What happens to the energy of two waves when destructive interference occurs?

Answer

This is a typical example of a ‘false’ problem, where the question suggests the (wrong) answer. If two (coherent) waves coincide in space, the amplitudes are added. If they are in opposite phase, one wave will compensate for the other and there will be nothing left.

The question suggests that the energies of the two waves would be addable, ie that each source would produce the same energy regardless of the presence of the other source. That is not true.

When you switch on a (single) source, it does work on the environment because the membrane pushes and pulls on the air molecules. If you switch on a source while a second source is working in opposite phase, the air will already move along with the membrane. The source no longer succeeds in providing work on the environment and the radiated power is … zero and the same applies to the first source.

This is what elaborated in the attached publication.

(don’t tell that ir student directly, let him look for something, that’s his job)