Question

The electric field part of an electromagnetic wave in an medium is represented by $E_x$ = 0,
$E_y=2.5\frac{N}{C}\cos [(2\pi \times {10}^6\frac{rad}{s})t-(\pi \times {10}^{-2}\frac{rad}{m})x]$
$E_z$ = 0. The wave is

Answer 1

The standard equation of electromagnetic wave

$E_y=E_0\cos (wt-kx)$

The given equation

$E_y=2.5\frac{N}{C}\cos [(2\pi \times {10}^6\frac{rad}{m})t-(\pi \times {10}^{-2}\frac{rad}{sec})x]$

Comparing with standard equation

we get $w=2\pi f=2\pi \times {10}^6\Rightarrow \lambda f={10}^{6}Hz$

Moreover, we know that

$\frac{2\pi }{\lambda }=k=\pi \times {10}^{-2}{m}^{-1}\Rightarrow f=\lambda =200m$
Hence, the wave is moving along $+ve$ $x-direction$ with frequency ${10}^{6}Hz$ and wavelength $200m$