Why does an ambulance siren change pitch as it passes?

As the source approaches, each wavefront is emitted from a closer point, so they bunch up and arrive more often — a higher pitch. After it passes, the wavefronts stretch out and the pitch drops. For sound in air, the observed frequency is f' = f·c/(c∓v) with c = 343 m/s.

Doppler effect

The pitch flips the instant it passes you.

A source crosses the listener. Wavefronts bunch up ahead — higher pitch — and stretch behind — lower pitch.

Source

440 Hz

You hear

440 Hz

Shift

0 Hz

Playback

🔊 Play real audioA tone that Doppler-shifts as it passes — Web Audio

Parameters

Source frequency440 Hz

Source speed100 m/s

Mach number · v/c0.29

c = 343 m/s · sound in air at 20 °C

How to use

The source sweeps left to right across the listener (the marked ear at centre). The You hear readout shows the live observed frequency: it sits high while the source approaches, snaps to the source value at the moment of passing, then drops below as it recedes.

Drag speed and frequency; toggle audio to hear it. Push speed toward 343 m/s and the wavefronts ahead pile into a shock front.

The math

For a source moving through still air, the listener hears

f′ = f · c / (c ∓ v)

with c = 343 m/s (speed of sound in air), v the source speed, minus when approaching, plus when receding.

A 440 Hz source at 100 m/s is heard at 440 · 343/(343−100) = 621.0 Hz approaching, and 440 · 343/(343+100) = 340.6 Hz receding. The closer v gets to c, the more the ahead-frequency blows up — at v = c the wavefronts coincide into a sonic boom.

Examples in life

Ambulance siren — pitches up on approach, drops as it passes. The textbook case.

Radar & lidar guns bounce a known frequency off your car and read the shift to compute speed.

Astronomical redshift — light from receding galaxies stretches redder. Edwin Hubble (1929) used exactly this to show the universe expands.

Doppler ultrasound images blood flow by the shift off moving red cells.

About the audio

Toggle audio on and watch the tone track the visual. The Web Audio API generates the source tone in real time; its frequency is continuously reset to the observed value f · c/(c − v_radial), where v_radial is the component of source velocity along the line to your ear. Approaching, it's positive (pitch up); receding, negative (pitch down). The pitch you hear is the genuine Doppler-shifted frequency, not a recording.

Citations

Doppler (1842) — Über das farbige Licht der Doppelsterne, Abh. K. Böhm. Ges. Wiss.
Buys Ballot (1845) — first experimental verification with trumpeters on a train.
Hubble (1929) — recession velocities of nebulae, PNAS 15, 168.
Rosen & Howell (2011) — Understanding Acoustics, ch. on Doppler in air (c = 343 m/s).
Griffiths (2017) — Introduction to Electrodynamics, §12 on relativistic Doppler for completeness.

Built by Joshua Chua · Fable rebuild · vanilla JS + Canvas + Web Audio