A passing siren drops in pitch the instant it goes by. The wave itself has not changed; the motion of the source has bunched the wavefronts ahead and stretched them behind, changing the frequency you receive.
When a source moves relative to an observer, the observed frequency differs from the emitted one: this is the Doppler effect. For a source of speed vₛ emitting frequency fₛ in a medium where the wave speed is v, the observed frequency is fₒ = fₛ v / (v ± vₛ), with the minus sign for an approaching source (higher pitch) and plus for a receding source (lower pitch).
Move the source and watch the circular wavefronts crowd together in front and spread out behind. The observed frequency rises on approach and falls on recession, exactly as the formula predicts.
One formula, two signs.
| Formula | Case | Effect |
|---|---|---|
| fₒ = fₛ v / (v − vₛ) | source approaching | observed frequency higher |
| fₒ = fₛ v / (v + vₛ) | source receding | observed frequency lower |
Four quick checks tied to this lesson. Each correct answer earns XP and lights this skill on your star map.
The Doppler effect is a change in observed frequency that occurs when:
As a source of sound moves toward a stationary observer, the observed frequency is:
For a moving source and a stationary observer, the observed frequency is given by:
After a source has passed the observer and is moving away, the observed frequency is:
The same physics works from sirens to galaxies.
Get the sign right: subtract the source speed in the denominator for an approaching source (which raises the frequency) and add it for a receding one. The wave speed v is the speed in the medium and does not change; it is the spacing of the wavefronts, and hence the frequency, that changes. The syllabus formula here is for a moving source with a stationary observer.
Unlocks once the checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
A siren emitting 400 Hz moves toward a stationary observer at 30 m s⁻¹. Taking the speed of sound as 340 m s⁻¹, the observed frequency is:
The same siren (400 Hz) now recedes from the observer at 30 m s⁻¹. The observed frequency is:
Light from distant galaxies shows a Doppler shift to longer wavelengths (redshift). This indicates that the galaxies are:
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