The Doppler effect Cambridge International AS & A Level Physics revision
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In plain words
An ambulance siren sounds higher as it comes towards you and lower as it goes away. The siren hasn't changed. Coming towards you, it is catching up with its own waves and bunching them together; going away, it is stretching them out.
Three things to know
- When a source moves relative to an observer, the observed frequency is different from the source frequency. Moving closer: higher frequency, shorter wavelength. Moving apart: lower frequency, longer wavelength.
- For a source moving at speed v_s with a stationary observer: f_o = f_s × v ÷ (v ± v_s), where v is the wave speed. Use minus for a source approaching and plus for one moving away.
- The same effect shifts the light from stars and galaxies: light from one moving away is redshifted.
Worked example
A source emits sound at 500 Hz and moves towards a stationary observer at 20 m/s. The speed of sound is 340 m/s. Find the frequency heard.
- The source is approaching, so use v − v_s.
- f_o = 500 × 340 ÷ (340 − 20) = 500 × 340 ÷ 320.
- = 531 Hz.
Tips and tricks
- Sense-check the sign: approaching must give a higher frequency, so the bottom of the fraction must be smaller.
- The source's actual frequency never changes. Only what the observer receives does.
It lands in your notebook with its questions as flashcards.
The Doppler effect: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
A sound source moves towards you. How does the frequency you hear compare with the frequency emitted?
The wavefronts are bunched together.
What happens to the observed wavelength when a source moves away?
The waves are stretched out.
In f_o = f_s v ÷ (v ± v_s), which sign is used for a source moving away?
A bigger denominator gives a lower frequency.
What does not change when a source moves relative to an observer?
The effect is in what is received.
Light from a distant galaxy is redshifted. What does this show?
Its light waves have been stretched.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 6 marks. Write your answers on paper, then check them.
The Doppler effect
Cambridge International AS & A Level Physics 9702 · 6 marks · papermunch.org
Name ______________________________ Date ______________
A car horn of frequency 400 Hz moves away from an observer at 30 m/s. The speed of sound is 340 m/s. Find the observed frequency.[3]
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368 Hz. 400 × 340 ÷ 370.
Explain why the observed frequency is higher when a source approaches.[2]
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The source moves towards the observer between emitting successive wavefronts, so the wavefronts are closer together: the wavelength is shorter and more arrive each second.
State what is observed in the light from a star that is moving away from the Earth.[1]
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Its spectral lines are shifted to longer wavelengths (redshift).
Answers: The Doppler effect
- 1. 368 Hz. 400 × 340 ÷ 370.
- 2. The source moves towards the observer between emitting successive wavefronts, so the wavefronts are closer together: the wavelength is shorter and more arrive each second.
- 3. Its spectral lines are shifted to longer wavelengths (redshift).