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 m/s away from the source, then the waves would seem to be traveling at only
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
in which is the propagation speed in the medium, is the velocity of the receiver, is the velocity of the source, and is the frequency of the source. In our example, ,
, and . The result is that a sound source with frequency
Hz would be perceived by the receiver as having frequency
. 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