About "why sine waves," the mantra I learned is: "Complex exponentials are the eigenfunctions of linear systems." This means that, if you put a complex expone

About "why sine waves," the mantra I learned is: "Complex exponentials are the eigenfunctions of linear systems." This means that, if you put a complex exponential in, you get the same complex exponential out, scaled by some constant, whose magnitude we call the "frequency response". No other functional form has this property. They are eigenfunctions, so they are orthogonal. We can represent any function in L2 using a weighted sum of them.