Sound Wave Maths in Processing

Simon has created animations visualizing sound waves (Triangle, Sawtooth, Square and Sine waves) in Processing (Java), using wave functions.

These are the functions he used for the Sawtooth, Square and Sine waves:

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Not to confuse “sine” with “sgn” (sgn standing for sign):

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He was inspired by the logarithmic and power functions that he was studying during his math class yesterday. Simon was trying to draw both types of functions in Grapher on his laptop, but only succeeded for the power functions (because there were no subscript option for the logarithms).

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Interactive Math Functions

Simon was reading about math functions on Wikipedia and came up with an idea to create an interactive math functions editor in JavaScript that would visualize (i.e. show the graphs for) all the functions. Simon was especially excited about cosecant, secant and cotangent (csc, sec and cot for short), which were new to him:

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Simon partially programmed the interactive math functions editor, but it remained unfinished: