A source of sound producing wavelength of $50\text{ cm}$ is moving away from stationary observer with…

A source of sound producing wavelength of $50\text{ cm}$ is moving away from stationary observer with $(1/5)\text{th}$ speed of sound. Then, what is the wavelength of sound heard by observer? [EAMCET 2011]
  1. $70\text{ cm}$
  2. $55\text{ cm}$
  3. $40\text{ cm}$
  4. $60\text{ cm}$

Solution

Wavelength, $\lambda' = \lambda \left(\frac{v + v_s}{v}\right)$ $\lambda' = 50 \left(\frac{330 + (330 / 5)}{330}\right)$ $\Rightarrow \lambda' = 50 \left(\frac{330 + 66}{330}\right)$ $= 50 \left(\frac{396}{330}\right) = 50 \times \frac{6}{5}$ $= 60\text{ cm}$

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