# Formula Acoustic Doppler Effect Observer frequency Emitter frequency Emitter speed Observer speed

## Observer frequency

`$$ f $$`Unit

`$$ \mathrm{Hz} $$`

Frequency perceived by an observer (who may hear a loud ambulance, for example).

## Emitter frequency

`$$ f_{\text s} $$`Unit

`$$ \mathrm{Hz} $$`

Frequency emitted for example by the siren of an ambulance.

## Speed of sound

`$$ c $$`Unit

`$$ \frac{\mathrm m}{\mathrm s} $$`

Speed of sound at which sound waves propagate. In air, the speed of sound is: \( c ~\approx~ 340 \, \frac{\text m}{\text s} \) at 20°C.

## Emitter speed

`$$ v_{\text s} $$`Unit

`$$ \frac{\mathrm m}{\mathrm s} $$`

Speed at which the emitter (for example an ambulance) moves relative to the observer.

"\( c ~-~ v_{\text s} \)" 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

`$$ \frac{\mathrm m}{\mathrm s} $$`

Speed at which the observer moves relative to the emitter.

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 \( v = 0 \).