Problem 5.6.9: Two components, one medium

Write both components as cosines:

Both have the same $\omega =10^7\pi rad/s$ and the same $\beta =0.2\pi rad/m$. The argument $\omega t-\beta x$ means travel towards $+x$, and there is no factor $e^{-\alpha x}$: the medium is lossless. The phasor is $E(x)=(-3j{a}_y+4a_z)e^{-j0.2\pi x}V/m$.

The phase grows by $2\pi$ over one wavelength:

Lossless ($\sigma =0$) and nonmagnetic ($\mu ={\mu }_0$):

$\omega /\beta =10^7\pi /0.2\pi =5\times 10^{7}m/s$, the same as $\lambda f$. In free space a $5\mathrm{MHz}$ wave is ${\lambda }_0=60\mathrm{m}$ long, here it is $\sqrt{36}=6$ times shorter.