1. The problem statement, all variables and given/known data The linear mass density of a non-uniform wire under constant tension gradually decreases along the wire while ensuring an incident wave is transmitted without reflection. The wire has constant density μ for x ≤ 0. In this region a transverse wave has the form y(x,t) = 0.003cos(30x -60t), where x,y are given in meters and t in seconds. From x=0 to x=20, the linear mass density decreases from μ to μ/9. For x > 20, the density remains constant at μ/9. i) What is the wave velocity for large values of x (>20m)? ii) What is the amplitude of the wave for large values of x? You should be able to determine this using conservation of mechanical energy, iii)Give y(x,t) for x>20. 2. Relevant equations y(x,t) = Acos(kx-wt) w/k = v v= sqrt(T/μ) P = 1/2sqrt(μT)w2A2 3. The attempt at a solution i) Comparing given wave equation and y=Acos(kx-wt) for x < 0 k = 30 w = 60 v = 60/30 =2 v2μ = T 4μ=T Tension remains constant so v20 = √4μ/μ/9 = 6m/s ii) E = 1/2mv2. At max kinetic energy potential energy = 0. Total energy = Kinetic energy P = ½√(μF)w2A2 Energy before = Energy After ½√(μ4μ).6020.0032 =½√(μ/9.4μ).v2k2A2 0.0027=k2A2 I have no idea if this is correct and if i can take k to be constant or not. Any help would be really appreciated!