1. The problem statement, all variables and given/known data A string with mass density u = 9.00 g/m extends from zero to infinity along the x-axis. It is under tension T = 25 N, and is driven by a mechanism at x = 0. The velocity of the drive mechanism depends on time as: vy(t) = 0 (if t = 0) 10.0 cm/s (if 0 < t ≤ 0.1 s) −20.0 cm/s (if 0.1 s < t ≤ 0.2 s) 10.0 cm/s (if 0.2 s < t ≤ 0.3 s) 0 if t > 0.3 s (a) Sketch a “snapshot graph” of the displacement of the string at time t = 0.5 s, from 0 to 30 m along the x-axis. Use a range of -1.0 cm to +1.0 cm on the y-axis. (b) Sketch the “history graph” at x = 10 m, for t = 0 to 0.6 s. 2. Relevant equations v = sqrt(T/u) Y = Yo cos(kx - w t) 3. The attempt at a solution I can calculate the wave speed from square root of (T/u) a) t = 0.5 s Therefore, vy(t) = -20.0 cm/s At x = 0, yo = -20.0 * 0.5 = -10.0 cm But I do not know how y will vary with x. I thought of using Y = yo cos(k x), where k is wave-number. But do not know how to calculate the value of k as I do not know how to find wavelength or frequency. b) x = 10 m How do I find vy(t) at this value of x ?