"Resonance occurs when two sources of excitation fall completely in sync, and reinforce one another endlessly."

This is incorrect, even according to the wikipedia article it links to.

Resonance occurs when the excitation frequency matches a natural frequency of the system being excited, causing it to vibrate at larger amplitudes, even perhaps uncontrollably.

It seems that the author misunderstands mixing also - the graph that he presents for the mixed signal seems to be incorrect according to the other wikipedia article he links to.