Problems $3[100$ pts$]$

$55m$ In the double$-$slit experiment of Fig. $35\mathrm{.}2\mathrm{.}5,$ the electric fields of the waves arriving at point $P$ are given by

$,E_1=(2\mathrm{.}00\frac{V}{m})sin[(1\mathrm{.}26{10}^{15})t]$

and $E_2=(2\mathrm{.}00\frac{V}{m})sin[(1\mathrm{.}26{10}^{15})t+39\mathrm{.}6$rad$],$

where time $t$ is in seconds. $($a$)$ What is the amplitude of the recultant electric field at voint $P?($b$)$ What is the ratio of the intensity $I_P$ at point $P$ to the intensity $I_{\text{c}\text{e}\text{n}}$ at the center of the interference pattern? $($c$)$ Describe where point $P$ is in the interference pattern by giving the maximum or minimum on which it lies, or the maximum and minimum between which it lies.