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.