MHT CET · Physics · Waves and Sound
The driver of a car travelling with a speed ' \(\mathrm{V}_1\) ' \(\mathrm{m} / \mathrm{s}\) towards a wall sounds a siren of frequency ' \(n\) ' Hz. If the velocity of sound in air is \(\mathrm{Vm} / \mathrm{s}\), then the frequency of sound reflected from the wall and as heard by the driver, in Hz , is
- A \(\left(\frac{V+V_1}{V-V_1}\right) n\)
- B \(\left(\frac{\mathrm{V}-\mathrm{V}_1}{\mathrm{~V}+\mathrm{V}_1}\right) \mathrm{n}\)
- C \(\left(\frac{V_1-V}{V_1+V}\right) n\)
- D \(\left(\frac{V_1}{V_1-V}\right) n\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{V+V_1}{V-V_1}\right) n\)
Step-by-step Solution
Detailed explanation
As source of sound (reflected sound) and the listener (car driver) are both moving towards each other, \(n^{\prime}=n\left(\frac{V+V_l}{V-V_s}\right)\)
Here \(\mathrm{V}_{\mathrm{l}}=\mathrm{V}_{\mathrm{s}}=\mathrm{V}_1\)
\(\therefore \quad \mathrm{n}^{\prime}=\mathrm{n}\left(\frac{\mathrm{~V}+\mathrm{V}_1}{\mathrm{~V}-\mathrm{V}_1}\right)\)
Here \(\mathrm{V}_{\mathrm{l}}=\mathrm{V}_{\mathrm{s}}=\mathrm{V}_1\)
\(\therefore \quad \mathrm{n}^{\prime}=\mathrm{n}\left(\frac{\mathrm{~V}+\mathrm{V}_1}{\mathrm{~V}-\mathrm{V}_1}\right)\)
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