Problem $2$

Soil is characterized by ${}_r=2\mathrm{.}23,{}_r=1,$ and $=5{10}^{-4}\frac{S}{m}.$ At each of the following frequencies, determine if soil can be considered a good conductor, a quasi$-$conductor, or a low$-$loss dielectric $($hint: use Table $7-1$ in the book$),$ and then calculate the attenuation constant $,$ propagation constant $,$ wavelength in the material $,$ phase velocity $u_p,$ and intrinsic impedance ${}_c$ :

$($a$).100$ Hz

$($b$).1$ kHz

$($c$).1$ MHz

$($d$).1$ GHz