Creating a negative copy of the ambient noise - won't that increase the noise for everyone else? Say you live across the street from a neighbor who has this device. Street noise happens. It reaches you, and your neighbor's cancellation device, at roughly the same time. The device creates the cancellation wave, timed perfectly for the neighbor. That wave also propagates back toward you, and you hear it as an echo, with a delay corresponding to the width of the street.
Only as much as having a window that reflects sound waves almost-perfectly, like... a really thick pane of glass.
For what it's worth, since humans perceive sound logarithmically, a doubling sound of intensity feels like a constant (+3dB) increase of noisiness. This window would not even double sound intensity unless you're right next to it.
This and one of its sibling comments make a good point - maybe this would partially cancel the sound being reflected by the solid part of the wall. We can entertain the possibility, because we know sound in air generally reflects from a wall in the same phase in which it arrived. (If it was reversing itself we'd be in trouble again.)
Sound decays exponentially as a function of distance, so speakers close to you don't need to be loud. Also most speakers are also fairly directional, so i'd expect any extra energy to be absorbed by the room (as heat).
Edit: more importantly these are destructive waves, so if anything you’d actually reduce reflections back out into the world.
quadratically (proportional to x^2, the surface of an expanding sphere) as opposed to cubically (x^3, the volume of an expanding sphere) or exponentially (2^x, objects that multiply over time)
If the speakers (or their combined phased-array effect) are directional, you can project antinoise with different effects in each direction.
So for the person inside the apartment it sounds like a wall in the way, attenuating sound from outside, but for the neighbour across the street, it sounds like a hole absorbing the sound instead of reflecting it like a wall.
With enough points in a directional array it starts to resemble an acoustic hologram, with some remarkable one-way properties.
If you wanted to go really far with this, you could cover the exterior walls of buildings with dense arrays, and it would dampen street sounds for everyone in the neighbourhood, indoors and outdoors. In the street it would sound a bit like there were no buildings either side to reflect sounds back into the street, yet at the same time the buildings would still block sound from neighbouring streets.
I am suddenly day dreaming of a button you can press so that walking through a city sounds like walking through a forested valley on a windless day, as steady snowfall deadens all the sounds around you.
In high school like twenty years ago, we actually did a simple experiment demonstrating sound cancellation like this with simply speakers facing each other with polarity reversed. That surprisingly works well enough to definitely notice it working, when you are positioned in the right place, which is pretty cool.
It also works well enough to see it doesn't really do what you are describing. The energy from negative copy sound waves is being used to cancel out the original sound waves, the better it's working the less energy there is going to sound waves "escaping" to be heard anywhere else.
If the two speakers were any closer to each other than say 80 feet or 25m (which is roughly how far sound travels in 0.1 second), I wouldn't expect you to have heard the effect I'm describing. There would have to be enough distance between the "source" and the "canceller" to throw off the timing.
