Question

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 $330m/s$, then the speed of engine will be

• A. 30 m/s
• B. 36.6 m/s
• C. 40 m/s
• D. 330 m/s

Answer 1

Answer: (B)

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