A source of sound of frequency $640 \mathrm{~Hz}$ is moving at a velocity of $\frac{100}{3} \mathrm{~m} /…

A source of sound of frequency $640 \mathrm{~Hz}$ is moving at a velocity of $\frac{100}{3} \mathrm{~m} / \mathrm{s}$ along a road, and is at an instant $30 \mathrm{~m}$ away from a point $A$ on the road (as shown in figure). A person standing at $O, 40 \mathrm{~m}$ away from the road hears sound of apparent frequency $v^{\prime}$. The value of $v^{\prime}$ is (velocity of sound $=340 \mathrm{~m} / \mathrm{s}$ )
  1. $620 \mathrm{~Hz}$
  2. $680 \mathrm{~Hz}$
  3. $720 \mathrm{~Hz}$
  4. $840 \mathrm{~Hz}$

Solution

We know that, $ n^{\prime}=n\left[\frac{v}{v-v_s \cos \theta}\right] $ Hence, $ \begin{aligned} n^{\prime} & =640\left[\frac{340}{340-\frac{100}{5}}\right] \\ n^{\prime} & =640 \times \frac{340}{320}=2 \times 340 \\ & =680 \mathrm{~Hz} \end{aligned} $

Asked in: AP EAMCET 2013

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