The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from $420 \mathrm{~Hz}$ to $490 \mathrm{~Hz}$ when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is $330 \mathrm{~ms}^{-1}$.
Correct Option: 1
(1) From the Doppler's effect of sound, frequency appeared at wall
$f_{w}=\frac{330}{330-v} \cdot f$
Here, $v=$ speed of bus,
$f=$ actual frequency of source
Frequency heard after reflection from wall $\left(f^{\prime}\right)$ is
$f^{\prime}=\frac{330+v}{330} \cdot f_{w}=\frac{330+v}{330-v} \cdot f$
$\Rightarrow 490=\frac{330+v}{330-v} \cdot 420$
$\Rightarrow v=\frac{330 \times 7}{91} \approx 25.38 \mathrm{~m} / \mathrm{s}=91 \mathrm{~km} / \mathrm{s}$
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