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(A) When an obstacle moves towards a stationary source with velocity $v$,the frequency of the reflected sound wave $f_{r}$ is given by the Doppler eff

Vedclass · Accepted Answer

$\lambda_{r} = \left(\frac{c-v}{c+v}\right) \lambda$

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(A) When an obstacle moves towards a stationary source with velocity $v$,the frequency of the reflected sound wave $f_{r}$ is given by the Doppler effect formula for a moving reflector: $f_{r} = f \left(\frac{c+v}{c-v}\right)$.Since the speed of sound $c$ remains constant in the same medium after reflection,we use the relation $c = f \lambda$.For the reflected wave,$c = f_{r} \lambda_{r}$,which implies $\lambda_{r} = \frac{c}{f_{r}}$.Substituting the expression for $f_{r}$:$\lambda_{r} = \frac{c}{f \left(\frac{c+v}{c-v}\right)} = \frac{c}{f} \left(\frac{c-v}{c+v}\right)$.Since $\frac{c}{f} = \lambda$,we get $\lambda_{r} = \left(\frac{c-v}{c+v}\right) \lambda$.

An obstacle is moving towards the source with velocity $v$. The sound is reflected from the obstacle. If $c$ is the speed of sound and $\lambda$ is the wavelength,then the wavelength of the reflected wave $(\lambda_{r})$ is

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