Doppler Effect Calculator
Calculate the observed frequency of a sound when the source or observer is moving, using the Doppler effect.
How it works
f' = f · (v + v_o) / (v − v_s)
When a source of sound moves toward you, each wave crest is emitted a little closer than the last, bunching the waves into a higher frequency; moving away stretches them into a lower one. This is why a siren’s pitch drops as it passes. Enter speeds toward the other party as positive: a positive source speed raises the pitch, and a positive observer speed does too.
Worked example
An ambulance emitting 440 Hz approaches at 20 m/s while you stand still (speed of sound 343 m/s): f′ = 440 × (343 + 0) ÷ (343 − 20) ≈ 467 Hz, about 27 Hz sharper.
Sources: Doppler effect — Wikipedia
Frequently asked questions
Why does a passing siren change pitch?
As the source approaches, the waves are compressed to a higher frequency; once it passes and recedes, they are stretched to a lower one. You hear that sudden drop as the vehicle goes by.
How do I enter the direction of motion?
Speeds toward the other party are positive. A source moving toward you (positive v_s) and an observer moving toward the source (positive v_o) both raise the pitch. Use negative values for motion away.
Does the Doppler effect apply to light?
Yes, though the exact formula differs because light needs no medium and relativity applies. The redshift of receding galaxies is the optical Doppler effect on a cosmic scale.
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