Doppler Effect Calculator
Find the observed frequency when a sound source or listener is moving.
Shift: +95.8 Hz higher — the pitch rises.
The Doppler effect shifts the pitch you hear when a sound source or listener moves. A 1000 Hz siren approaching you at 30 m/s (with sound at 343 m/s) is heard at f′ = 1000 × 343 ÷ (343 − 30) = 1095.8 Hz — higher. It drops to about 920 Hz once the siren passes and recedes.
What the Doppler effect is
The Doppler effect is the change in a wave’s observed frequency caused by motion between the source and the observer. As a sound source moves toward you, each wavefront is emitted a little closer than the last, so the crests arrive more often and the pitch rises. As it moves away, the crests spread out and the pitch falls. The wave’s speed through the air does not change — only how often the crests reach your ear.
f′ = observed frequency, f = source frequency, v = speed of sound (343 m/s in air), vₒ = observer speed (+ toward source), vₛ = source speed (+ toward observer)
Worked example
An ambulance siren emits f = 1000 Hz and drives toward a stationary listener at vₛ = 30 m/s, with the speed of sound v = 343 m/s and the observer at rest (vₒ = 0):
- 1 Write the Doppler equation. f′ = f · (v + vₒ) ÷ (v − vₛ), with all speeds in m/s and frequency in Hz.
- 2 Sign the speeds. Toward the other party is positive. Here vₒ = 0 (listener still) and vₛ = +30 m/s (source approaching).
- 3 Substitute the values. f′ = 1000 × (343 + 0) ÷ (343 − 30) = 343000 ÷ 313.
- 4 Compute the observed frequency. f′ ≈ 1095.8 Hz — about 96 Hz higher than the emitted 1000 Hz.
Sign conventions for vₒ and vₛ
Motion that shortens the gap between source and observer raises the pitch (a positive shift).
| Who is moving | Direction | Sign in the formula | Effect on pitch |
|---|---|---|---|
| Observer (vₒ) | Toward the source | +vₒ (adds to numerator) | Higher |
| Observer (vₒ) | Away from the source | −vₒ (subtracts) | Lower |
| Source (vₛ) | Toward the observer | +vₛ (subtracts in denominator) | Higher |
| Source (vₛ) | Away from the observer | −vₛ (adds in denominator) | Lower |
Why the pitch drops as it passes
The switch happens at the moment of passing. While the source approaches, vₛ is positive and the denominator (v − vₛ) is small, so f′ is high. The instant it goes by and starts receding, vₛ flips sign, the denominator grows, and f′ drops below the emitted frequency. That sudden fall — high to low — is the familiar “neeeow” of a passing car or siren.
Supersonic sources break the model. If the source reaches the speed of sound (vₛ = v) the denominator hits zero and the formula blows up; beyond it (vₛ > v) the source outruns its own wavefronts and a shock wave — a sonic boom — forms instead of a simple pitch shift. This everyday formula applies only when the source moves slower than sound.