Doppler Effect Calculator (Moving Source & Observer)
Find the pitch a listener hears when the sound source, the observer, or both are moving, using the full Doppler formula.
How it works
f' = f · (c + v_observer) ÷ (c − v_source) · speeds positive when moving toward the other party
The Doppler effect shifts the pitch of a sound when the source, the listener, or both move through the medium. An approaching source crowds its wavefronts together, raising the pitch; a receding one stretches them, lowering it — the classic drop you hear as a siren passes. The full formula f′ = f(c + v_o)/(c − v_s) uses the sign convention that speeds are positive when each party moves toward the other, and it fails once the source reaches the speed of sound, where the wavefronts pile into a shock wave.
Worked example
A 440 Hz horn approaches at 30 m/s while you stand still, with sound at 343 m/s: f′ = 440 × (343 + 0) ÷ (343 − 30) = 440 × 343 ÷ 313 ≈ 482 Hz — a rise of about 42 Hz. After it passes, flip the source speed to −30 m/s and the pitch drops to about 405 Hz.
Sources: Doppler effect — Wikipedia
Frequently asked questions
Why does a siren’s pitch drop as it passes?
While approaching, the source moves toward each wave it emits, bunching the wavefronts and raising the frequency you hear. Once it passes and recedes, the wavefronts spread out and the pitch falls — a sudden drop right as it goes by.
How do I set the signs for the speeds?
Enter each speed as positive when that party moves toward the other and negative when moving away. A source approaching you and an observer chasing the source both raise the pitch.
Why does the formula break down at the speed of sound?
When the source speed reaches the speed of sound, the denominator (c − v_s) hits zero and the predicted frequency diverges. Physically the wavefronts stack into a shock wave — the sonic boom — and this subsonic formula no longer applies.
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This calculator is for educational purposes. Double-check important results before acting on them.