1. The problem statement, all variables and given/known data If a wave y(x, t) = (6.0 mm) sin(kx + (600 rad/s)t + θ) travels along a string, how much time does any given point on the string take to move between displacements y=+2.0 mm and y=-2.0 mm? 2. Relevant equations ω=2πf (but it's not necessary in this problem, this problem just requires algebra, I think) 3. The attempt at a solution For a point to travel between y=+2.0mm to y=-2.0mm, the distance x is (y_2 - y_1)/(2A)* 0.5λ = 1/6 λ (This is what I think since if it's 6.00mm (amplitude) to -6.00mm (-amplitude) it'll be 0.5λ) So, x_2 = x_1 + (1/6) λ So, I write equation for (x_1,t_1) and (x_1 + (1/6) λ, t_2) 6 sin(kx_1 + 600t_1 + θ) = 2 => kx_1 + 600t_1 + θ = arc sin (2/6) ................... (1) 6 sin(k(x_1 + λ/6) + 600t_2 + θ) = -2 => kx_1 + π/3 + 600t_2 + θ = arc sin (-2/6) .................... (2) Subtracting (2) and (1), we get 600 (t_2 - t_1) + π/3 = -0,6796 t_2 - t_1 = -2.8781 * 10^-3 s Where did I get wrong? Why t_2 - t_1 is negative though I have relate x_2 to x_1? I see the solution manual the answer is 0.011 s, but it assumes that x_1 = x_2, and it subtracts (1) and (2), NOT (2) and (1). I really don't get it. As long as the time ticks, the position of the point changes so the x changes, right ???