Two coherent waves represented by `y_(1) = A sin ((2 pi)/(lambda) x_(1) - omega t + (pi)/(6))` and `y_(2) = A sin (( 2pi)/(lambda) x_(2) - omega t + (pi)/(6))` are superposed. The two waves will produce

Options

A. constructive interference at `(x_(1) - x_(2)) = 2 lambda`
B. constructive interference at `(x_(1) - x_(2)) = 23//24 lambda`
C. destructive interference at `(x_(1) - x_(2)) = 1.5 lambda`
D. denstructive interference at `(x_(1) - x_(2)) = 11//24 lambda`

Answer

B, D

Explanation

`Delta phi = ( 2 pi x_(1))/(lambda) - omega t + (pi)/(4) - 2 pi (x_(2))/(lambda) + omega t - (pi)/(6)`
` = ( 2 pi)/(lambda) (x_(1) - x_(2)) + (pi)/(12)`
for constructive interference
`( 2pi)/( lambda) (x_(1) - x_(2)) + (pi)/( 12) = 2 n pi` `n = 0 , 1 ,2 , ...`
for destructive interference
`(2 pi)/(lambda) (x_(1) - x_(2)) + (pi)/(12) = ( 2n - 1)pi`