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A bat flies at a steady speed of $4 \mathrm{~ms}^{-1}$ emitting a sound of $\mathrm{f}=90 \times 10^{3} \mathrm{~Hz}$. It is flying horizontally towards a vertical wall. The frequency of the reflected sound as detected by the bat will be (take velocity of sound in air is $330 \mathrm{~ms}^{-1}$ )
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Verified Answer
The correct answer is:
$92.1 \times 10^{3} \mathrm{~Hz}$
Frequency of reflected sound heard by the bat
$$
\begin{aligned}
v^{\prime} &=v\left[\frac{v-\left(v_{0}\right)}{v-v_{s}}\right] \\
&=v\left[\frac{v+v_{0}}{v-v_{s}}\right]=v\left[\frac{v+v_{b}}{v-v_{b}}\right]
\end{aligned}
$$
$$
\begin{aligned}
&=v\left[\frac{330+4}{330-4}\right] 90 \times 10^{3} \\
&=92.1 \times 10^{3} \mathrm{~Hz}
\end{aligned}
$$
$$
\begin{aligned}
v^{\prime} &=v\left[\frac{v-\left(v_{0}\right)}{v-v_{s}}\right] \\
&=v\left[\frac{v+v_{0}}{v-v_{s}}\right]=v\left[\frac{v+v_{b}}{v-v_{b}}\right]
\end{aligned}
$$
$$
\begin{aligned}
&=v\left[\frac{330+4}{330-4}\right] 90 \times 10^{3} \\
&=92.1 \times 10^{3} \mathrm{~Hz}
\end{aligned}
$$
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