When acoustic or electromagnetic waves cancel by destructive interference, the wave impedance reflected to the sources of the wave energy changes so that the input power is reduced correspondingly. Because this rather subtle point is not discussed in most instructional treatments of wave physics, misconceptions concerning the apparently ’’missing’’ energy are widespread, as reflected in semipopular science writing. This paper presents an analysis of the cases of destructive and constructive wave interference, and analogous problems for lumped electrical and mechanical systems.