In the case of the sound cancelling headphones, so called "experts" blindly claim the energy is converted to heat and dissipated, but this is not the case.
When conducting similar tests on waves through other mediums such as water or light the heat generated comes no where near the amount of...
Bose sound cancellation head phones are a great example of using energy to cancel out unwanted waves.
I've demonstrated this personally in a wave tank full if water and seen it demonstrated with an interferometer.
The energy of the canceled photons could become bosons or quarks or some other type of tiny particles. But a similar experiment in water waves illustrates that the waves can be canceled out complely by adding additional energy to a wave to completely eliminate it.
I've seen a polarized beam of coherent light split and recombined out of phase and canceled out without constructive interference.
Physisists like to cling to the notion that energy can't be destroyed because if not they would have to admit it could be created and everything we "know" might be...