Stationary Source and Moving Observer

If the source is at rest but we, the observer, are moving, there is also a Doppler effect. In the case of water or sound waves, if we are moving through the medium toward the source, then the wave crests pass by us at an increased relative speed v_rel = v_wave + v_us . Even though the wavelength is unchanged, the increased speed of the wave will carry the crests by faster, giving us an apparently shorter period and higher frequency. If our velocity through the medium is small compared to the wave speed, then we observe essentially the same decrease in period and increase in frequency as in the case when the source was moving. In particular, Equation (1) is approximately correct.
On the other hand, when the waves are in water or air and the relative speed of the source and observer approaches or exceeds the wave speed, there can be a considerable difference between a moving source and a moving observer. As illustrated in Figure (1a), if the source is moving faster than the wave speed, there is a shock wave and the observer detects no waves until the source passes. But if the source is at rest as in Figure (1b), there is no shock front and the observer moves through waves before getting to the source, even if the observer is moving faster than the wave speed.

Figure 1: For waves in water or air, there can be a significant difference between a moving source with a stationary observer, and a moving observer with a stationary source, even though the source and observer have the same relative velocity in the two cases. For light, the principle of relativity requires that the two cases be identical.