Doppler effect
The Doppler effect is a change in observed frequency caused by relative motion along the line joining source and observer. For sound, the medium matters: moving the source and moving the observer alter the wave encounter in different ways.
Moving toward raises received frequency
When a sound source moves toward an observer, each new crest is emitted from a position closer to the previous crest, shortening the wavelength ahead. Moving away stretches the wavelength behind.
Source motion: change the wavelength pattern
Stationary observer, moving source: fobs = fs v/(v ∓ vs).
Use the minus in the denominator for approach and plus for recession.
Moving-source sound Doppler
Stationary observer; source moves directly toward or away. fobs = fs v/(v ∓ vs).
This classical expression assumes speeds below the wave speed and motion along the source-observer line.
Observer motion: cross wavefronts faster or slower
Stationary source, moving observer: fobs = fs(v ± vobs)/v.
Use plus for motion toward the source and minus for motion away.
The wavefront spacing in the medium is unchanged by observer motion; only the rate at which the observer encounters those fronts changes.
Not every “relative speed” formula is interchangeable
For sound, the medium defines a preferred frame for wave propagation, so source and observer velocities enter differently. At everyday speeds the qualitative rule remains simple: approach raises observed frequency; separation lowers it.
For light in vacuum, relativistic Doppler formulas replace the classical sound expressions. Astronomical redshift and blueshift therefore should not be calculated with the sound formula above.
What the Doppler effect changes—and what it does not
For a source with a fixed emitted frequency, Doppler motion changes the frequency received by the observer. It does not require the source oscillator itself to speed up or slow down. For sound from a moving source, the medium-frame wavelength changes because successive crests are emitted from different source positions.
The velocity that matters is the component along the source-observer line. Pure sideways motion at one instant has no first-order classical Doppler shift along that line. As a vehicle passes, that radial component changes sign, which explains the characteristic high-to-low transition.
Worked examples
1. Moving source toward observer
A 600 Hz siren approaches a stationary observer at 20 m s−1. Take sound speed 340 m s−1.
Solution
fobs = 600[340/(340−20)] = 637.5 Hz.
2. Moving observer toward source
A stationary 500 Hz source emits sound at 340 m s−1. An observer moves toward it at 10 m s−1.
Solution
fobs = 500[(340+10)/340] ≈ 514.7 Hz.
3. Passing source concept
Why does a passing siren shift from high to low frequency near the moment it passes?
Solution
Before passing, the radial component of relative motion is mainly toward the observer, raising received frequency. After passing it is mainly away, lowering it. The source frequency itself has not suddenly changed.