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A police car with a siren of frequency $8 \mathrm{kHz}$ is moving with uniform velocity $36 \mathrm{~km} / \mathrm{h}$ towards a tall building which reflects the sound waves. The speed of sound in air is $320 \mathrm{~m} / \mathrm{s}$. The frequency of the siren heard by the car driver is
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Verified Answer
The correct answer is:
$8.50 \mathrm{kHz}$
$8.50 \mathrm{kHz}$
Apparent frequency of sound heard by car driver (observer) reflected from the building will be
$$
\begin{aligned}
f^{\prime} & =f\left(\frac{v+v_0}{v-v_s}\right) \\
& =8\left(\frac{320+10}{320-10}\right) \\
& =8.5 \mathrm{kHz}
\end{aligned}
$$
$\therefore$ Correct option is (a).
Analysis of Question
(i) Question is simple.
(ii) Driver will listen two sounds, direct and reflected. Direct sound will be of $8 \mathrm{kHz}$ as driver has no relative motion with the car. But reflected sound is of increased frequency because driver and image of car both are approaching towards each other.
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