Two waves having equaitons
`x_1=asin(omegat+phi_1)`,`x=asin(omega+phi_2)`
If in the resultant wave the frequency and amplitude remain equal to those of superimposing waves. Then phase difference between them is

Options

A. `(2pi)/(3)`
B. `(pi)/(3)`
C. `(pi)/(6)`
D. `(pi)/(4)`

Answer

A

Explanation

The frequency and the amplitude of the resultant wave are the same as those of the superimposing waves. In this case `a_(1) = a, a_(2) = a and a_(g) = a`
Using, `R^(2) = P^(2) + Q^(2) + 2PQ cos phi`, we get
`a^(2) = a^(2) + a^(2) + 2a^(2) cos phi`
`a^(2) = 2a^(2) (1 + cos phi)`
`:. 1 + cos phi = (1)/(2) " " :. cos phi = - (1)/(2)`
`:. phi = 120^(@) = (2pi)/(3)`