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

Answer

B, D

Explanation

`Deltaphi=(2pi)/(lambda)(x_(1)-x_(2))+(pi/4-pi/6)`
when `x_(1)-x_(2)=23lambda//24`
then`Deltaphi=2pi`(constructive interference)
when`x_(1)-x_(2)=11lambda//24`
then`Deltaphi=pi`(destructive interference)