Doppler Effect Calculator
The Doppler effect is the change in observed frequency that occurs when a wave source and an observer are moving relative to each other. When an ambulance rushes towards you, the sound waves arriving at your ears are compressed into a shorter effective wavelength, raising the pitch. As it passes and moves away, those waves are stretched, dropping the pitch. The same phenomenon applies to any wave, including light (where it produces redshift and blueshift), radar waves, and ultrasound. The Doppler formula for sound is f observed equals f0 times the quantity v plus v observer divided by the quantity v minus v source, where f0 is the emitted frequency, v is the speed of sound in the medium, v observer is the speed of the observer toward the source (positive = approaching), and v source is the speed of the source toward the observer (positive = approaching). When either party is moving away instead of toward, the sign of that velocity term is reversed. This calculator handles three scenarios: moving source only (observer stationary), moving observer only (source stationary), or both moving. You select the scenario, set whether each party is approaching or receding, and enter the relevant speeds and the emitted frequency. The calculator returns the observed frequency, the frequency shift, and the change in perceived wavelength. The default example models a 440 Hz sound source approaching at 30 m/s, which produces a classic upward pitch shift that you will hear restored to 440 Hz as it passes.
This calculator is for mechanical waves (sound). The relativistic Doppler formula applies to light and electromagnetic waves.
How it works
The Doppler formula for sound is fobs = f0 × (v ± vo) / (v &mnusplus; vs). For the numerator: use + vo when the observer approaches the source, and − vo when receding. For the denominator: use − vs when the source approaches the observer, and + vs when receding. Emitted wavelength λ0 = v / f0. Observed wavelength λobs = v / fobs.
Worked example
A stationary observer hears a siren emitting f0 = 440 Hz. The source (ambulance) approaches at vs = 30 m/s. Wave speed in air is v = 343 m/s. Using the Doppler formula: fobs = 440 × 343 / (343 − 30) = 440 × 343 / 313 = 482.17 Hz. The frequency is higher (approaching) with a shift of +42.17 Hz. Emitted wavelength = 343/440 = 0.780 m; observed wavelength = 343/482.17 = 0.711 m. These match the default values pre-filled above.
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