Physics · Oscillations & waves

Doppler effect calculator

Find the observed sound frequency for a moving source and observer in a stationary medium. Positive source and observer velocities each mean motion toward the other.

Created Oct 3, 2026v1.0

By Thibaut Grzelak, Mechanical Analysis Engineer

Oscillations & waves

Source left, observer right. Positive v_s points right; positive v_o points left. Wavefront spacing is illustrative.

Quantity to calculate

Source frequency f_s

Strictly positive, before the Doppler shift.

Wave speed v

Speed in the medium: 343 m/s is an editable example, not a universal value.

Source velocity v_s

Positive toward the observer; negative away. |v_s| < v.

Observer velocity v_o

Positive toward the source; negative away. |v_o| < v.

Results

Observed frequency

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Frequency received by the observer.

Frequency shift

—

Positive for an increase, negative for a decrease.

Relation and numerical substitutionf_obs = f_s × (v + v_o) / (v − v_s)

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Uniform stationary medium, constant wave speed and collinear subsonic motion. Velocities are measured relative to the medium.

01Formulas and symbols

Formulas used

f_obsf_obs = f_s × (v + v_o) / (v − v_s)Signed classical Doppler formula in the rest frame of the medium.

ΔfΔf = f_obs − f_sObserved frequency minus emitted frequency.

02Assumptions and limits

Scope of validity

Uniform stationary medium, constant wave speed and collinear subsonic motion. Velocities are measured relative to the medium.

03Validation example

Reference numerical case

Given f_s = 1000 Hz, v = 343 m/s, v_s = 20 m/s and v_o = 0: f_obs = 1000 × 343 / (343 − 20) = 1061.9195… Hz (≈ 1.1 kHz); Δf ≈ 62 Hz.

04References

Technical references

Physics, §14.3 Doppler Effect and Sonic Booms — OpenStax

FAQ

Why does a receding source lower frequency?

A negative v_s increases v − v_s, reducing the received frequency.

What wave speed should I enter?

Use the propagation speed for the medium and conditions of your problem. Temperature and composition affect sound speed.

05How it works

An approaching source reduces the spacing between successive wavefronts. An approaching observer encounters more wavefronts per second. The numerator and denominator represent these distinct effects.

06Model limits

This model excludes sonic or supersonic motion, shock waves and relativistic light Doppler. For oblique motion use radial components only when the approximation is appropriate; changing geometry is not simulated.

07Common mistakes

Do not assign both velocities the same global-axis sign. The positive arrow points right for the source and left for the observer in this diagram. Do not substitute relative closing speed for both velocities.