Physics

Doppler Effect Calculator

Calculate the observed frequency of sound due to the Doppler effect for moving sources and observers.

CALCULATOR

Enter your numbers

Instant results
478.48 Hz
Observed Frequency
38.48 Hz (8.75%)
Frequency Shift
f' = f × (v + v_o) / (v - v_s)
f' = 440 × (343 + 30) / (343 - 0)
f' = 440 × 373 / 343
f' = 478.48 Hz
Frequency shift = 38.48 Hz
Shift = 8.75%

THE NUMORIX GUIDE

How to use the Doppler Effect Calculator

Last reviewed September 14, 2026

What this calculator does

For sound in a stationary medium, the engine uses f' = f (v + v_o) / (v - v_s), where positive observer and source velocities follow the toward-the-source and toward-the-observer convention.

Formula and method

For sound in a stationary medium, the engine uses f' = f (v + v_o) / (v - v_s), where positive observer and source velocities follow the toward-the-source and toward-the-observer convention. It then reports the shift f' - f and its percentage of f.

Variables and inputs

Source frequency f is in Hz, source velocity v_s and observer velocity v_o are in m/s, and sound speed v is in m/s. Defaults are 440 Hz, 0 m/s, 30 m/s, and 343 m/s; the form recalculates as values change.

Worked example

With f = 440 Hz, v_s = 0, v_o = 30 m/s, and v = 343 m/s: f' = 440(343 + 30)/(343 - 0) = 478.48 Hz. The shift is 38.48 Hz, or 8.75% above the source frequency.

How to interpret the result

The observed frequency changes because source and observer motion changes the arrival rate of wavefronts. A positive shift means the displayed frequency is higher; the sign depends on the velocity convention used in the formula.

Common mistakes to avoid

Use signed velocities consistently and do not enter speed magnitudes without deciding their directions. Keep source and observer speeds in m/s, and do not apply this sound-wave formula to light, where relativistic Doppler equations are required.

Assumptions and limitations

This is a one-dimensional, nonrelativistic sound model with a stationary medium and constant sound speed. The engine does not validate that source speed is below sound speed or prevent a zero denominator, and it does not model wind, three-dimensional angles, echoes, or changing temperature.

Sources and references

COMMON QUESTIONS

Frequently asked questions

How should source and observer velocity signs be chosen?

Use the convention in the formula: positive observer velocity moves the observer toward the source, and positive source velocity moves the source toward the observer. Reverse a direction by entering a negative value.

Can this calculate the Doppler shift of light?

No. The engine is written for sound using a medium's wave speed. Light requires a relativistic treatment and does not use a sound speed input.