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You can cancel out noise by making the "opposite" noise in one specific point, like one eardrum, but not over a whole area.

ANC/R works by sending out the opposite waveform of the noise, at about the same volume. It does not remove noise.

Passive noise control through insulation is the best solution for residential buildings.

I have long wanted to investigate advanced methods of reducing noise transmission between rooms; it seems to me that's a area that will clearly need improvement if we really expect cities of the future to be towers and condos instead of standalone houses. But you're correct that whatever solution does exist won't look / act like noise-canceling headphones.

I think that's an area that would benefit less from investigating and more from acting. But for some reason people think a room that's 20cm wider is "better" than one with sound-proofed walls.

You build the wall, you put in insulation, sand, water, glue and stick ceramic tiles on it. That could be a sound-insulating step two, but, you know. Has to be built that way.