In a large room , a person receives waves from the same source which reach , being reflected from the `25 m` high ceiling at a point halfway between them . The two waves interfere constructively for a wavelength of

Options

A. `20 , 20/3 , 20/5` , etc.
B. `10 , 5 , 2.5 `, etc.
C. `10 , 20 , 30 `, etc.
D. ` 15 , 25 , 35 `, etc.

Answer

B

Explanation

Length of the path for direct sound ` = 120 m`
Length of the path for reflected sound
` = 2 sqrt((60)^(2) + (25)^(2)) = 130 m`
Geometrical path difference
` = 130 - 120 = 10 m`
Two waves interfere constructively when `10 = n lambda`
Putting , `n = 1 , 2, 3,..., lambda = 10 , 5 , 2.5 , .....`