Two waves having same amplitude A , angular frequency and propagation constant k , traveling in opposite directions, have a phase difference of 60^ . If they interfere with each other, the resultant displacement y of the wave is

Step-by-step solution

Let the equations of the two waves traveling in opposite directions be y₁ = A ( t - kx) and y₂ = A ( t + kx + ) . Given that the phase difference is = 60^ . The resultant displacement is given by the principle of superposition: y = y₁ + y₂ y = A ( t - kx) + A ( t + kx + 60^ ) Using the trigonometric identity C + D = 2 ( C+D 2 ) ( C-D 2 ) , we get: y = 2A ( t - kx + t + kx + 60^ 2 ) ( t + kx + 60^ - ( t - kx) 2 ) y = 2A ( t + 30^ ) (kx + 30^ ) Answer: 2A ( t + 30^ ) (kx + 30^ )