Doppler effect

The sound pressure variations described above were for a fixed receiving point. If the point is moving away from the source, then the wavefronts will arrive at a reduced frequency. For example, if the receiver moves at $ 43.2$m/s away from the source, then the waves would seem to be traveling at only $ 343.2 - 43.2 = 300$ meters per second. The received frequency shifts due to the relative motion between the source and receiver. This is known as the Doppler effect, and the frequency as measured at the receiver can be calculated as

$\displaystyle f_r = \left( s + v_r \over s + v_s \right) f_s ,$ (11.2)

in which $ s$ is the propagation speed in the medium, $ v_r$ is the velocity of the receiver, $ v_s$ is the velocity of the source, and $ f_s$ is the frequency of the source. In our example, $ s = 343.2$, $ v_r = -43.2$, and $ v_s = 0$. The result is that a sound source with frequency $ f_s = 1000$Hz would be perceived by the receiver as having frequency $ f_r \approx 876.7$. This is the reason why a siren seems to change pitch as a police car passes by. The Doppler effect also applies to light, but the effect is negligible in normal VR contexts (unless developers want to experiment with virtual time dilation, space travel, and so on).

Steven M LaValle 2020-01-06