1. The problem statement, all variables and given/known data A standing wave is maintained in a homogenous string of cross-sectional area a and density [tex]\rho[/tex] . It is formed by the superposition of two waves travelling in opposite directions given by the equations y1 = Asin(wt-kx) y2 = 2Asin(wt +kx) Find the total mechanical energy confined between the section corresponding to the adjacent antinodes. 2. The attempt at a solution The wave is given by y = Asin(wt-kx) + 2Asin(wt +kx) KE of a small element is 1/2 u dx v^2 , where u = mass per unit length. I find v by differentiating y wrt t. Then I integrate with proper limits. But the integration looks outrageous looking at the simple answer. Is there any shortcut ? Also using above method we only get the KE, what about the PE?