Physics
General Doppler formula for sound
Observed frequency with any combination of source and observer motion.
The Formula
f' = f x (c + vo) / (c - vs)
Observed frequency with any combination of source and observer motion.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| f' | Observed frequency | hertz | The frequency the listener hears, in hertz. |
| f | Source frequency | hertz | The frequency the source emits, in hertz. |
| c | Speed of sound | m/s | About 343 metres per second in air at room temperature. |
| vo | Observer speed | m/s | Positive when the observer moves toward the source. |
| vs | Source speed | m/s | Positive when the source moves toward the observer. |
What Each Symbol Means
f'hertz
Observed frequency
The frequency the listener hears, in hertz.
fhertz
Source frequency
The frequency the source emits, in hertz.
cm/s
Speed of sound
About 343 metres per second in air at room temperature.
vom/s
Observer speed
Positive when the observer moves toward the source.
vsm/s
Source speed
Positive when the source moves toward the observer.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate the doppler effect page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate The Doppler Effect, filed under Science. Every number the guide produces comes from substituting into this one line.