Halliday, Resnick & Walker — Waves-I: Problem 12

12 A rope, with mass 1.39 kg 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 tension of the rope? (d) If the rope oscillates in a third-harmonic standing wave pattern, what will be the period of oscillation?