% Plot addition of two sin waves and sum.
% Standing Waves, Beats, dispersion.
% See Kenyon p. 328 sec. 10.6.2
% Steven Sahyun Nov. 19, 2014

clf();
xmax = 20;
x=0:0.01:xmax;
ymax = 8;
E01 = 2.5;
E02 = 2.5;
k1= 1;
w1= 0.05;
k2= 1;
w2= -0.05;


for t = 1:100 % % of period to animate; 25 = 1/4 period, 50 = 1/2 etc.
    E1 = E01*sin(k1*x-w1*t);
    E2 = E02*sin(k2*x-w2*t);
    Esum = E1+E2;
    plot(x, E1, x, E2, x, Esum);
    xlim([0, xmax]);
    ylim([-ymax, ymax]);
    group_v = (w2-w1)/(k2-k1);
    title(['Superposition of 2 EM Waves.    v_g =' num2str(group_v)]);
    xlabel('Distance');
    ylabel('E field');
    legend('E1', 'E2', 'Combined');
	%axis equal
	M(t) = getframe;
end