1. The problem statement, all variables and given/known data There's a string with tension T & mass density μ that has a transverse wave with ψ(x,t) = f(x±vt). f(x) is an even function & goes to zero as x→±∞ Show that the total energy in the string is given by ∫dw*T*((f'(w))2; limits of integration are ±∞ 2. Relevant equations The kinetic energy of an infinitesimal part of string is KE = 0.5*μ*dx*(dψ/dt)2. Its potential energy is 0.5*T*dx*(dψ/dx)2. Note that w=ck. c = √(T/μ) 3. The attempt at a solution Total energy = KE + PE = μ/2[(dψ/dt)2 + v2*(dψ/dx)2]. I add them & integrate over ±∞. However, where does the f(w) come from. What does it have to do with f(x±vt)?