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A bat emitting an ultrasonic wave of frequency $4.5 \times 10^4 \mathrm{~Hz}$ at speed of $6 \mathrm{~m} / \mathrm{s}$ between two parallel walls. The two frequencies heard by the bat will be
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Verified Answer
The correct answer is:
$4.67 \times 10^4 \mathrm{~Hz}, 4.34 \times 10^4 \mathrm{~Hz}$
$$
Frequency received by bat after reflection from wall-1,
$$
f_1=f\left[\frac{v+u}{v-u}\right]=4.5 \times 10^4\left[\frac{330+6}{330-6}\right]
$$
Given, $f=4.5 \times 10^4 \mathrm{~Hz}$
$$
\Rightarrow \quad f_1=4.67 \times 10^4 \mathrm{~Hz}
$$
Frepuency received by bat after reflection from wall-2
$$
\begin{aligned}
f_2 & =f\left[\frac{r-11}{v+u}\right] \\
& =4.5 \times 10^4\left[\frac{330-6}{300+6}\right] \\
& =4.34 \times 10^4 \mathrm{~Hz}
\end{aligned}
$$
Frequency received by bat after reflection from wall-1,
$$
f_1=f\left[\frac{v+u}{v-u}\right]=4.5 \times 10^4\left[\frac{330+6}{330-6}\right]
$$
Given, $f=4.5 \times 10^4 \mathrm{~Hz}$
$$
\Rightarrow \quad f_1=4.67 \times 10^4 \mathrm{~Hz}
$$
Frepuency received by bat after reflection from wall-2
$$
\begin{aligned}
f_2 & =f\left[\frac{r-11}{v+u}\right] \\
& =4.5 \times 10^4\left[\frac{330-6}{300+6}\right] \\
& =4.34 \times 10^4 \mathrm{~Hz}
\end{aligned}
$$
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