Earth is measured to have a wavelength of 689 nm. State whether the galaxy is
approaching the Earth or moving away, and calculate the speed of the galaxy.
(ans: 1.4 107 ms-1 away from Earth)
16) A spectral line has a wavelength of 500 nm when observed in the laboratory. When
observed from the Earth, the same line emitted by a distant star has an apparent wavelength
of 550 nm. Deduce whether the star is approaching or receding from the Earth and calculate
its velocity. (ans: 3 107 ms-1)
17) The sun rotates about its axis with a period of 27 days, emits monochromatic light of
wavelength 0.5 m and has a radius of about 7 108 m. Calculate the shift in frequency of
the light emitted from the Sun’s equator and received on Earth. (ans: 3.78 GHz)
18) A whistle emitting sound of frequency 512 Hz is whirled in a horizontal circle of radius
0.50 m at a constant rate of 100 revolutions per minute.
Taking speed of sound in air as 344 ms-1, calculate the maximum and minimum frequencies
heard by a stationary observer standing some distance away. (ans: 520 Hz, 504 Hz)
19) The diagram shows wavefronts produced by a stationary wave
source S. The spacing of the wavefronts is equal to the wavelength
of the waves. The wavefronts travel with speed 𝑉.
1
(a) The source S now moves to the right with speed 2 𝑉. Draw four
successive wavefronts to show the pattern of waves produced by the
moving source.
(b) Derive the Doppler formula for the observed frequency 𝑓0 of a
sound source, as heard by a stationary observer, when the source
approaches the stationary observer with speed 𝑣. The speed of sound is 𝑉 and the frequency
of the sound emitted by the source is f.
The Sun rotates about its centre. The light from one edge of the Sun, as seen by a stationary
observer, shows a Doppler shift of 0.004 nm for light of wavelength 600.000 nm.
(c) Assuming that the Doppler formula for sound may be used for light, estimate the linear
speed of a point on the surface of the Sun due to its rotation. (ans: 2000 m s-1)
20) When looking at distant stars and galaxies, the further a star or galaxy is from Earth, the
more the light emitted from the star is shifted towards the red end of the spectrum.
(a) State and explain whether the stars and galaxies are moving towards or away from the
Earth,
(b) Explain what the greater shift in frequency for stars that are further away implies.
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21) In a binary star system, two stars orbit a common point and move so that they are always
in diametrically opposite positions. Light from both stars reaches an observer on earth.
Assume that both stars emit light of wavelength 6.58 10-7 m.
(a) When the stars are in the position shown in figure 1, the observer on earth measures a
wavelength of light of 6.58 10-7m for both stars. Explain why there is no Doppler shift in
the wavelength
towards the earth
star A star B
Fig 1
(b) When the stars are in the position shown in figure 2, the earth observer measures two
wavelengths in the received light, 6.50 10-7 m and 6.76 10-7 m. Determine the speed of
each of the stars.
star B
towards the earth
star A
Fig 2
(ans: 3.65 ×106 ms-1, 8.21 ×106 ms-1)
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22) The Doppler effect can be used to measure the speed of blood. Ultrasound, which is
sound of high frequency, is passed from a transmitter into the body, where it reflects off
particles in the blood. The shift in frequency is measured by a stationary detector, placed
outside the body and close to the transmitter.
In one patient, particles in the blood are moving at a speed of 30 cms -1 in a direction directly
away from the transmitter. The speed of ultrasound in the body is 1500 cms -1.
The situation is partly modeled by considering the particles to be emitting sound of frequency
4.00 MHz as they move away from the detector. This sound passes to the detector outside the
body and the frequency measured by the detector is not 4.000 MHz.
(a) State and explain whether the frequency received by the stationary detector is higher or
lower than the frequency emitted by the moving particles.
(b) Calculate the difference between the frequency emitted by the moving particles and the
frequency measured by the detector. (ans: 78 kHz)
(c) Suggest why there is also a frequency difference between the sound received by the
particles and the sound emitted by the transmitter.
