The Doppler effect is also known as the Doppler shift is the change in the frequency of a wave to an observer relative to the moving wave source. The reason for the Doppler effect is that when the source of the waves is moving towards the observer, each successive wave crest is emitted from a position closer to the observer than the crest of the previous wave. Therefore, each wave takes slightly less time to reach the observer than the previous wave. Hence, the time between the arrivals of successive wave crests at the observer is reduced, causing an increase in the frequency.

The change in the apparent frequency of sound as heard by the listener due to the relative motion between the source and the listener was first studied by Austrian physicist Doppler and is called the Doppler's effect.

Let us consider, source S is moving towards observer with velocity u_{s} an observer O is moving towards the source with the velocity u_{o}, then

The velocity of wave relative to the observer, v' = v + u_{o}

And the apparent wavelength, \(\lambda'=\frac{v-u_s}f\)

But, we have,

\(f'=\frac{v'}{\lambda'}=\frac{v+u_o}{(v-u_s)/f}=\left(\frac{v+u_0}{v-u_s}\right)\times f\)

So, the frequency of wave increases. In such case as \(v+u_0>v-u_s\)