If two waves of the same frequency and amplitude respectively on superposition produce a resultant disturbance of the same amplitude the waves differ in phase by

Options

A. `pi`
B. zero
C. `pi//3`
D. `2pi//3`

Answer

D

Explanation

Two waves `y_(1)=Asin(kx-2pivt)`
=`y_(2)=Asin(kx-2pivt+phi)`after superposition resultant wave is `y=(2Acos(phi)/(2))sin(kx-2piv+(phi)/(2))`
As given, A = `2Acos(phi)/(2)`
`rArr`   `cops(phi)/(2)=(1)/(2)rArr(phi)/(2)=(pi)/(3)rArrphi=(2pi)/(3)` phase difference between two waves.