Question: Concern a vibrating guitar string. Snapshots of the guitar string at millisecond intervals are in Figure.
The guitar string is stretched tight along the x-axis from x = 0 to x = π. Each point on the string has an x-value, 0 ≤ x ≤ π. As the string vibrates, each point on the string moves back and forth on either side of the x-axis. Let y = f(x, t) be the displacement at time t of the point on the string located x units from the left end. A possible formula is y = f(x, t) = cos t sin x, 0 ≤ x ≤ π, t in milliseconds.
Describe the motion of the guitar strings whose displacements are given by the following:
(a) y = g(x, t) = cos 2t sin x
(b) y = h(x, t) = cos t sin 2x