A sound source 
, emitting a sound of frequency 400 Hz and a receiver 
of mass m are at the same point. R is performing SHM with the help of a spring offeree constant 
. At a time 
is at the mean position and moving towards the right, as shown. At the same time, the source starts moving away from 
with some acceleration a. The frequency registered by the receiver at a time 
is 250 Hz . What is the time (in seconds) at which the corresponding registered frequency of 250 Hz was emitted by the source? [Given that 
and amplitude of oscillation 
Text Solution
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The time period of oscillation 
So at 
, the receiver passes through mean position towards the right with a speed
Using doppler's formula
So the velocity of the source is 
at the time of emission of the wave which was received by the receiver at 
Let's say the time instant when the wave was emitted is 
, then the distance of the source from the receiver is 
at 
. This distance is travelled by the wave in a time 
. So,
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