Explain the Doppler effect for a moving source
Relate observed sound frequency to source motion toward or away from a stationary observer.
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 7. These original wave examples and diagrams are conceptual study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use frequency, period, wavelength, amplitude, speed and trigonometric ratios with consistent units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
For a source approaching a stationary observer, is the observed frequency higher or lower?
What you will learn
- Explain why source motion changes observed sound frequency
- Use the moving-source Doppler equation for a stationary observer
- Choose the sign according to source approach or recession
A moving source changes wavefront spacing
A source emits successive sound wavefronts. When it moves toward a stationary observer, each later wavefront starts closer to the previous one in the direction of motion, so the wavelength in front is shorter and observed frequency is higher.
When the source moves away, wavefronts reaching the observer are more spread out, so observed frequency is lower. The source frequency is the emission frequency; the observer's changed frequency does not mean the source has changed its oscillation rate.
Apply the moving-source formula with the right sign
For a source moving relative to a stationary observer, use fₒ = fₛv/(v − vₛ) when the source approaches and fₒ = fₛv/(v + vₛ) when it recedes. Here v is sound speed and vₛ is source speed.
The denominator is smaller during approach, giving fₒ > fₛ; it is larger during recession, giving fₒ < fₛ. This syllabus treatment is for a stationary observer and a moving source; do not add a moving-observer term.
Pause and explain
Which denominator applies to a source receding from a stationary observer?
Worked example
A siren emits 500 Hz sound and moves toward a stationary observer at 20 m s⁻¹. Take sound speed as 340 m s⁻¹. Find the observed frequency.
Show the worked solution
- For approach, use the minus sign in the denominator.
- fₒ = 500 × 340/(340 − 20).
- Evaluate the ratio and compare with 500 Hz.
Answer fₒ = 531.25 Hz, approximately 531 Hz, higher than the emitted frequency.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A source emits 600 Hz sound and moves away from a stationary listener at 30 m s⁻¹. Take sound speed as 330 m s⁻¹. Calculate the observed frequency.
Give me a hint
For a receding source, add source speed in the denominator.
Compare my reasoning
- Use fₒ = fₛv/(v + vₛ).
- fₒ = 600 × 330/(330 + 30).
- Compare with the emitted 600 Hz.
550 Hz, lower than the emitted frequency.
Look for these in your work
- Receding sign selected
- Values substituted
- Frequency trend checked
A source moving toward a stationary observer emits 800 Hz sound. Let v = 340 m s⁻¹ and vₛ = 20 m s⁻¹. Find the observed frequency.
Give me a hint
Use v − vₛ for approach.
Compare my reasoning
- fₒ = 800 × 340/(340 − 20).
- The denominator is 320 m s⁻¹.
- Calculate the result in hertz.
850 Hz.
Look for these in your work
- Approach sign selected
- Substitution correct
- Hertz unit stated
A stationary listener hears a siren rise in pitch as an ambulance approaches and fall after it passes. Explain the frequency change and state which speed is used in the formula.
Give me a hint
Connect wavefront spacing with observed frequency; distinguish source speed from wave speed.
Compare my reasoning
- Before the pass, the source approaches, so wavefronts reaching the listener are closer and frequency is higher.
- After passing, the source recedes, wavefronts spread and frequency is lower.
- The formula uses sound speed v in the medium and source speed vₛ relative to the stationary observer.
Observed frequency is higher on approach and lower on recession because emitted wavefront spacing changes. Use the sound speed in the medium and the source's speed; the listener is stationary.
Look for these in your work
- Approach and recession distinguished
- Wavefront reason stated
- Both speeds correctly identified
Common mistakes
- Using the approach sign when the source recedes
- Changing the source frequency rather than the observed frequency
- Including motion of the observer in this syllabus formula
What can you explain now?
For a source approaching a stationary observer, is the observed frequency higher or lower?
Compare with the explanation
Higher
Wavefronts in front of the moving source are compressed.
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Make it stick
Why does the moving-source formula use different signs for approach and recession?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.