Doppler Effect Calculator

Our Doppler effect calculator allows you to calculate the frequency of sound if either the source of sound or the observer is moving.

Frequency while approaching482.141 Hz9.577% higher than the source

Frequency while receding404.634 Hz8.038% lower

Total shift through the pass77.507 Hzthe drop you hear as a siren goes past — and it happens over the instant of passing, not gradually

Source frequency440 Hz

Speed of sound used343.235 m/sat 20 °C

Source Mach number0.0874subsonic

If only the SOURCE moved at 30 m/s482.1409 Hz

If only the OBSERVER moved at that speed478.4576 HzNOT the same answer — a moving source compresses the wavelength itself, while a moving observer merely meets the wavefronts sooner. The two agree only in the low-speed limit

Difference between the two cases3.6833 Hz0.8371% of the source frequency — the asymmetry grows with the square of the speed ratio

Wavelength ahead of the source711.8977 mmcompressed — this is the physical change a moving source makes

Wavelength behind it848.2613 mmstretched

Speed for a musical semitone up19.26 m/sabout 69 km/h — which is why traffic noise is audibly pitched

The formula

f' = f(c + v_o) ÷ (c − v_s)

Source and observer are not symmetric

A moving source and a moving observer produce genuinely different shifts, even at the same speed. A moving source physically compresses the wavelength ahead of it — the waves leave closer together — while a moving observer travels through waves of unchanged wavelength and simply meets them more often. The formula reflects that: the source velocity appears in the denominator and the observer velocity in the numerator.

At everyday speeds the two agree closely, which is why the distinction is easy to miss. It grows with the square of the speed ratio and becomes stark near the speed of sound: a source at Mach 1 gives an infinite shift, because every wavefront it emits piles up in the same place. That is not a divergence to be calculated around — it is a shock front, and the Doppler formula stops describing the situation.

Beyond Mach 1 there is no approaching shift at all, because no sound reaches the observer before the source does. The sonic boom arrives first and the aircraft is already past.

The pitch drop as a siren passes happens at the instant of passing, not gradually — before that the source is approaching and after it is receding, so the shift flips over a very short interval.