# Doppler effect

The phenomena of apparent change in frequency of source due to a relative motion between the source and observer is called Doppler’s effect.

When source is moving with velocity( vs ) ,towards an observer at rest, then apparent frequency is

n' = n \left(\frac{v}{v-v_{s}}\right)

if source is moving away from observer, then

n' = n \left(\frac{v}{v+v_{s}}\right)

When observer is moving with velocity (v0) towards a source at rest,then apparent frequency is

n' = n \left(\frac{v+v_{0}}{v}\right)

When observer is moving away from source, then

n' = n \left(\frac{v-v_{0}}{v}\right)

When observer and source are moving in same direction along the direction of propagation of sound, then

n' = n \left(\frac{v-v_{0}}{v-v_{s}}\right)

When both are moving in same direction opposite to the direction of propagation of sound, then

n' = n \left(\frac{v+v_{0}}{v+v_{s}}\right)

When both are moving towards each other, then

n' = n \left(\frac{v+v_{0}}{v-v_{s}}\right)

When both are moving in opposite direction ,away from each other, then

n' = n \left(\frac{v-v_{0}}{v+v_{s}}\right)

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For sound the observed frequency ν is given in terms of the source frequency ν0 by \nu = \nu_{0}\left[\frac{V \pm V_{0}}{V \pm V_{s}}\right]