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A train moving at a speed of $220 \mathrm{~ms}^{-1}$ towards a stationary object, emits a sound of frequency $1000 \mathrm{~Hz}$. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is (speed of sound in air is $330 \mathrm{~ms}^{-1}$ )
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Verified Answer
The correct answer is:
$5000 \mathrm{~Hz}$
From Doppler's shift, we know for this case
$$
\begin{aligned}
n^{\prime} & =n\left(\frac{v+v_s}{v-v_s}\right) \\
& =1000\left(\frac{330+220}{330-220}\right) \\
& =1000\left(\frac{550}{110}\right)=5000 \mathrm{~Hz}
\end{aligned}
$$
$$
\begin{aligned}
n^{\prime} & =n\left(\frac{v+v_s}{v-v_s}\right) \\
& =1000\left(\frac{330+220}{330-220}\right) \\
& =1000\left(\frac{550}{110}\right)=5000 \mathrm{~Hz}
\end{aligned}
$$
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