16.9.1 A Stationary Source and a Moving Observer

Suppose the police car in Example 16.11 is at rest while you drive toward it at $34.3\text{m}\text{/}\text{s}$. You might think that this is equivalent to having the police car move toward you at $34.3\text{m}\text{/}\text{s}$, but it isn’t. Mechanical waves move through a medium, and the Doppler effect depends not just on how the source and the observer move with respect to each other but also on how they move with respect to the medium. We’ll omit the proof, but it’s not hard to show that the frequencies heard by an observer moving at speed $v_{\text{o}}$ relative to a stationary source emitting frequency $f_0$ are

A quick calculation shows that the frequency of the police siren as you approach it at $34.3\text{m}\text{/}\text{s}$ is 545 Hz, not the 550 Hz you heard as it approached you at $34.3\text{m}\text{/}\text{s}$.