% example script for Problem 1.8 in Ulaby
% which is problem on 4 on Problem Set 1 of 518 in 2012.
% Brian Hornbuckle, January 16, 2012.  

clear all;  close all;

% let's visualize the wave
% easiest perhaps to do this first by looking how the wave behaves in space
% at a certain time

alpha = 1;      % attenuation constant, Np (I just made up this value in order to visualize the wave)

f = 1e9;        % frequency, Hz

T = 1/f;        % period, s

lambda = 0.2;   % wavelength, m

omega = 2*pi*f;     % radial frequency, rad/s

beta = 2*pi/lambda; % wavenumber, rad/m

t = 2.5;        % what does the wave look like at t = 2.5 s?  

z = linspace(0,10*lambda,1001);     % space coordinate, m

v = 3.*exp(-alpha.*z).*sin(omega.*t - beta.*z);     % voltage of wave, V
                                                    % note carefully how I have used * vs .*

figure(1)                                                    
subplot(1,2,1)                                                  
plot(z,v,'m-');
xlabel('space, m');  ylabel('voltage, V');  grid on;
legend(['using \alpha = ',num2str(alpha),' Np']);

% so the amplitude of the wave decreases in space, like we discussed in class

% now let's solve the problem, 
% look at how the wave behaves in time at a certain point in space

z = 2;      % position, m

t = linspace(0,6*T,1001);       % let's look at, say, six periods of this wave

v = 3.*exp(-alpha.*z).*sin(omega.*t - beta.*z);     % voltage of wave, V

subplot(1,2,2)
plot(t,v,'m-');  legend(['z = ',num2str(z),' m']);
xlabel('time, s');  ylabel('voltage, V');  grid on;

% what does alpha need to be so that the amplitude at z = 2 m is equal to 1 V?
% right now with alpha = 1 the amplitude is about 0.4 V