The difference between the apparent frequency of a source of sound as perceived by an observer during its approach and recession is 2% of the natural frequency of the source. If the velocity of sound in air is 300 m/sec, the velocity of the source is (It is given that velocity of source << velocity of sound)
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When the source approaches the observer
Apparent frequency $n' = \frac{v}{v - v_s} \cdot n = n \left[ \frac{1}{1 - \frac{v_s}{v}} \right]$
= $n\left[1-\frac{v_{s}}{v}\right]^{-1}=n\left[1+\frac{v_{s}}{v}\right]$
(Neglecting higher powers because v S << v)
When the source recedes the observed apparent frequency $n'' = n \left[ 1 - \frac{v_s}{v} \right]$
$Given n' - n'' = \frac{2}{100} n, v = 300 m/sec \therefore \frac{2}{100} n = n \left[ 1 + \frac{v_s}{v} \right] - n \left[ 1 - \frac{v_s}{v} \right] = n \left[ 2 \frac{v_s}{v} \right] \Rightarrow \frac{2}{100} = 2 \frac{v_s}{v} \Rightarrow v_s = \frac{v}{100} = \frac{300}{100} = 3 m / sec .$
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