function travelling_wave
%This function allows students to visualize a travelling wave in a 1-D
%chain of N atoms having a wave vector defined by n (N and n are variables
%that can and should be changed).  Currently the lattice parameter (a), 
%spring constant (K), and mass (m) are arbitrarilly set to 1, but can be 
%changed to evaluate real material properties (this requires a concurrent 
%change to t, so that an  appropriate time step is considered.  The 
%analysis for a 1-D chain comes from Charles Kittel,"Introduction to Solid 
%State Physics", Chapter 4.  

warning off;
a = 1;
a_fine = .01;
N = 10;
L = N*a;
j = 0:1:L/a;
j_fine = 0:1:L/a_fine;
n = [5];
k = 2.*pi.*n./L;
[j_mesh k_mesh] = meshgrid(j,k);
[j_fine_mesh k_fine_mesh] = meshgrid(j_fine, k);
u = exp(-i.*(-k_mesh.*j_mesh.*a));
u_fine = exp(-i.*(-k_fine_mesh.*j_fine_mesh.*a_fine));



K = 1; m = 1;
omega = sqrt(4*K/m)*abs(sin(k.*a./2));
box on;
for t = 1:.02:100;
    plot(j_fine.*a_fine,u_fine.*exp(-i.*omega.*t),'linewidth',2,'color',[1 1 1]);
    hold on
    plot(j.*a,u.*exp(-i.*omega.*t),'o','markersize',12,'markerfacecolor',[1 .5 0],'markeredgecolor','k','linewidth',1)
    hold off
    set(gca,'fontsize',16,'linewidth',2);
    xlabel('index')
    ylabel('displacement (mm)')
    %axis([0 N -1 1])
    pause(.01)
end