Math
Doppler Effect Calculator
Solve the Doppler effect for sound or light. Compute observed frequency, frequency shift, and redshift, or solve backward for source or relative velocity.
Doppler Effect Calculator
Classical Doppler effect for sound waves traveling through a medium.
Frequency emitted at the source. Must be greater than zero.
Speed of sound in the medium. Defaults to 343 m/s in air at 20 C.
Positive when moving toward the source. Magnitude must stay below the wave speed.
Positive when moving away from the observer. Magnitude must stay below the wave speed.
Observed frequency
1,095.8466 Hz
Approaching (blueshift)
Source frequency
1,000 Hz
Frequency shift
+95.8466 Hz
Wavelength change
-0.087464
Frequently Asked Questions about the Doppler Effect Calculator
What is the Doppler effect?
The Doppler effect is the change in observed wave frequency when the source and observer move relative to each other. Approaching motion raises the frequency (blueshift); receding motion lowers it (redshift).
Which formula does the sound mode use?
f_observed = f_source x (v + v_observer) / (v + v_source), where v is the wave speed (343 m/s by default for air at 20 C), v_observer is positive when moving toward the source, and v_source is positive when moving away from the observer.
Which formula does the light mode use?
The longitudinal relativistic Doppler formula: f_observed = f_source x sqrt((1 - beta) / (1 + beta)), where beta is the relative velocity divided by the speed of light. Positive velocity means receding.
Why does the calculator reject velocities equal to or above the wave speed?
The classical sound model breaks down at and above the medium's wave speed: a source at the wave speed produces a sonic boom, and a faster-than-sound observer outruns the wavefront. For light, the calculator rejects any speed at or above c because no real object reaches it.
How is redshift z related to frequency shift?
Redshift z equals (observed wavelength minus source wavelength) divided by the source wavelength, which simplifies to (source frequency divided by observed frequency) minus 1. The calculator reports this value as the wavelength change for light.