Doppler Effect Formula

Doppler Effect Formula

The Doppler effect changes the observed frequency of a wave when the source or the observer moves.
The formula for sound waves is

$f’ = f \frac{v \pm v_o}{v \pm v_s}$f′=fv±vs​v±vo​​

Here, $f$f is the actual frequency of the source.
$f’$f′ is the frequency heard by the observer.
$v$v is the speed of sound in the medium.
$v_o$vo​ is the speed of the observer.
$v_s$vs​ is the speed of the source.

The plus and minus signs depend on the direction of motion.
Use the plus sign in the numerator when the observer moves toward the source.
Use the minus sign in the numerator when the observer moves away from the source.
Use the minus sign in the denominator when the source moves toward the observer.
Use the plus sign in the denominator when the source moves away from the observer.

When the source approaches the observer, the observed frequency increases.
When the source moves away, the observed frequency decreases.
The same rule applies when the observer moves.

This formula applies to sound waves in a medium.
It explains the change in pitch of a siren as a vehicle passes.
The effect also appears in light waves, though the formula differs for electromagnetic radiation.