Doppler Shift Calculator
Find the frequency a listener hears when a sound source and observer move, using the classic Doppler equation.
How it works
f' = f · (c + v_observer) ÷ (c − v_source) · speeds positive toward the other party
The Doppler effect raises the pitch of an approaching source and lowers it for one receding, because the motion compresses or stretches the wavefronts reaching the listener. Here speeds are signed toward the other party: a positive source speed shortens the effective wavelength and lifts the frequency. When the source reaches the speed of sound the denominator hits zero and the formula fails — that is the sonic-boom limit.
Worked example
A 440 Hz horn approaching at 30 m/s in 343 m/s air, observer stationary, is heard at 440 × (343 + 0) ÷ (343 − 30) = 440 × 343 ÷ 313 ≈ 482.2 Hz — about a semitone sharp.
Sources: Doppler effect — Wikipedia
Frequently asked questions
Why does an approaching siren sound higher?
As the source moves toward you it emits each successive wave crest a little closer than the last, packing more crests into each second. The higher frequency of arrival is heard as a higher pitch; the pitch drops as the source passes and recedes.
What sign convention does this use?
Each speed is positive when that party moves toward the other. A source approaching you is positive; an observer moving toward the source is positive. Use negative values for receding motion.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.