Doppler Effect Calculator

The Doppler effect is the shift in a wave's observed frequency caused by relative motion between its source and the observer — the classic example is a siren sounding higher-pitched as it approaches and lower-pitched as it recedes. For a wave traveling through a medium at speed v (sound in air, here), the observed frequency is f' = f0 × (v + v_o) / (v − v_s), where f0 is the frequency the source actually emits, v_o is the observer's velocity (positive when moving toward the source), and v_s is the source's velocity (positive when moving toward the observer).

Both velocities use the same sign convention — 'positive means moving toward the other party' — so a source or observer moving away is simply entered as a negative value; the same formula covers approaching and receding without a separate case for each.

The formula only holds for a source moving slower than the wave itself. At or beyond the speed of sound, the source outruns its own wavefronts and this classical formula breaks down (the shock-wave / sonic-boom regime), so this calculator rejects a source velocity at or above the speed of sound rather than returning a number that no longer means anything.