Is Noise Cancelling Done Biologically?

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I've been wondering about the benefits of noise cancelling headphones. For those who aren't familiar with these devices, they essentially generate a sound wave that is $180^o$ out of phase with the low-frequency noise that is picked up by the microphones that are present in the headset.

For example, see the attached picture. If the noise waveform was the red sine wave, the waveform generated by the headphones would be the blue sine wave, and when added together, these waveforms cancel out, resulting in no sound. (Note this is an idealized view, in reality the headphones can't generate the "anti-noise" waveform immediately, resulting in an incomplete cancellation, which is perceived as a quiet hissing sound.)

However, my question is, is this addition of waveforms done in the air, or by one's ear?

The reason I ask is if the cancellation is done in the air, then no sound actually reaches one's ear, and thus the ear does no work. But, if and the summation is done inside one's ear, i.e. biologically, then the ear is working twice as hard as it has to, leading to the twice the damage that constant exposure to the noise would inflict.

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the head set has a speaker in it with a reasonably big diaphgram, the mic reads the level and runs it through an amplifier to get to the speakers. the result is a sound output almost out of phase and almost 100% cancelled. the head set is a full ear covering thing so the cancelling is done far before it reaches your ear.

they all give off a bunch of white noise and it's never 100% cancelled it's far reduced ambient noise plus a bit of static.

there's no real added strain on your ear, if a bomb went off, you'd get a peircing amount of static but it's far less than the noise itself.

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I would say yes, the mixing of the two signals takes place in the air between the speaker and your eardrum; the actual energy reaching your eardrum is reduced compared to the energy that would reach your ears if you had no headphones on. Of course, it doesn’t matter if you crank up the music.

If you get a frequency generator program and some mixing software, you can make a sine wave come out of the left channel and make its inverse come out of the right channel. If you put one speaker to each ear, if will sound normal, but if you face the speakers at each other, the sound you hear is reduced the closer the speakers get to each other. You will still hear some sound however, because some of it leaks out and isn’t cancelled.

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Even if it were done in the ear, which I'm taking Pleiades and Rocket Man's word for, it would not be "twice" that of the music in the headphones. It would be the music playing + 2 times the noise outside. So assuming there isn't all that much noise outside, the extra "damage" would be negligible.

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EXCELLENT QUESTIONS HERE. I have a friend who is an electronics whiz employing ten people in designing prototypes for the BIG like Motorola, whoever, and he is quite knowlegeable in theory of noise. I said, why can't we just add a trailing half-wave response to cancel what just came in? He said, you're too late. CHAOS IS HERE AND NOW and that's the point. So the limit of responding here and now is a few hundred Hertz. I figure I'd better learn something about chaos to talk about zero-point fluctuations and such.

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