Doppler effect review

Sound waves are longitudinal waves that spread out spherically from their source in all directions, such as from the police car siren in figure 1 below. The distance between two consecutive wavefronts represents the wavelength of the sound wave. The frequency of the wave can be measured by counting the number of wavefronts detected by the observer over a period of time.

For a source and observer with no relative motion, the wavefronts are all centered at the source at all times. Observers on any side will hear the frequency of sound from the source.

When the source and observer are moving relative to each other, the distance between the wave fronts changes depending on where the observer is. For example, if the siren is moving toward the observer on the right, the wave fronts are closer together for observer $R$‍ and further apart for observer $L$‍ (Figure 2).

Keep in mind that the speed of the waves is not changing. The speed depends only on the medium, and the medium isn’t changing. The waves travel at the same speed, but the observed frequency depends on any relative motion between the observer and source.

When the observed frequency changes, so does the wavelength. If the observer and source are moving toward each other, then the frequency increases and the wavelength decreases. In figure 2, observer $R$‍ on the right sees wave fronts more frequently, so the wave front spacing (or wavelength) is also reduced.

If the observer and source are moving away from each other, then the observed frequency decreases and the wavelength increases. In Figure 2, observer $L$‍ on the left sees wave fronts less frequently than when the source was at rest, so the wave front spacing is increased. These observations match the when velocity is constant.

To check your understanding and work toward mastering these concepts, check out the exercises in this tutorial.