# 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.  
# Converted to Python by Jason Patton, January 16, 2012

from __future__ import division # this forces float division
from numpy import *
from matplotlib.pyplot import *

# 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

lambd = 0.2;   # wavelength, m

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

beta = 2*pi/lambd; # wavenumber, rad/m

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

z = linspace(0,10*lambd,1001);     # space coordinate, m

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

rc('mathtext', fontset='stix') # fix font glitch in Fedora
figure(1)                                                    
subplot(121)                                                  
plot(z,v,'m-');
xlabel('space, m');  ylabel('voltage, V');  grid(True);
legend(['using $\\alpha$ = %d Np' % (alpha)]);

# 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(122)
plot(t,v,'m-');  legend(['z = %d m' % (z)]);
xlabel('time, s');  ylabel('voltage, V');  grid(True);
show()

# 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