A source and listener are both moving towards each other with speed $\frac{\mathrm{V}}{10}$. (where V is…

A source and listener are both moving towards each other with speed $\frac{\mathrm{V}}{10}$. (where V is speed of sound) If the frequency of sound note emitted by the source is ' $n$ ', then the frequency heard by the listener would be nearly
  1. 1.1 n
  2. 1.22 n
  3. n
  4. 1.27 n

Solution

$\begin{aligned} \mathrm{n}^{\prime} & =\left(\frac{\mathrm{V}+\mathrm{V}_{\mathrm{L}}}{\mathrm{V}-\mathrm{V}_{\mathrm{S}}}\right) \mathrm{n} \\ & =\left(\frac{\mathrm{V}+\frac{\mathrm{V}}{10}}{\mathrm{~V}-\frac{\mathrm{V}}{10}}\right) \mathrm{n} \\ & =\frac{11}{9} \mathrm{n} \\ & =1.22 \mathrm{n}\end{aligned}$

Asked in: MHT CET 2024 (16 May Shift 2)

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