Active, passive, pass-through: how do noise-cancelling headphones do it?

Active noise-cancelling headphones: undoubtedly one of the breakthrough audio features in consumer headphones since the turn of the century. 

Pioneered by Bose and Sennheiser, active noise-cancelling (ANC) is now found in wired and wireless headphones, from the tiny, true wireless Sony WF-1000XM3 and AirPods Pro, to the over-ear Sennheiser Momentum Wireless and Bose Noise Cancelling Headphones 700. And it’s a splendid piece of tech. Done well, it’s the cherry on top of the wireless headphone sundae.

Some wireless noise-cancelling headphones now offer levels of noise cancellation (not just ‘on’ or ‘off’) and even pass-through or ‘ambient aware’ toggles, to filter specific sounds like speech into your ears once you’re done shutting the world out. 
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https://www.whathifi.com/advice/how-things-work-active-noise-cancelling-headphones