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Waves · Relative motion

Doppler Effect Frequency Calculator

Calculate the observed frequency when a sound source, observer, or both move along their line of sight through a stationary medium.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Classical longitudinal waves in a stationary medium along one line of sight

Observed frequency

fₒ = fₛ(v + vₒ)/(v − vₛ)

Observer sign

vₒ > 0: toward source

Source sign

vₛ > 0: toward observer
Doppler effect

Hear relative motion as a frequency shift

Use negative velocity when moving away. Inputs accept at most three decimal places; displayed results are rounded to at most three decimal places. The source must remain subsonic in this classical model.

fo = fs(v + vo)/(v − vs)

Enter the wave speed and signed source and observer velocities.

Using the model

Symbols, assumptions and limitations

Interpretation notes

This is the classical longitudinal-wave model for a stationary medium. Positive observer velocity means motion toward the source; positive source velocity means motion toward the observer. It is appropriate for sound and other mechanical waves at subsonic source speeds, not for relativistic light Doppler shift.

Worked examples

See the method in practice

01

Approaching siren

A 500 Hz source approaching at 20 m/s through 343 m/s air is heard at about 530.960 Hz by a stationary observer.

02

Observer approaches

A stationary 800 Hz source heard by an observer approaching at 15 m/s produces about 834.985 Hz when sound speed is 343 m/s.

Questions

Frequently asked

Why do source and observer speeds enter differently?

Observer motion changes the rate at which wavefronts are encountered; source motion changes the spacing of the emitted wavefronts in the medium.

Which direction is positive?

Use positive observer speed toward the source and positive source speed toward the observer. Use negative values when either moves away.

Can this calculate Doppler shift for light?

No. Light requires the relativistic Doppler formula because there is no stationary propagation medium and velocities combine relativistically.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax University Physics — The Doppler Effect

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology