What is Doppler`s effecteffect? Prove Doppler`s effect ? And write the applications?

Doppler effect helps to study the change of relative frequency with respect to the relative motion of source and observer.Let fa = apparent frequencyfo= original frequency v= velocity of soundVo= velocity of observerVs= velocity of sourcefa= fo [( v+-vo)/(v+-vs) ]Vo= + observer moves towards source - --------- away from sourceVs= + source move away from sourceVs - source move towards observerIf vs perpendicular to vo then no Doppler effect is observed.Then fa = fo