Suppose you create a periodic function by adding together only sine functions whose amplitudes decrease like \(1 / n^{2}\), where \(n\) is any odd integer multiple of the fundamental frequency, and where every other term is subtracted rather than added.

(a) What general properties would this periodic function exhibit?

(b) Describe the shape of the function obtained by adding only the four terms of frequencies f, 3f, 5 f, and \(7 f\). (Construct the graph using superposition.)