If two waves of same frequency and same amplitude superimpose and produce third wave of same amplitude, then waves differ in phase by –

Options

A. zero
B. `pi`
C. `pi//2`
D. `pi//4`

Answer

D

Explanation

`A_(R)=sqrt(A_(1)^(2) + A_(2)^(2) + 2A_(1)A_(2) cos theta)`
where `theta ` is the phase difference between the waves but
`A_(R) = A_(1) = A_(2) = A`
So, `" "A^(2) = A^(2) + 2A^(2) cos theta`
`" "cos theta = -(1)/(2)`
`" " theta = -(2pi)/(3)`