Halliday, Resnick & Walker — Waves–I: Problem Problem_52

A rope, under a tension of 200 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by \(y = (0.10 \text{ m})(\sin \pi x/2) \sin 12\pi t\), where \(x = 0\) at one end of the rope, \(x\) is in meters, and \(t\) is in seconds. What are (a) the length of the rope, (b) the speed of the waves on the rope, and (c) the mass of the rope? (d) If the rope oscillates in a third-harmonic standing wave pattern, what will be the period of oscillation?