Hi, friendsi! My text of physics, Gettys', shows how the energy, both kynetic and potential, of a small element ##\Delta x## of a string, through which a wave (whose wave function is ##y:\mathbb{R}^2\to\mathbb{R}##, ##(x,t)\mapsto y(x,t)##) runs, is:
##\Delta E=\Big[...