Doppler Effect Calculator
Why a Siren's Pitch Drops as It Passes You
An ambulance racing toward you sounds noticeably higher-pitched than the same siren as it speeds away — the source hasn't changed, but the sound waves reaching your ears have been compressed on approach and stretched on departure. This is the Doppler effect, and it applies to any wave, from sound to light to radar returns, whenever a source and observer are moving relative to each other.
The Formula
f is the source's true frequency, v is the wave's speed through the medium (343 m/s for sound in air by default), vo is the observer's speed, and vs is the source's speed. The observer term adds when moving toward the source and subtracts when moving away; the source term subtracts (increasing frequency) when the source approaches and adds when it recedes.
Where the Doppler Shift Is Put to Work
- Police and sports radar — vehicle and pitch speeds are measured by the frequency shift of a reflected radio wave.
- Medical ultrasound — blood flow velocity is measured non-invasively by the Doppler shift in reflected sound waves.
- Astronomy — the redshift and blueshift of starlight reveal whether distant objects are moving away from or toward Earth, and how fast.
- Weather radar — Doppler shift in returned radar pulses reveals wind speed and direction inside storm systems.
A Worked Example
A siren emitting a steady 700 Hz tone approaches a stationary listener. Using the speed of sound in air (343 m/s):
| Source speed | Observed frequency |
|---|---|
| 10 m/s (~36 km/h) | 721.02 Hz |
| 20 m/s (~72 km/h) | 743.34 Hz |
| 30 m/s (~108 km/h) | 767.09 Hz |
Computed with f' = f × v / (v − vs); the pitch keeps climbing as the source's speed approaches the speed of sound itself.
How to Use This Calculator
- Enter the Source Frequency in Hz.
- Optionally enter a Wave Speed in m/s — leave blank to use the speed of sound in air (343 m/s).
- Select whether the Observer is stationary, moving toward, or moving away from the source, and enter their speed if applicable.
- Select whether the Source is stationary, moving toward, or moving away from the observer, and enter its speed if applicable.
- Select Calculate to get the observed frequency along with the worked formula.
Related Calculations
To relate that observed frequency back to a physical wavelength, see the Wavelength Calculator, or work with frequency and period directly using the Frequency Calculator.