1. The problem statement, all variables and given/known data Two very long strings are tied together at the point x = 0. In the region x < 0, the wave speed is v1, while in the region x > 0, the speed is v2. A sinusoidal wave is incident on the knot from the left (x < 0); part of the wave is reflected and part is transmitted. For x < 0, the displacement of the wave is described by... y(x,t) = Asin(k1x - wt) + Bsin(k1x + wt) For x > 0, the displacement of the wave is described by... y(x,t) = Csin(k2x - wt) where, w/k1 = v1 w/k2 = v2 a) if we assume that both the wave function y and its first spatial derivative dy/dx must be continuous at x = 0, show that: C/A = 2v2/(v1 + v2), and that: B/A = (v1 - v2)/(v1 + v2) b) Show that B2 + (v1/v2)C2 = A2 2. Relevant equations y(x,t) = Asin(kx +- wt) This shows that A, B, C are the amplitudes of their portions. 3. The attempt at a solution I'm really unsure how to go about his problem. I am getting stuck on the idea of getting C/A or B/A because I don't really see how you can solve for them.