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WBJEEA police car with a siren of frequency \(8 \mathrm{kHz}\) is moving with...
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
Solution:
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.
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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