It does seem that energy just kind of disappears here, doesn't it? I mean, an audio wave traveling through air has a certain amount of energy associated with it. If you expend even more energy to launch another wave 180 out of phase, you now have twice as much energy traveling through the air, but the energy is indetectable. Where did it go?
Anyone?
From a practical perspective, yes, it's good for the ears. The eardrum converts the incoming pressure waves to mechanical motion; if portions of the incoming wave are cancelled, the eardrum will move less, reducing damage to the inner ear.
From what I've heard, the noise-cancelling headsets work best for noise sources that have significant discrete frequencies - for example, a private prop plane has most of it's noise at stationary frequencies related to the current RPM of the engine. The headsets can filter that out OK. For something like a vacuum, where most of the noise may be essentially "white noise", they don't tend to work very well.
BTW, be a good kid and mow your mom's grass for her.
/frank
