Question

Consider that the wave length function is defined as ϕn1,n2 (x,y) = 2/a sin(n1πx/a)sin(n2πy/a).

Make a contour graph in 2D for each of the following functions: ϕ1,1 , ϕ1,2 , and ϕ2,1

(use a=1)

Answer 1

$\phi_{1,1}$

0.8 0.6 0.4 0.2 -0.2 0.4 -0.6 0.8 -1 1 0.8 -0.6 -0.4 -0.2 0 0.2 04 0.6 0.81

01.2

0.8 0.6 0.4 0.2 -0.2 -0.4 0.6 0.8 -1 1 0.8 -0.6 -0.4 -0.2 0 0.2 04 0.6 0.81

021

0.8 0.6 0.4 0.2 0.2 0.6 0.8 -1 1 0.8 -0.6 -0.4 -0.200.2 0.4 0.6 0.8 1

I have plotted in matlab live script, here is the code in case you need

clc;
clear;

x=-1:0.01:1;
y=-1:0.01:1;
[X,Y] = meshgrid(x,y);

%phi_1,1
Z1 = 2.*sin(1.*pi.*X).*cos(2.*pi.*Y);

%phi_1,2
Z2 = 2.*sin(1.*pi.*X).*cos(4.*pi.*Y);

%phi_2,1
Z3 = 2.*sin(2.*pi.*X).*cos(2.*pi.*Y);

contour(X,Y,Z1)
contour(X,Y,Z2)
contour(X,Y,Z3)