In a hall, a person receives direct sound waves from a source `120 m` away. He also receives waves from the same source which reach him after being reflected from the `25 m` high ceiling at a point halfway between them. The two waves interfere constructively for wavelengths (in metres)

Options

A. `10, (10)/(2) m (10)/(3)`
B. `20, (20)/(3) m (20)/(5)`
C. `30, 20, 10, …`
D. `35, 25, 15, …`

Answer

A

Explanation

Path difference `Delta x = SPO - SO = 25 P - 50`
`= 2sqrt((60)^(2) + (25)^(2)) - 120 =10 m`
For constructive interference
`Delta x =n lambda rArr 10 = n lambda`
`lambda=10/n m`
`lambda = 10, (10)/(2), (10)/(3), (10)/(4)...m`