Doppler Effect Calculator
Sound in a medium and longitudinal light shifts, with explicit velocity signs.
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Model assumptions
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Results are estimates from the formulas shown, not a professional design or certification. Have a qualified engineer verify anything safety-critical (structures, electrical installations, gas or pressure systems).
About the Doppler Effect Calculator
Compare a sound source and observer moving along one line, or switch to the longitudinal relativistic model for light. Sound mode returns the observer's frequency and the wavefront spacing in the medium. Two inverse modes solve a source or observer speed from an emitted and measured frequency.
The free preview masks the computed figures; a Pro pass opens the complete values, copy and reports. Sound speeds are measured relative to the medium, with motion toward the other participant positive. Light uses a separate convention: a positive recession speed lowers the received frequency. A cosmological redshift is not automatically a velocity in this special-relativity model.
How to use it
- Choose the sound, inverse-speed, light or redshift model.
- Enter the known frequency and medium wave speed, or the signed fraction of the vacuum speed of light.
- For sound, use positive velocities toward the other participant and negative velocities away; keep the source subsonic.
- Calculate, inspect the stated assumptions, then copy or export the full report with a pass.
Examples
1,000 Hz source, c = 343 m/s, source toward observer at 20 m/s, observer stationary
About 1,061.9195 Hz; medium wavefront spacing 0.323 m
1,000 Hz emitted, 1,100 Hz received, stationary source, c = 343 m/s
Observer speed 34.3 m/s toward the source
v/c = 0.6
Observed/emitted frequency = 0.5; redshift z = 1
Models and reference frames
For sound, f_observed = f_emitted (c + v_observer)/(c - v_source). The medium wavelength is (c - v_source)/f_emitted. A moving observer changes the rate at which it meets wavefronts, so dividing c by that observer's received frequency does not give the medium's physical wavefront spacing.
For light, f_observed/f_emitted = sqrt((1-beta)/(1+beta)), with positive beta for recession. z = f_emitted/f_observed - 1; inversion gives beta = ((1+z)^2-1)/((1+z)^2+1). The speed must remain below c.
Sources
The sound model follows OpenStax: Doppler effect. The light-frequency ratio follows OpenStax: Doppler effect for light. The vacuum light speed uses NIST: speed of light.
Limitations
- The calculations describe collinear motion, rather than a complete pass-by geometry.
- The illustrative 343 m/s sound speed is editable; actual medium conditions change it.
- Sonic booms, wind gradients, reflections, transverse light shifts and cosmological expansion are excluded.
- This is a physics estimate, not a professional navigation or acoustic design.
Privacy
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Frequently asked questions
What do I get without a pass?
Without a pass, Doppler Effect Calculator shows the rules, dates and checks that apply to your figures, with every computed amount hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
Which direction is positive?
In sound modes, source and observer speeds are positive toward the other participant. In light modes, positive beta means recession. The labels state the convention because the two equations use different signs.
Can I solve a speed from a measured shift?
Yes. Select the source-speed or observer-speed mode for sound and give the remaining speed, emitted frequency, received frequency and medium speed. For light, select the redshift inverse.
Why is the source restricted to subsonic speeds?
The simple sound formula describes successive wavefronts reaching an observer before the source crosses them. At or above the wave speed a shock/Mach-cone model is needed.
Does every redshift measure an ordinary recession velocity?
No. The inverse here assumes a longitudinal special-relativistic shift in flat spacetime. Cosmological and gravitational redshifts require their own models.