Doppler Effect for Sound Waves:
In general Doppler Effect is the change in frequency of electromagnetic waves due to the relative motion between source and observer. The effect was first observed by Christian Doppler in 1842. The effect is used to measure velocities usually by reflection of a transmitted wave from the moving objects like galaxies (red shift), radar for speeding cars and thunderstorms, etc.
It is commonly observed when a vehicle with sounding a siren approaches, passes and recedes from an observer. The received frequency is higher during its approach, identical at the instant of passing and is lower in recession.
The relative increase in frequency is explained as given. As the source moves toward the observer, there forms a compression of waves between the source and the observer reducing its length which in effect increases the frequency.
For waves that propagate in a medium like sound waves, the velocities of the observer and the source are relative to the medium in which the waves are transmitted. Therefore the total Doppler Effect is the result of motion of source, observer or medium. Each of these effects can be analyzed separately. The apparent frequency observed by the observer is,
f =apparent frequency,
f0 = frequency of the source,
v = velocity of sound,
v0 = velocity of the observer and
vs = velocity of source.
The choice plus (+) or minus (-) sign is according to the convention that if the source and observer are moving towards the perceived frequency (f') is higher than the original frequency (f0), using eq(1). In a similar way, if the source and observer are moving away the perceived frequency (f') is lower than the original frequency (f0), see eq(2).
The Doppler Effect for light waves is commonly expressed in terms of colours rather than frequency. A red shift occurs when the source and observer are moving away each other and a blue shift occurs when the source and observer are moving towards each other.