Phase velocity of electric field?

Question

A y-directed propagating electric field travels in the +z direction and has an initial amplitude of 34Vm^-1, an attenuation constant of 0.002Npm-1, a phase shift of 4 π rad, a wavelength of 0.20m and a frequency of 1GHz.

Write a mathematical expression for the instantaneous form of the field and determinen how far the wave must travel before its amplitude is reduced to 1Vm-1. What is the phase velocity?

Any ideas anyone?

Answer 1

EDITED ANSWER

The sinusoidal plane wave equation for a y-directed electric field in the z direction is

Ey(t,z) = E0*e^(-a*z)*cos(k*z - w*t + ø)

a = 0.002Np/m;

E0 = 34 V/m

k = 2π/L where L = 0.20 m

w = 2πF where F = 10^9 s^-1

ø = 4π

The phase velocity is L*F.

For the attenuation, 34*e^-a*z) = 1

a*z =ln(34/1)

The attenuation is ln(34/1) Np;   a = 0.002 Np/m so

= ln(34)/.002 = 1763 m