IIT JEE , AIEEE Forum - Physics , Mechanics - Find the frequency heard by the observer?

vky75

A source emitting a sound of frequency v is placed at a large distance from an observer. the source starts moving towards the observer with a uniform acceleration a . find the frequency heard by the observer corresponding to the wave emitted just after the source starts. the speed of sound in the medium is v.

rooney

Let the initial distance between the two be d
Let the source emit a pulse just after it starts moving
So, velocity of this pulse is v ( = speed of sound in medium)
It reaches the observer in time T₁= d/ v

Also, the source is also moving. So, after timeperiod T, it emits a second pulse.
At t=T, it has moved by s=0.T +1/2aT²=1/2aT²

So, time takento reach the observer for this pulse is = (Distance travelled to reach the Observer)/v = (d-1/2aT²⁾/v

So,

t = Time diff in reaching of the 2 pulses =( T + (d-1/2aT²⁾/v) - d/v
=T - aT²/2v
So, apparent frequency = 1/

t = 2v/(2vT - aT²)
Replace u = 1/T ,
Apparent frequency = 2vu²/(2vu - a)

krishna.gopal

Perfect answer rooney. Superb

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