Alexander Fufaev
My name is Alexander FufaeV and here I will explain the following topic:

Acoustic Doppler Effect: How Frequency Shift of Sound Occurs

Formula

Formula: Acoustic Doppler Effect
Doppler effect - approaching & receding observers
What do the formula symbols mean?

Observer frequency

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

Emitter frequency

Unit
Frequency emitted for example by the siren of an ambulance.

Speed of sound

Unit
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

Unit
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

Unit
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 \( v = 0 \).

Explanation

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.

Formula anchor
fufaev.org Doppler effect - approaching & receding observers
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!