Beats

Beats occur when two waves with slightly different frequencies are superimposed. We can see this phenomenon by plotting, for example, sin(10x) + cos(9x). Or better yet, we could animate sin(10x+t) + cos(9x+t) as t varies. Here is the result:

Groovy Warping Waves

The images above were generated with the following Mathematica code:

Table[Plot[Sin[10x+t] + Cos[9x+t], {x,-2Pi,2Pi}, 
	Axes->None, AspectRatio -> Automatic, PlotPoints -> 300], 
	{t,0,2Pi-Pi/6,Pi/6}]

The images were then assembled into an animated gif using GifBuilder.

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