Step 1: Identify the Wavelength Formula: When a source moves away from a stationary observer, the apparent wavelength $\lambda'$ is given by:
$$\lambda' = \lambda \left( \frac{v + v_s}{v} \right)$$
Where:
• $\lambda = 50 \text{ cm}$ (original wavelength)
• $v$ = speed of sound
• $v_s = \frac{1}{5}v$ (speed of source)
Step 2: Substitute and Solve: $$\lambda' = 50 \left( \frac{v + \frac{1}{5}v}{v} \right)$$
$$\lambda' = 50 \left( \frac{\frac{6}{5}v}{v} \right)$$
$$\lambda' = 50 \times \frac{6}{5}$$
$$\lambda' = 10 \times 6 = 60 \text{ cm}$$
The wavelength heard by the stationary observer is $60$ cm.