Suppose that a moving sound source emits
a sound of frequency s
. Let v
be the speed of sound
, and let the source approach the listener
at speed vs
, measured relative
to the medium conducting the sound. Suppose further that the observer is moving toward the source at speed vo
also measured relative to the medium. Then the observer will hear a sound of frequency o
o = s( v + vo ) / ( v - vs )
If either the source or the observer is moving away from the other, the sign on its speed must be changed.
When the source and the observer are approaching each other, more wave crests strike the ear each second than when both are at rest. This causes the ear to perceive a higher frequency thatn that emitted by the source. When the two are receding, the opposite effect occurs; the frequency appears to be lowered.
Because v + vo is the speed of a wave crest relative to the observer, and because v - vs is the speed of a wave crest relative to the source, an alternative form is
o = s · crest speed relative to the observer / crest speed relative to the source