[ars]

You would need a latency of something like 0.01ms or even less.

If I remember right such a low latency is basically impossible, so sound canceling headphones have to try to predict the sound before it happens.

There are large problems with simply the speed of sound - you don't really have time to emit the new sound, and if you move the mic farther from the speaker you don't accurately match the sound, and can make things worse.

That's why the headphones use fancy algorithms to try to guess what the sound will be, and that's why good ones cost so much, instead them being a simple analog circuit.

[brokenmachine]

I would imagine that the physical inertia of the speaker would also be a factor.

Opamps can respond that quickly electrically, but you need more power the faster you want to move the speaker cone.

Say the mic is 5mm from the speaker. Sound travels at 340m/s. so 0.005/340=0.00001471s. So it takes 14.71 microseconds for the sound wave to travel that 5mm. That sounds awfully quick to have to reactively move a speaker cone accurately. Obviously speakers can move quickly enough to play at the correct frequencies but I don't know what their latency would be.

I'm sure there are other complications that I'm forgetting but it's definitely harder than you would think to cancel out sounds.