Why a passing siren drops in pitch.
The siren's own note never changes — but its sound waves bunch up ahead of the car and stretch out behind it, so what you hear does. Steer the car below and watch the pitch fall the instant it passes you.
Car speed vₛ
vₛ↑ ⇒ bigger shift
0 km/ha car you steer past a fixed listener160 km/h
Watch the car cross the fixed listener — the pitch you'd hear switches the instant it passes, from the higher approaching note to the lower receding one.
What the listener hears
Hz
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Named for physicist Christian Doppler, who described the effect in 1842 — see Doppler effect on Wikipedia. The siren is modelled at a fixed 700 Hz, a typical dominant tone for an emergency-vehicle siren, and sound travels at 343 m/s, the standard reference figure for dry air at about 20°C (a touch faster when warmer, slower when colder). To keep the equation tractable this page holds the listener still (vₒ = 0); the full formula also has a ±vₒ term in the numerator for a moving listener, shown above only in its stationary-listener form. As the car's speed climbs toward 343 m/s itself, the denominator v − vₛ shrinks toward zero and the approaching frequency shoots toward infinity — the mathematical signature of the sonic boom a supersonic vehicle would produce, well beyond anything on the slider above and not modelled here. The same equation, applied to light instead of sound and corrected for relativity, is how astronomers measure galaxies receding from us via redshift — a related idea, not the one modelled on this page.