Q133 / 170 · Manipal (MET) 2017 · Physics

The apparent frequency of the whistle of an engine changes in the ratio $9: 8$ as the engine passes a stationary observer. If the velocity of the sound is $340 \mathrm{~ms}^{-1}$, then the velocity of the engine is

Correct answer
A
$40 \mathrm{~ms}^{-1}$
B
$20 \mathrm{~ms}^{-1}$
C
$340 \mathrm{~ms}^{-1}$
D
$180 \mathrm{~ms}^{-1}$

Solution

From Doppler's effect, perceived frequency $\begin{aligned} f^{\prime} & =f\left(\frac{v-v_o}{v-v_s}\right) \\ \frac{9}{8} & =\frac{340}{340-v_s}\end{aligned}$ $\Rightarrow 9\left(340-v_s\right)=8 \times 340$ $\therefore v_s=37.7 \mathrm{~ms}^{-1} \approx 40 \mathrm{~ms}^{-1}$

Hence, the correct answer is option: 'A'.

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