you can observe standing wave in the form of skipping rope as zarathustra... also, u can pluck a guitar string... the wave it is forming is a standing wave... the energy transfers from kinetic (maximum movement of the string) to PE(when the string has being stretched the furthest) continuously...
as regard to de broglie's proposal that electron exist as standing waves around a nucleous - if that's the case, then the total energy of the electron is not lost, but rather transfered from KE to PE and back continuously...
this explains one of the limitations of bohr's model of atoms, that if a charged particle is travelling, it must emit EMR, hence lose energy... hence spiral into nucleous...