An obstacle is moving towards the source with velocity 'v'. The sound is reflected from the obstacle. If '…

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
  1. $\lambda_{r}=\left(\frac{c-v}{c+v}\right) \lambda$
  2. $\lambda_{r}=\left(\frac{c-v}{c}\right) \lambda$
  3. $\lambda_{r}=\left(\frac{c+v}{c-v}\right) \lambda$
  4. $\lambda_{r}=\left(\frac{c+v}{c}\right) \lambda$

Solution

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, $\begin{array}{l} \frac{c}{\lambda_{r}}=\frac{c}{\lambda}\left(\frac{c+v}{c-v}\right) \Rightarrow \frac{1}{\lambda_{r}}=\frac{1}{\lambda}\left(\frac{c+v}{c-v}\right) \\ \lambda_{r}=\frac{c-v}{c+v} \lambda \end{array}$

Asked in: MHT CET 2020 (16 Oct Shift 2)

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