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**1. Homework Statement**

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. Homework Equations**

A MATLAB code to generate such a surface is

Code:

```
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);
```

**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.