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)

(1) 6 m/sec

(2) 3 m/sec

(3) 1.5 m/sec

(4) 12 m/sec

(2) When the source approaches the observer

Apparent frequency $n\text{'}=\frac{v}{v-{v}_{s}}.n=n\left[\frac{1}{1-\frac{{v}_{s}}{v}}\right]$

= $n{\left[1-\frac{{v}_{s}}{v}\right]}^{-1}=n\left[1+\frac{{v}_{s}}{v}\right]$

(Neglecting higher powers because vS << v)

When the source recedes the observed apparent frequency ${n}^{\text{'}\text{'}}=n\left[1-\frac{{v}_{s}}{v}\right]$

Given

$\frac{2}{100}n=n\left[1+\frac{{v}_{s}}{v}\right]-n\left[1-\frac{{v}_{s}}{v}\right]=n\left[2\frac{{v}_{s}}{v}\right]$

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