What this calculator does
The Doppler effect is why a siren drops in pitch as it passes. The source emits the same frequency throughout; what changes is how quickly the waves reach you, because the source is closing the distance and then opening it.
The effect is not symmetric between a moving source and a moving listener. Mathematically the source term sits in the denominator and the observer term in the numerator, so identical speeds produce slightly different shifts.
The formula
Multiply the source frequency by the speed of sound plus the observer velocity, divided by the speed of sound plus the source velocity. Signs follow the convention that observer velocity is positive when moving toward the source and source velocity is positive when moving away from the observer.
| Term | Meaning |
|---|---|
| Source frequency | The frequency the source actually emits, which never changes regardless of motion. |
| Observed frequency | The frequency reaching the listener, raised when closing and lowered when separating. |
| Speed of sound | About 343 m/s in air at 20°C. It varies with temperature, rising as air gets warmer. |
The inputs explained
| Field | What to enter |
|---|---|
| Source frequency (Hz) | The frequency emitted by the source, in hertz. |
| Speed of sound in the medium (m/s) | The speed of sound in the medium. Air at room temperature is about 343 m/s; water is far higher. |
| Observer velocity (+ toward source) (m/s) | The observer's velocity, positive when moving toward the source. |
| Source velocity (+ away from observer) (m/s) | The source's velocity, positive when moving away from the observer. |
When to use it
Explaining a passing siren
The pitch drop happens at the moment of passing, as the source switches from approaching to receding.
Understanding speed measurement
Radar and sonar speed measurement work on the same principle, comparing emitted and returned frequencies.
Working a physics problem
Doppler questions turn on getting the sign convention right, which is where most errors occur.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much does an approaching or receding source shift the pitch?
A 440 Hz source moving at a range of velocities relative to a stationary listener.
| Source velocity | Observed frequency | Shift as a percentage |
|---|---|---|
| -30 m/s | 482.17 Hz | 9.58% |
| -15 m/s | 460.12 Hz | 4.57% |
| 0 m/s | 440.00 Hz | 0.000% |
| 15 m/s | 421.56 Hz | -4.19% |
| 30 m/s | 404.61 Hz | -8.04% |
Questions
Does the source actually change pitch?
No. The source emits exactly the same frequency throughout. Only the frequency arriving at the listener changes, because the waves are being compressed ahead of the source and stretched behind it.
Why are the approaching and receding shifts different sizes?
Because the source velocity appears in the denominator of the formula. Subtracting from the denominator raises the result more than adding to it lowers it, so approach shifts pitch up further than recession shifts it down.
Does it matter whether the source or the listener moves?
Slightly. For a medium like air the two cases give marginally different results, because the medium provides a frame of reference. For light there is no medium, and only relative motion matters.
What happens at the speed of sound?
The denominator approaches zero and the predicted frequency rises without limit. Physically the waves pile up into a shock front, which is the sonic boom.
For the speed of sound itself, which this calculation depends on, see the speed of sound calculator. For how loud a sound is rather than its pitch, see the decibel calculator.