Moving Source, Stationary Observer

Case 1: Moving Source, Stationary Observer

Let us consider a source of sound waves with a constant frequency and amplitude. The sound waves can be represented as concentric circles where each circle represents a crest or peak as the wavefronts radiate away from the source. This is because the waves travel away from the source in all directions and the distance between consecutive crests or consecutive troughs in a wave is constant (the wavelength as we learnt in a previous lesson). In this figure the crests are represented by by the black lines and the troughs by the orange lines.

Stationary sound source as more wavefronts are emmitted.

The sound source is the police car in the middle and is stationary. For the Doppler effect to take place (manifest), the source must be moving relative to the observer.

Let's consider the following situation: The source (represented by the black dot) emits one wave (the black circles represent the crests of the sound wave) that moves away from the source at the same rate in all directions. The distance between the crests represents the wavelength (\(\lambda\)) of the sound. The closer together the crests, the higher the frequency (or pitch) of the sound according to \(f=\frac{v}{\lambda}\), where \(v\) (speed of sound) is constant.

As this crest moves away, the source also moves and then emits more crests. Now the two circles are not concentric any more, but on the one side they are closer together and on the other side they are further apart. This is shown in the next diagram.

If the source continues moving at the same speed in the samedirection, then the distance between crests on the right of thesource is constant. The distance between crests on the left isalso constant. The distance between successive crests on the left is constantbut larger than the distance between successive crests on the right.

When a car approaches you, the sound waves that reach you have a shorter wavelength and a higher frequency. You hear a sound with a higher pitch. When the car moves away from you, the sound waves that reach you have a longer wavelength and lower frequency. You hear a sound with a lower pitch.

Moving sound source as more wavefronts are emmitted.