The driver of a car travelling with a speed ' $\mathrm{V}_1$ ' $\mathrm{m} / \mathrm{s}$ towards a wall…

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
  1. $\left(\frac{V+V_1}{V-V_1}\right) n$
  2. $\left(\frac{\mathrm{V}-\mathrm{V}_1}{\mathrm{~V}+\mathrm{V}_1}\right) \mathrm{n}$
  3. $\left(\frac{V_1-V}{V_1+V}\right) n$
  4. $\left(\frac{V_1}{V_1-V}\right) n$

Solution

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 $\mathrm{V}_{\mathrm{l}}=\mathrm{V}_{\mathrm{s}}=\mathrm{V}_1$ $\therefore \quad \mathrm{n}^{\prime}=\mathrm{n}\left(\frac{\mathrm{~V}+\mathrm{V}_1}{\mathrm{~V}-\mathrm{V}_1}\right)$

Asked in: MHT CET 2024 (15 May Shift 1)

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