If the two waves of the same frequency and same amplitude, on superposition produce a resultant disturbance of the same amplitude, then the phase difference between the two arriving wave will be

Options

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

Answer

B

Explanation

`R = sqrt(A_(1)^(2) + A_(2)^(2) + 2A_(1)A_(2) cos (alpha_(1) - alpha_(2)))`
`A = sqrt(2A^(2) + 2A^(2) cos alpha_(1) - alpha_(2))`
`A^(2) - 2A^(2) 2A^(2) cos alpha_(1) - alpha_(2)`
`- (1)/(2) = cos alpha_(1) - alpha_(2)`
`:. alpha_(1) - alpha_(2) = (2pi)/(3)`