Sums of Sine Waves with Several Step Sizes (Sawtooth or Square Approximations)

This Demonstration shows the functions , for values of that run from 1 to the maximum frequency in steps of size in the bottom plot, and their sum in the top plot. This illustrates an approximation of standard waves (sawtooth, square, etc.) by adding sine waves (Fourier method).

Adding 30 waves with step size , the graph of the sum approximates a sawtooth curve:

.

With 30 waves and step size , the graph of the sum approximates a square wave:

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With 15 waves and step size :

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In general, for the step size :

).

The step size parameter gives interesting artificial waves such as natural harmonics.