1. The problem statement, all variables and given/known data Beat pattern is superposition of two sine functions with a little frequency difference. (http://en.wikipedia.org/wiki/Beat_(acoustics)#Mathematics_and_physics_of_beat_tones) We use this pattern to generate a surface, by adding another beat pattern with 60 degrees difference. Now, normal beat pattern has a well known super-period. But I need a similar formula for determining super-period of any cross-section from the origin. I need such a formula to use it in simulations. 2. Relevant equations A MATLAB code to generate such a surface is Code (Text): l1 = 0.295; % Period 1 l2 = 0.305; % Period 2 % This is the formula for determining period for beat curve period = l1*l2/(abs(l1-l2)); x = -period:0.01:period; y = -period:0.01:period; [X,Y] = meshgrid(x,y); S = sin(2*pi*X/l1) + sin(2*pi*X/l2) + sin(2*pi*(X/2+sqrt(3)*Y/2)/l1) + sin(2*pi*(X/2+sqrt(3)*Y/2)/l2); Resulting surface is 3. The attempt at a solution Taking the Fourier transform, we can determine the four k values that generate this surface. But one problem is to determine the resulting cross-section pattern. This is not for a homework, but for a simulation problem I struggle with.