In the past, we've discussed questions of energy and momentum
transfer for waves on a string. (Try typing "Benumof" into the PHYS-L
archive searcher for example.)
Anyhow, there's a recent Letter paper by Burko in Eur. J. Phys.
31:L71 (2010) claiming the usual textbook formula for energy of a
string wave is wrong. The gist is that instead of the square of dy/dx
in the PE term, one should have y * second deriv. of y w.r.t. x.