For the case of motion along a line, where the source moves
with speed v
and the observer moves with speed v
through still air in which the speed of sound is S,
the general equation describing the change in frequency heard
by the observer is
In this equation the speeds of the source and the observer will be negative if the relative motion between the source and observer is moving them apart, and they will be positive if the source and observer are moving together.
From this equation, it can be deduced that a Doppler effect
will always be heard as long as the relative speed between the
source and observer is less than the speed of sound. The speed
of sound is constant with respect to the air in which it is
propagating, so that, if the observer moves away from the source
at a speed greater than the speed of sound, nothing will be
heard. If the source and the observer are moving with the same
speed in the same direction, v
and v
will be equal in magnitude but with the opposite sign; the
frequency of the sound will therefore remain unchanged, like
the sound of a train whistle as heard by a passenger on the
moving train.