Doppler effect calculator
Enter the frequency of the sound, the speed of sound and how fast the source and the listener move, toward or away from each other. The calculator gives the frequency you hear, how much higher or lower it is and the wavelength that reaches you.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Enter the frequency the source emits, in hertz.
- Check the speed of sound (343 m/s in air at about 20 °C).
- Enter the source’s and the listener’s speeds and choose the direction of each.
- Read the frequency heard and the shift.
f′ = f × (c + vₒ) ÷ (c − vₛ)
- vₒ is positive when the listener moves toward the source, negative when away;
- vₛ is positive when the source moves toward the listener, negative when away;
- the wavelength reaching the listener is (c − vₛ) ÷ f;
- the shift in semitones is 12 × log₂(f′ ÷ f).
Worked example
An ambulance siren at 440 Hz drives toward you at 30 m/s: f′ = 440 × 343 ÷ (343 − 30) = 482.17 Hz, 42.17 Hz (9.58%, about 1.58 semitones) higher. Once it has passed and drives away at the same speed: 440 × 343 ÷ 373 = 404.61 Hz.
Tips
- The pitch does not keep rising as the source comes closer. It stays at the higher value and drops when the source passes.
- Wind changes the result; the formula assumes still air.
- For light, the Doppler shift uses the speed of light and relativity, so this sound formula does not apply.
Frequently asked questions
What is the Doppler effect formula for sound?
f′ = f × (c + vₒ) ÷ (c − vₛ), where c is the speed of sound, vₒ the listener's speed toward the source and vₛ the source's speed toward the listener. Motion away is entered as away, which flips the sign.
Why does a siren sound higher as it approaches?
The source catches up with its own sound waves, squeezing them closer together, so more wave crests reach you each second. As it moves away the waves are stretched and the pitch drops.
Which speed of sound should I use?
343 m/s is the speed in dry air at about 20 °C. It changes with temperature, roughly 0.6 m/s per degree; use the speed of sound calculator for other temperatures or for water.
Does it matter whether the source or the listener moves?
Yes. A source moving at 30 m/s toward a still listener gives a slightly bigger shift than a listener moving at 30 m/s toward a still source, because the air is the reference.