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Question

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

A
vf22vfa
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B
2vf22vf+a
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C
2vf23vfa
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D
2vf22vfa
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Solution

The correct option is D 2vf22vfa
Suppose at t = 0, distance between source and observer is l. First, wave pulse (say p1) is emitted at this instant. This pulse will reach the observer after a time

t1=lv
Source will emit the next pulse (say p2) after a time T(=1f).
During this time the source will move a distance (12) aT2 towards the observer. This pulse p2 will reach the observer in a time
t2=T+112aT2v
The changed time period as observed by the observer is
T1=t2t1=T+1v12aT2v1v
Substituting T1=1f and t=1f in the above equation, we get
f=2vf22vfa

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