Answer to Question #117805 in Optics for rawad

Question

Let say you have two electromagnetic wave
y1=2sin(2πx −20πt)
y2=2sin(2πx −20πt+ϕ),
Assume that these to waves start to propagate at the same instant t_0.1=t_0.2=0sec, but at different initial positions from an observation point.
The amplitude of the resultant wave due to
interference of these to waves would be maximum at the observation point if the phase difference is how much?

Answer 1

At different initial positions from an observation point

$y_1=2\sin(2\pi x_1-20\pi t)$

$y_2=2\sin(2\pi x_2-20\pi t+\phi)$

The amplitude of the resultant wave due to interference of these two waves will be maximum at the observation point if the phase difference is

$\Delta\alpha=2\pi(x_2-x_1)+\phi=\pm2\pi k, k=0,1,2,...$