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

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)

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