Doppler effect calculator
The heard frequency when the source or the listener moves.
Fill in the fields and the result will appear here automatically.
Calculate the classical frequency shift for motion along the source–observer line in a stationary medium. Both velocities are relative to the medium; a positive value points towards the other party. This model uses a subsonic source, and a receding observer must move slower than the arriving wave. Light and an arbitrary passing trajectory require a different model.
How it works
Formula and logic
f′ = f · (c + v_obs) / (c − v_src).
Example
A 440 Hz siren approaching at 20 m/s is heard as 467.24 Hz.
Fields and units
- Source frequency — Hz
- Source speed towards — m/s
- Observer speed towards — m/s
- Wave speed in the medium — m/s
How to use
- — Speed towards is positive, away is negative. One field replaces the choice between approaching and receding.
- — Observer motion and source motion enter the formula differently, so the fields are separate.
- — Use wave speed for the actual medium and conditions. The 343 m/s default is an air example, not a universal constant.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: sound Doppler effect in a medium
- Limitation
- One-dimensional classical wave in a stationary medium; |vsource|<c and vobserver>−c. Not relativistic Doppler or a reflected radar-signal calculation.
FAQ
Why does the tone drop exactly at the pass?
Approach on one line raises frequency and recession lowers it. Passing at a nonzero distance changes the line-of-sight direction smoothly, so the shift normally changes smoothly too. An ideal jump belongs to a one-dimensional pass through the observation point; this calculator uses instantaneous longitudinal velocities.
Why do source and observer get different formulas?
Observer motion changes the rate at which they meet the waves and sits in the numerator. Source motion changes the wavelength in the medium itself and sits in the denominator. At low speeds the difference is invisible; at high speeds it matters.
What happens at the wave speed?
The denominator goes to zero and the formula stops describing anything. Physically the waves cannot get away from the source and pile into a shock front — the calculation rejects such inputs.
Does this work for light?
Do not use this formula for light: it distinguishes motion relative to a material medium. Use relativistic Doppler with specified geometry. Reflected ultrasound or radar also requires the return path of the signal.