Yea so basically it has microphones that listen to what you are hearing right now, and then it sends the exact opposite of the sound wave to the speaker, so for example if the sound you are hearing has a frequency (pitch) of 500hz at an amplitude (loudness) of 30db it would send a signal of 500hz at -30db (so basically the same sound wave but flipped) to the speaker, where the two waves collide and cancel out (destroy) eachother (this is why it is called noise cancelling), and this is also why bad implementations of it can cause a high pressure in your ear, making you feel uncomfortable, yes it will drain the battery considerably
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