What is phase difference between two waves, if the resultant amplitude due to their superposition is same as that of the waves?

Options

A. `pi//2`
B. `pi`
C. `2pi//3`
D. `pi//4`

Answer

C

Explanation

`R=sqrt(A^2+A^2+2A^2cos(prop_1 - prop_2)`
`R^2 = 2A^2 +2A^2 cos (prop_1 - prop_2)`
`1=2+2cos(prop_1-prop_2)`
`1-2 = 2cos (prop_1-prop_2)`
`-1/2 = cos (prop - prop_2)`
`prop_1 - prop_2 = cos^(-1) (-1/2) = (2pi)/(3)`