# Doppler Effect Formula

The Doppler Shift, also called as the Doppler effect was proposed by the Austrian physicist Christian Doppler in 1842. The Doppler Shift is defined as the change in frequency of a sound wave for an observer moving relative to its source. For example: a vehicle sounding a siren or horn approaches, passes, and recedes from an observer.

The doppler effect formula has been given to calculate doppler shift when both observer and source are in motion and rest state.

# Doppler Shift Formula

### Formula:

When the source is moving towards a observer at rest

f´= ( ν / ν - ν _{s} )* f

When the source is moving away from the observer at rest

f´= ( ν / ν + ν _{s} )* f

When observer is moving towards the stationary source

f´= ( ν+ν_{o} / ν )* f

When observer moving away from a stationary source

f´= ( ν-ν_{o} / ν )* f

When both Source and observer moves towards each other

f´= ( ν+ν_{o}/ ν-ν_{s} )* f

When both Source and observer move away from each other

f´= ( ν-ν_{o}/ ν+ν_{s} )* f

When the Source is approaching the Stationary observer and observer moving away from it

f´= ( ν-ν_{o}/ ν-ν_{s} )* f

When the Observer is approaching the Stationary source and source moving away from it

f´= ( ν+ν_{o}/ ν+ν_{s} )* f

**Where,**

ν_{s} = Velocity of the Source

ν_{o} = Velocity of the Observer

ν = Velocity of sound or light in medium

f = Real frequency

f' = Apparent frequency

As per the Doppler Shift, the received frequency is higher compared to the emitted frequency during the approach, and both are identical at the time of passing by and the received frequency is lower than the emitted one during the recession.