Acoustic Doppler Effect: How Frequency Shift of Sound Occurs
Formula
What do the formula symbols mean?
Observer frequency
$$ f $$ Unit $$ \mathrm{Hz} = \frac{ 1 }{ \mathrm{s} } $$Emitter frequency
$$ f_{\text s} $$ Unit $$ \mathrm{Hz} = \frac{ 1 }{ \mathrm{s} } $$Speed of sound
$$ c $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$Emitter speed
$$ v_{\text s} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$"\( c ~~ v_{\text s} \)" is used when the emitter moves towards the observer. "\( c ~+~ v_{\text s} \)" when the emitter is moving away from the observer. If the emitter is stationary, then \( v_{\text s} = 0 \).
Observer speed
$$ v $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$Use "\( c ~+~ v \)" when the observer moves towards the emitter. "\( c ~~ v \)" when the observer moves away from the emitter. If the observer is standing still, use \( v = 0 \).
Video
The basic idea of the acoustic Doppler effect is similar to the Doppler effect for electromagnetic waves such as light, but here it is applied to sound waves. When a sound source or an observer moves relative to the medium in which the sound is transmitted (usually air), there is a change in the perceived frequency of the sound.
Consider illustration 1: An ambulance drives to the right. It has a siren that emits a certain transmitter frequency \( f_{\text S} \) from its point of view. Depending on how an observer moves, they perceive the transmitter frequency differently. The frequency that they perceive is referred to as \( f \).

When the ambulance and the observer move away from each other, the observer hears a deeper siren sound.

When the ambulance and the observer approach each other, the observer hears a higherpitched siren sound.