7.22 ignoring reflection at the air–water boundary, if the amplitude of a 1 ghz incident wave in air is 20 v/m at the water surface, at what depth will it be down to 1 μv/m? water has μr = 1, and at 1 ghz, r = 80 and σ = 1 s/m.

z = 0.8 (approx)

Explanation:

given,

Amplitude of 1 GHz incident wave in air = 20 V/m

Water has,

μr = 1

at 1 GHz, r = 80 and σ = 1 S/m.

depth of water when amplitude is down to  1 μV/m

Intrinsic impedance of air = 120 π  Ω

Intrinsic impedance of  water =

Using equation to solve the problem

E(z) is the amplitude under water at z depth

E_o is the amplitude of wave on the surface of water

z is the depth under water

now ,

taking ln both side

21.07 x z = 16.81

z = 0.797

z = 0.8 (approx)

this could be newton#'s law of cooling. the cooling curve is exponential