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An obstacle is moving towards the source with velocity 'v'. The sound is reflected from the obstacle. If ' $\mathrm{c}^{\prime}$ is the speed of sound and ${ }\lambda^{\prime}$ ' is the wavelength, then the
wavelength of the reflected wave $\left(\lambda_{r}\right)$ is
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wavelength of the reflected wave $\left(\lambda_{r}\right)$ is
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Verified Answer
The correct answer is:
$\lambda_{r}=\left(\frac{c-v}{c+v}\right) \lambda$
The frequency of reflected sound wave is $f_{r}=f\left(\frac{c+v}{c-v}\right)$
$\because$ No change in velocity occurs due to reflection of sound wave.
Hence,
$\begin{array}{l}
\frac{c}{\lambda_{r}}=\frac{c}{\lambda}\left(\frac{c+v}{c-v}\right) \Rightarrow \frac{1}{\lambda_{r}}=\frac{1}{\lambda}\left(\frac{c+v}{c-v}\right) \\
\lambda_{r}=\frac{c-v}{c+v} \lambda
\end{array}$
$\because$ No change in velocity occurs due to reflection of sound wave.
Hence,
$\begin{array}{l}
\frac{c}{\lambda_{r}}=\frac{c}{\lambda}\left(\frac{c+v}{c-v}\right) \Rightarrow \frac{1}{\lambda_{r}}=\frac{1}{\lambda}\left(\frac{c+v}{c-v}\right) \\
\lambda_{r}=\frac{c-v}{c+v} \lambda
\end{array}$
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