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BITSAT 2021

Exam: BITSAT
Year: 2021
Subject: Physics
Chapter: Waves and Sound

BITSAT 2021 · Physics · Waves and Sound

The frequency of whistle of an engine appears to be (4 / 5)^ th of...

The frequency of whistle of an engine appears to be

(4 / 5)^{\text{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

Options

A $30 \mathrm{ m} / \mathrm{s}$
B $36.6 \mathrm{ m} / \mathrm{s}$
C $40 \mathrm{ m} / \mathrm{s}$
D $330 \mathrm{ m} / \mathrm{s}$

Correct answer

B. $36.6 \mathrm{ m} / \mathrm{s}$

Step-by-step solution

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}

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