The Doppler effect
When a sound source moves toward you, each wave crest is emitted a little closer than the last, so the waves bunch up and you hear a higher frequency. When it moves away, the waves stretch out and the pitch drops. The same happens if you move toward or away from the source.
The formula for sound
f’ = f × (c + vo) ÷ (c − vs)
- f: frequency emitted by the source
- c: speed of sound, about 343 m/s in air at 68 °F
- vo: speed of the observer toward the source
- vs: speed of the source toward the observer
When they move apart, reverse the signs: f’ = f × (c − vo) ÷ (c + vs).
Worked example
An ambulance siren emits 700 Hz and drives past you at 55 mph (24.6 m/s) while you stand still.
- Approaching: 700 × 343 ÷ (343 − 24.6) = 754.1 Hz, about 7.7% higher.
- Moving away: 700 × 343 ÷ (343 + 24.6) = 653.2 Hz.
- Pitch drop as it passes: 12 × log₂(754.1 ÷ 653.2) = 2.5 semitones, a clearly audible change.
Speed of sound
| Medium | Speed of sound |
|---|---|
| Air at 32 °F (0 °C) | 331 m/s |
| Air at 68 °F (20 °C) | 343 m/s |
| Water | about 1,480 m/s |
| Steel | about 5,900 m/s |
As a source approaches the speed of sound, the waves pile up into a shock wave: that is the sonic boom of a supersonic jet.
Applications
- Police radar and speed guns measure the frequency shift of reflected radio waves.
- Doppler weather radar detects rain moving toward or away from the antenna and the rotation in thunderstorms.
- Medical ultrasound measures blood flow in arteries and in a baby’s heart.
- Astronomy: light from galaxies moving away is shifted toward red, which revealed the expansion of the universe. For light, a relativistic formula is used instead.
- Bats and dolphins use Doppler shifts in their echolocation to track moving prey.