Comment by Tade0

Regular alarm sounds already do that, because above 1kHz or so it's the cushioning in the device that does the majority of the cancelling. There's a dip in effectiveness before that because to cancel noise effectively it's best to have a latency lower than a quarter of the wave's period.

Also ANC works best on wide-spectrum sounds, so any kind of siren or the cries of a child will go through, as the spectrum is a series of narrow peaks.