Suppose that the electric field part of an electromagnetic wave in vacuum is $E=\{(3.1$ $\left.\mathrm{N} / \mathrm{C}) \cos \left[(1.8 \mathrm{rad} / \mathrm{m}) \mathrm{y}+\left(5.4 \times 10^{6} \mathrm{rad} / \mathrm{s}\right) \mathrm{t}\right]\right\}^{\wedge} \mathrm{i}$
(a) What is the direction of propagation?
(b) What is the wavelength $\lambda$ ?
Suppose that the electric field part of an electromagnetic wave in vacuum is $E=\{(3.1$ $\left.\mathrm{N} / \mathrm{C}) \cos \left[(1.8 \mathrm{rad} / \mathrm{m}) \mathrm{y}+\left(5.4 \times 10^{6} \mathrm{rad} / \mathrm{s}\right) \mathrm{t}\right]\right\}^{\wedge} \mathrm{i}$
(a) What is the direction of propagation?
(b) What is the wavelength $\lambda$ ?

(a) The motion is going in the opposite direction of the y-axis. To put it another way, along -j.

(b) The given equation is compared with the equation and we get,

$E=E_{0} \cos (k y+\omega t)$

$\Rightarrow \mathrm{k}=1.8 \mathrm{rad} / \mathrm{s}$

$\omega=5.4 \times 10^{6} \mathrm{rad} / \mathrm{s}$

$\lambda=2 \pi / \mathrm{k}=(2 \times 3.14) / 1.8=3.492 \mathrm{~m}$