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A wall is moving with velocity u and a source of sound moves with velocity u/2 in the same direction as shown in the figure. Assuming that the sound travels with velocity 10u, the ratio of incident sound wavelength on the wall to the reflected sound wavelength by the wall is equal to

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9:11

11:9

4:5

5:4

answer is A.

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Detailed Solution

Wavelength of the incident sound is

$λ_{l} = \frac{10 u - \frac{u}{2}}{f} = \frac{19 u}{2 f}$

Frequency of the incident sound is

$F_{i} = \frac{10 u - u}{10 u - \frac{u}{2}} f = \frac{18}{19} f = f_{r}$

when f_r is the frequency of the reflected sound.
Wavelength of the reflected sound is

$λ_{r} = \frac{10 u + u}{f_{r}} = \frac{11 u}{18 f} \times 19 = \frac{11 \times 19}{18} \frac{u}{f}$

$∴ \frac{λ_{i}}{λ_{r}} = \frac{19 u}{2 f} \times \frac{18 f}{11 \times 19 u} = \frac{9}{11}$

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