By Zencalcy Editorial TeamLast reviewed About us
Motion changes the rate at which wavefronts reach a listener. A source moving toward you compresses the waves and raises the pitch; moving away stretches them and lowers it. A listener moving toward the source meets the fronts sooner, with the opposite sign in the same equation. This page uses the non-relativistic acoustic form.
Observed frequency for a moving source or listener.
f′ = f₀ (a + v_o) / (a − v_s)
a is the sound speed, v_o the observer speed toward the source and v_s the source speed toward the observer. Use negative values for motion away. The source term diverges as v_s approaches a.
| Symbol | Meaning |
|---|---|
| f′ | Observed frequency. |
| f₀ | Emitted frequency. |
| a | Speed of sound in the medium. |
| v_o | Observer speed, positive toward the source. |
| v_s | Source speed, positive toward the observer. |
A 440 Hz siren approaching at 30 m/s in 343 m/s air is heard at 440 × 343 / (343 − 30) = 482.2 Hz, about 166 cents sharp.
Continue with the Sound Distance Attenuation Calculator, Mach Number Calculator, or the Resonance Tube Calculator — or browse more acoustics and sound tools and all physics calculators.
The sign of the source velocity flips. Before passing, the source closes the gap and raises the pitch; afterward it opens the gap and lowers it, so the apparent jump is one continuous sweep.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026