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 ' $V$ ' $\mathrm{m} / \mathrm{s}$, then the frequency of the sound reflected from the wall and as heard by the driver in Hz is
  1. $\left(\frac{V_1}{V-V_1}\right) n$
  2. $\left(\frac{V_1-V}{V+V_1}\right) n$
  3. $\left(\frac{V+V_1}{V-V_1}\right) n$
  4. $\left(\frac{V-V_1}{V+V_1}\right) n$

Solution

For the source moving towards the wall, $\therefore \quad \mathrm{n}_1=\mathrm{n}\left[\frac{\mathrm{~V}}{\mathrm{~V}-\mathrm{V}_1}\right]$
For the reflected sound waves, the driver acts as an observer moving towards the wall $\begin{array}{ll} \therefore & \mathrm{n}_2=\mathrm{n}_1\left[\frac{\mathrm{~V}+\mathrm{V}_1}{\mathrm{~V}}\right] \\ \therefore & \mathrm{n}_2=\left[\frac{\mathrm{V}+\mathrm{V}_1}{\mathrm{~V}}\right] \times\left[\frac{\mathrm{V}}{\mathrm{~V}-\mathrm{V}_1}\right] \times \mathrm{n} \\ \therefore & \mathrm{n}_2=\mathrm{n}\left[\frac{\mathrm{~V}+\mathrm{V}_1}{\mathrm{~V}-\mathrm{V}_1}\right] \end{array}$

Asked in: MHT CET 2024 (02 May Shift 2)

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