[mdp2021]

Active noise cancelling is placing between ears and source an inverted wave generator.

A soundwave is coming, you intake it with a microphone and attempt producing its inversion in real time in speakers, to cancel it.

As I have written, it may not work properly with impactive noise - it can do the opposite, because the impactive sound is cleaner. Or, it may be calibrated for impactive noise - so there exist earmuffs that recognize shooting sounds at their inception, to reduce these selectively.