A discrete chain of beads approximates the continuous sine shape of an ideal string

Evidence

In the case of the string that we are now studying, sinusoids make another appearance of a different sort. For sufficiently many beads, the shape of the individual modes starts to trace out a recognizable sinusoid. Even in the cases with relatively few beads, the beads fall on a curve belonging to each mode; this curve is exactly the sinusoidal one followed for an infinite number of beads. — Eric J. Heller, Why You Hear What You Hear- An…, 798

Categorization

• XREF: Discretization converging to continuous sine curves mirrors how sampled digital audio approximates continuous waveforms.