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. `5,2,5, (5)/(3) ....m`
B. `10,5, (1)/(3).....m`
C. `2, (20)/(3) , 4 ....m`
D. `10, (10)/(3), 2 .....m`

Answer

B

Explanation

Let , the length of path of the sound directly from the source be `x_(1)`
the length of path of the sound after getting reflected from the ceilling be `x _(2)`
`x _(1) = 120 m`


`x _(2) = 65 + 65 = 130 m`
Path difference between the waves is
`Delta x = 130 - 120 = 10 m`
Also, for constructive interference path difference, `Delta x = n lamda `
`lamda = ( Delta x )/(n) = (10)/( n)`
The wavelengths of the wave for maximum are
`lamda = 10,5, (10)/(3), (10)/(4) , (10)/(5)...`
`[because n =1,2,3,...]`