Question $5$: In the figure below, the three $(3)$ monochromatic light waves coming from the corresponding light sources $S_1,S_2$ and $S_3$ interfere at point $P$ on the screen. The three light waves can be expressed as$,$

$E_k=E_{0}sin(kx-t+(k-1))$;kin$\{1,2,3\}$

Also, the point $P$ on the screen is located at $y$ meter above $O$ and about $L$ meters from the three sources of light waves. Show that the intensity at position $P$ is given by$,$

$I(y)=\frac{I_0}{9}[2cos(\frac{2dy}{L})+1{]}^2$