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Nope.
So what you hear as frequency is the variation of pressure- hi-low-hi-low-hi-low, right?
We tend to visualize it as a line going up and down, etc, but that’s just a conceptual aid.
To “cancel” noise, it plays a tone whose high and low pressure is out of phase but otherwise identical. So instead of hi-low-hi-low, it plays low-hi-low-hi noise, and you don’t “hear” it.
Great for tuning out the noise of a jet engine, and the loser who keeps trying to talk to you while you’re stuck in a tin can with a bunch of other sardines for 10+hours.
But that pressure is still there pushing against your eardrum, and no matter how good the pick up and driver is for the ANC, it’s never going to perfectly match noise anyhow.
There’s a reason most ANC ear cans are closed back- the passive noise isolation reduces the amount of work they have to do.
I believe, you've got some big misunderstanding in that. The wave is the variation in pressure. It doesn't exert pressure beyond that. There is general air pressure, but that is always there, whether you've got a wave going or not.
Maybe it helps you understand it logically to think of how a speaker membrane moves. It does this motion:
So, when it bulges to the right, it pushes air molecules closer together, which locally increases pressure on the right and continues to travel to the right, because the molecules push each other.
Then the membrane bulges to the left, which locally reduces pressure on the right and continues to travel to the right, because the molecules make room for each other, so the general air pressure causes air molecules to fill that room back in.
Both of those travel at the same speed, so they reach your eardrum, which is just another membrane and therefore does the same motion that the speaker membrane did.
So, a speaker is like a Newton's Cradle, it doesn't actually cause the molecules on the way to traverse across the room, like a fan would.
This may only be within the range of human hearing, and you can and do still suffer damage from excessive amplitude by frequencies above and below what is human detectable. ANC is not a protective technology for this reason, it is a quality of life technology.
So what you're telling me is, i should really be wearing hearing protection when i go underwater? All that pressure must be wreaking havoc on my hearing.