Doppler Effect Calculator (Sound)
Doppler effect calculator for sound: observed frequency from a moving source or observer, or the speed that causes a shift.
f' = f · c + voc − vs
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
f' = f·(c + vₒ)/(c − vₛ), with speeds positive when moving towards each other. The pitch rises as a siren approaches and falls as it leaves.
Formula
f' = f · c + voc − vs
| Symbol | Quantity | Units |
|---|---|---|
| f | Source frequency | Hz, kHz, MHz, GHz, THz, rpm |
| c | Speed of sound (343 m/s in air) | m/s, km/h, mph, kn, ft/s, c |
| vo | Observer speed (+ towards) | m/s, km/h, mph, kn, ft/s, c |
| vs | Source speed (+ towards) | m/s, km/h, mph, kn, ft/s, c |
| f' | Observed frequency | Hz, kHz, MHz, GHz, THz, rpm |
Worked example
Given: f = 440 Hz · c = 343 m/s · vo = 0 m/s · vs = 20 m/s
f' = f c + voc − vs
Result: f' = 467.245 Hz
Frequently asked questions
A 440 Hz source approaching at 20 m/s?
You hear about 467.2 Hz.