Energy and Power
it takes energy to set up a wave on a stretched string y(x,t)=ym sin( kx- ?t)
the wave transports the energy both as kinetic energy and elastic potential energy
an element of length dx of the string has mass dm = ?dx
this element (at some pt x) moves up and down with varying velocity u = dy/dt (keep x fixed!)
this element has kinetic energy dK=(1/2)(dm)u2
u is maximum as element moves through y=0