๐จ Doppler Effect Calculator
Uses the speed of sound at 343 m/s (20ยฐC air). Enter velocities as positive when moving toward the other party.
Enter a sound sourceโs frequency along with the observerโs and sourceโs velocities to calculate the observed frequency using the standard Doppler effect formula. This models the effect where a siren sounds higher-pitched as it approaches and lower-pitched as it moves away.
How to use
- Enter the source frequency (Hz).
- Enter the observerโs velocity (positive when moving toward the source).
- Enter the sourceโs velocity (positive when moving toward the observer).
- The observed frequency is calculated automatically.
How the calculation works
This tool calculates how the pitch (frequency) you hear changes when the sound source or the listener is moving. fโฒ = f ร (V + vo) รท (V โ vs) f is the source frequency, V the speed of sound (343 m/s in 20ยฐC air), vo the observerโs speed and vs the sourceโs speed. Enter both as positive when moving toward the other party and negative when moving away. Approaching squeezes the sound waves together so the pitch sounds higher; moving apart stretches them so it sounds lower. If the source approaches at or above the speed of sound, or the observer moves away so fast that the sound never arrives, the formula breaks down and no result is shown.
Worked example
A 700 Hz siren approaching at 30 m/s (108 km/h) 700 ร 343 รท (343 โ 30) โ 767.09 Hz The same siren moving away at 30 m/s 700 ร 343 รท (343 + 30) โ 643.70 Hz An observer moving at 30 m/s toward a stationary siren 700 ร (343 + 30) รท 343 โ 761.22 Hz At the same speed, a moving source and a moving observer give slightly different results.
Things to be aware of
- The speed of sound depends on temperature, roughly 331.5 + 0.6 ร temperature (ยฐC) m/s. At 0ยฐC it is about 331 m/s, which shifts the result a little.
- The Doppler effect for light (such as the redshift of galaxies) uses a different formula based on relativity.
- Wind moves the air that carries the sound, so results in windy conditions differ from this calculation.
FAQ
What formula does this use?
It uses the standard Doppler effect formula f' = f ร (v + observer velocity) / (v - source velocity), where v is the speed of sound.
What speed of sound does this use?
It uses the standard value for the speed of sound in air at 20ยฐC: 343 meters per second.
What happens if the source moves faster than the speed of sound?
This tool only supports subsonic source speeds. Above the speed of sound the formula breaks down, so no result is shown.