Consider a source produces sound of frequency f. If v is the speed of sound in air then the wavelength of the sound wave
Now suppose the source S moves towards stationary observer O with a speed vs. In one time period T, S moves a distance v s T, before it emits next pulse. As a result the wavelength becomes
Because of this changed wavelength, frequency of the sound appears to change. If f cis the apparent frequency, then
If the source moves away from the observer, then
Alternate method:
At t = 0, suppose the source is at a distance L from the observer and emits a compressional pulse. It reaches the observer at time
The source emits next compressional pulse after a time T. In the mean time, the source has moved a distance vs T towards the observer and is now a distance L – vs T from the observer. The next compressional pulse reaches the observer at time
The time interval between two successive compression pulses
