Loudspeaker Phasing.

how does noise cancelling work, does it alter phasing?

In short its all about the phase, and the intention is to obtain an electronic copy of the unwanted noise via microphone, and gently adjust its amplitude and phase so that when you  play it back via loudspeakers, then  at the place your ears are it is exactly equal and opposite so the air is both pushed by the acoustic noise and pulled by the speaker and in the middle is an  oasis of calm where the air does not move so you hear neither. It works well for headphones where the position of the ear and therefore where the level of cancellation is needed is pretty much fixed. It is much harder in free space, and then really only works with low frequencies where the long wavelength means that the cancellation zone occupies a significant volume and you can tolerate a fair amount of spatial inaccuracy.

In theory cancellation can be perfect at all frequencies at one pin point in space, but we usually settle for a few cubic feet such as the cockpit of a plane, and a reduction that removes the top 10-20 dB or so to reduce pilot fatigue.

I variation on the technique is 'equalising' a building to compensate for frequency dependent acoustic reflections and absorption by deliberately abusing  the wave-forms  to loudspeakers to boost missing trebles or whatever, and give a good listening experience over as much of the audience as possible. In that case the area of near cancellation may be much bigger, but the set up is more complex.
There is no free lunch - this takes extra power, and adds extra noise in other places where there was none before - it will cancel in one place, though it may well add somewhere else usually on the other side of the speakers for a start.
Mike

how does noise cancelling work, does it alter phasing?

In short its all about the phase, and the intention is to obtain an electronic copy of the unwanted noise via microphone, and gently adjust its amplitude and phase so that when you  play it back via loudspeakers, then  at the place your ears are it is exactly equal and opposite so the air is both pushed by the acoustic noise and pulled by the speaker and in the middle is an  oasis of calm where the air does not move so you hear neither. It works well for headphones where the position of the ear and therefore where the level of cancellation is needed is pretty much fixed. It is much harder in free space, and then really only works with low frequencies where the long wavelength means that the cancellation zone occupies a significant volume and you can tolerate a fair amount of spatial inaccuracy.

In theory cancellation can be perfect at all frequencies at one pin point in space, but we usually settle for a few cubic feet such as the cockpit of a plane, and a reduction that removes the top 10-20 dB or so to reduce pilot fatigue.

I variation on the technique is 'equalising' a building to compensate for frequency dependent acoustic reflections and absorption by deliberately abusing  the wave-forms  to loudspeakers to boost missing trebles or whatever, and give a good listening experience over as much of the audience as possible. In that case the area of near cancellation may be much bigger, but the set up is more complex.
There is no free lunch - this takes extra power, and adds extra noise in other places where there was none before - it will cancel in one place, though it may well add somewhere else usually on the other side of the speakers for a start.
Mike