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

Options

A. `9:11`
B. `11:9`
C. `4:5`
D. `5:4`

Answer

A

Explanation

Wavelength of the incident sound is `lamda_(1)=(10u-(u)/(2))/(f)=(19u)/(2f)`
Frequency of the incident sound is `f_(1)=(10u-u)/(10u-(u)/(2))f=(18)/(19)f-f_(r)`
When `f_(r)` is the frequency of the reflected sound
Wavelength of the reflected sound is
`lamda_(r)=(10u+u)/(f_(r))=(11u)/(18f)xx19=(11xx19)/(18)(u)/(f)`
`(lamda_(i))/(lamda_(r))=(19u)/(2f)xx(18f)/(11xx19u)=(9)/(11)`