Doppler effect calculator
Approaching raises the pitch and receding lowers it, by the ratio of closing speed to wave speed.
Hz
Frequency while approaching
482.1725Hz
- Frequency after passing
- 404.6113 Hz
- Shift while approaching
- 42.1725 Hz
- Relative shift
- 9.5847 %
- Shift in semitones
- 1.5846
Show the working
- Source frequency = 440
- Source speed toward the observer = 30
- Observer speed toward the source = 0
- Speed of sound = 343
- Frequency while approaching = 343 != 30 ? 440 * (343 + 0) / (343 - 30) : 0 = 482.173
- Shift while approaching = 482.173 - 440 = 42.1725
- Relative shift = 440 > 0 ? 42.1725/440*100 : 0 = 9.584 66
- Frequency after passing = 440 * (343 - 0) / (343 + 30) = 404.611
- Shift in semitones = 482.173 > 0 && 440 > 0 ? 12 * log2(482.173/440) : 0 = 1.584 55
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- f_observed = f0 (c + v_observer) / (c - v_source)
This is the classical acoustic Doppler shift. Light needs the relativistic version, which depends only on relative velocity.
A source at the speed of sound gives an infinite predicted frequency — the formula breaking down at the sound barrier.