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.

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Solution

Required frequency n

$= \frac{ν + v_{0}}{v - v_{s}} v = \frac{v}{v - a t} . v$

$= \frac{v . v}{v - a . \frac{1}{2 v}} = \frac{2 ν v^{2}}{2 ν v - a}$

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Required frequency n =ν+v0v−vsv=vv−at.v =v.vv−a.12v=2νv22νv−a

Required frequency n

$= \frac{ν + v_{0}}{v - v_{s}} v = \frac{v}{v - a t} . v$

$= \frac{v . v}{v - a . \frac{1}{2 v}} = \frac{2 ν v^{2}}{2 ν v - a}$