My name is Alexander FufaeV and here I write about:

Acoustic Doppler Effect: How Frequency Shift of Sound Occurs

Important Formula

Formula: Acoustic Doppler Effect

$$f ~=~ f_{\text s} \, \left( \frac{c ~\pm~ v}{c ~\mp~ v_{\text s}} \right)$$ $$f ~=~ f_{\text s} \, \left( \frac{c ~\pm~ v}{c ~\mp~ v_{\text s}} \right)$$ $$f_{\text s} ~=~ f \, \left( \frac{c ~\mp~ v_{\text s}}{c ~\pm~ v} \right)$$ $$v_{\text s} ~=~ \frac{ f_{\text s} }{ f } \, \left( c - v \right) ~\pm~ c$$ $$v ~=~ c \mp \frac{ f }{ f_{\text s} } \, \left( c - v_{\text s} \right)$$

Rearrange formula

What do the formula symbols mean?

Observer frequency

$$ f $$ Unit $$ \mathrm{Hz} = \frac{ 1 }{ \mathrm{s} } $$

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

Emitter frequency

$$ f_{\text s} $$ Unit $$ \mathrm{Hz} = \frac{ 1 }{ \mathrm{s} } $$

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 $.

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.

$$ \begin{align} f ~=~ f_{\text s} \, \left( \frac{c ~\pm~ v}{c ~\mp~ v_{\text s}} \right) \end{align} $$

Doppler effect - approaching & receding observers

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 higher-pitched siren sound.

How can speeds be measured acoustically?

The speed of an object can be measured using the Doppler effect. A sound wave with a known frequency $ f_{\text s} $ is emitted towards the object and reflected back. Due to the motion of the object, the reflected sound wave is frequency-shifted. The received frequency $ f $ differs from the transmitted frequency. The speed of the object can be determined based on this frequency shift!