$(14$ points$)$ EM Plane Wave Consider a plane wave traveling through empty space which has an intensity of $500\frac{W}{m^2}$ and whose wavelength is $700$ nm $.$ This wave travels in the negative$-$x$-$direction and is polarizedrith its electric field along the $y-$direction.

$($a$)$ What are the wave number and frequency f this wave? $(4$ pts$)$

$($b$)$ What are the amplitudes of the electric and magnetic fields in this wave? $(4$ pts$)$

$($c$)$ Write$-$down the equation which gives the magnetic field as a function of time and position, vec$(B)(x,t),$ where you may choose coordinates so that the field is at a maximum at $x=t=0.$ Plug in any relevant numerical values from above $-$ the only variables in your formula should be $x$ and $t.(6$ pts$)$