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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 $=340 \mathrm{~m} / \mathrm{s}$ )
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Verified Answer
The correct answer is:
$680 \mathrm{~Hz}$
We know that,
$$
n^{\prime}=n\left[\frac{v}{v-v_s \cos \theta}\right]
$$
Hence,
$$
\begin{aligned}
n^{\prime} & =640\left[\frac{340}{340-\frac{100}{5}}\right] \\
n^{\prime} & =640 \times \frac{340}{320}=2 \times 340 \\
& =680 \mathrm{~Hz}
\end{aligned}
$$
$$
n^{\prime}=n\left[\frac{v}{v-v_s \cos \theta}\right]
$$
Hence,
$$
\begin{aligned}
n^{\prime} & =640\left[\frac{340}{340-\frac{100}{5}}\right] \\
n^{\prime} & =640 \times \frac{340}{320}=2 \times 340 \\
& =680 \mathrm{~Hz}
\end{aligned}
$$
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