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A source of frequency $240 \mathrm{~Hz}$ is moving towards an observer with a velocity of $20 \mathrm{~m} / \mathrm{s}$. The observer is now moving towards the source with a velocity of $20 \mathrm{~m} / \mathrm{s}$. Apparent frequency heard by observer, if velocity of sound is $340 \mathrm{~m} / \mathrm{s}$, is
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The correct answer is:
$270 \mathrm{~Hz}$
Frequency of source $n=240 \mathrm{~Hz}$ Velocity of source $\quad v_s=20 \mathrm{~m} / \mathrm{s}$ Velocity of observer $v_0=20 \mathrm{~m} / \mathrm{s}$ Velocity of sound $\quad v=340 \mathrm{~m} / \mathrm{s}$
Given both the source and the observer are moving towards each other. Hence the apparent frequency of the source is,
$$
\begin{aligned}
n^{\prime} & =n\left[\frac{v+v_0}{v-v_s}\right] \\
& =240 \times\left[\frac{340+20}{340-20}\right] \\
& =240 \times \frac{360}{320}=270 \mathrm{~Hz}
\end{aligned}
$$
Given both the source and the observer are moving towards each other. Hence the apparent frequency of the source is,
$$
\begin{aligned}
n^{\prime} & =n\left[\frac{v+v_0}{v-v_s}\right] \\
& =240 \times\left[\frac{340+20}{340-20}\right] \\
& =240 \times \frac{360}{320}=270 \mathrm{~Hz}
\end{aligned}
$$
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