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

Answer

C

Explanation

Let A and `upsilon` be the amplitude and frequency of each wave differing in phase by `phi`. Then
`y_(1)=Asin(kx-2piupsilont)`
and `y_(2)=Asin(kx-2piupsilont+phi)`
According to the principle of superposition, the resultant wave is
`y=y_(1)+y_(2)=Asin(kx-2piupsilont)+Asin(kx-2piupsilont+phi)`
or `y=(2Acos.(phi)/(2))sin(kx-2piupsilont+(phi)/(2))`
But as per question `2Acos.(phi)/(2)=A`
or `cos.(phi)/(2)=(1)/(2)or(phi)/(2)=(pi)/(3)`
or `phi=(2pi)/(3)`