Doppler Effect Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
The Doppler effect shifts the perceived frequency when a sound source moves relative to the observer: higher-pitched if it approaches, lower-pitched if it moves away. For a 1000 Hz source moving at 30 m/s toward the observer, the perceived frequency rises to about 1096 Hz.
Explanation
The Doppler effect is the frequency shift perceived by an observer when a wave source (sound, here) is in relative motion with respect to them — the best-known example is an emergency vehicle's siren, perceived as higher-pitched while approaching then lower-pitched once it has passed, even though the siren itself emits a constant frequency. The phenomenon is explained by the compression or stretching of the wave fronts emitted by the moving source: as the source approaches, each successive wave front is emitted a little closer to the observer than the previous one, which compresses the perceived wavelengths and raises the perceived frequency; the opposite happens as it moves away. This calculator covers the most common case in introductory physics: a moving source and a stationary observer, in a medium (air) where sound propagates at a given speed. The source's speed must stay below the speed of sound in the medium for this classical formula to remain valid: beyond that (supersonic regime), the phenomenon changes nature entirely (shock wave, sonic boom) and this formula no longer applies. The Doppler shift changes the perceived frequency, and therefore also the corresponding wavelength (see our wavelength and frequency calculator for that relationship); and for a source whose motion is a rotation rather than a straight-line translation, the speed to consider follows from our angular velocity calculator.
Example: a 1000 Hz source, speed 30 m/s, approaching
Inputs
Source frequency: 1000 Hz. Source speed: 30 m/s. Speed of sound: 343 m/s. Motion: approaching.
Calculation
f' = 1000 × 343 ÷ (343 − 30) = 343,000 ÷ 313 ≈ 1095.8 Hz.
Result
The observer perceives a frequency of about 1095.8 Hz, higher-pitched than the 1000 Hz emitted.
Frequently asked questions
Why is the perceived frequency higher when approaching and lower when moving away?
When the source approaches, it partly "catches up" to its own previously emitted wave fronts, which bunches them together in space: the observer therefore receives more wave fronts per second, perceived as a higher frequency. Moving away, it's the opposite: the wave fronts stretch out, and the observer receives fewer per second, hence a lower perceived frequency.
What happens if the source's speed approaches the speed of sound?
The formula's denominator (speed of sound minus source speed, when approaching) then approaches zero, which would push the perceived frequency toward infinity — a sign that the classical subsonic formula is reaching the limit of its validity. Beyond the speed of sound (supersonic regime), the physical phenomenon changes nature entirely and this formula no longer applies.
Does this formula also apply to light waves?
No, not directly. The Doppler effect also exists for light (redshift or blueshift, used in astronomy), but its formula is different: it relies on special relativity, since the speed of light is a universal constant, unlike the speed of sound, which depends on the propagation medium. This calculator covers only the classical acoustic case.