Answer
a.) $6.94\cdot10^{14}$ Hz
b.) $375$ V/m
c.)
$\displaystyle B(x,t) =(1.25\cdot10^{-6})\cos(2\pi[\frac{x}{432\cdot10^{-9}} - (6.94\cdot10^{14})t])$
$\displaystyle E(x,t) = 375\cos(2\pi[\frac{x}{432\cdot10^{-9}} - (6.94\cdot10^{14})t])$
Work Step by Step
a.) $\displaystyle \lambda f = c \qquad\rightarrow\qquad f = \frac{\lambda}{c} = \frac{432\cdot10^{-9}}{3.00\cdot10^8} = 6.94\cdot10^{14}$ Hz
b.) $E = cB = (3.00\cdot10^8)(1.25\cdot10^{-6}) \approx 375 $ V/m
c.)
$\displaystyle B(x,t) = B_{max}\cos(kx-\omega t)$
$\displaystyle B(x,t) = B_{max}\cos(2\pi[\frac{x}{\lambda} - ft]) = (1.25\cdot10^{-6})\cos(2\pi[\frac{x}{432\cdot10^{-9}} - (6.94\cdot10^{14})t])$
$\displaystyle E(x,t) = E_{max}\cos(kx-\omega t)$
$\displaystyle E(x,t) = E_{max}\cos(2\pi[\frac{x}{\lambda} - ft]) = 375\cos(2\pi[\frac{x}{432\cdot10^{-9}} - (6.94\cdot10^{14})t])$
