The frequency of whistle of an engine appears to be $(4 / 5)^{ ext {th }}$ of initial frequency when it crosses a stationary observer. If the velocity of sound is $330 \mathrm{~m} / \mathrm{s}$, then the speed of engine will be

Question

The frequency of whistle of an engine appears to be $(4 / 5)^{	ext {th }}$ of initial frequency when it crosses a stationary observer. If the velocity of sound is $330 \mathrm{~m} / \mathrm{s}$, then the speed of engine will be

Aicharya · Accepted Answer

$n^{\prime}=\frac{n v}{v-v_{s}} \ldots \ldots \ldots(1)$
$n^{\prime \prime}=\frac{n v}{v+v_{s}} \ldots \ldots . .(2)$
From (1) and (2), $\frac{n^{\prime}}{n^{\prime \prime}}=\frac{v+v_{s}}{v-v_{s}} \ldots \ldots . .(3)$
According to question, $\frac{n^{\prime}}{n^{\prime}}=\frac{5}{4}$
$v_{s}=? v=330 \mathrm{~m} / \mathrm{s} \ldots \ldots \ldots .(4)$
From eq. (3) and (4)
$\frac{5}{4}=\left[\frac{330+v_{s}}{330-v_{s}}\right] \Rightarrow 9 v_{s}=330$
$\therefore v_{s}=36.6 \mathrm{~m} / \mathrm{s}$

The frequency of whistle of an engine appears to be $(4 / 5)^{\text {th }}$ of initial frequency when it…

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