How do noise cancelling headphones work?

After asking myself this question, I decided to look it up in youtube to receive the answers only to find James May (Top Gear) has a done a video to answer this question. Whilst listenting to the soft/easy calming sound of May’s voice which nearly put me to sleep. He said that sound is just “compression and rarefaction of the air around you” and that noise cancelling headphones are more useful when their are continuos sounds around you, rather than abrupt sounds. Also states that the best passive noise-canceling headphones, are circumaural types that are specially constructed to maximise noise-filtering properties. That means they are packed with layers of high-density foam or other sound-absorbing material, which makes them heavier than normal headphones. The tradeoff of all that extra weight is a reduction in noise of about 15 to 20 decibels (dB). But considering jet engines create 75 to 80 dB of noise inside the aircraft cabin, passive models have some serious limitations. That’s where active noise-canceling headphones come in.

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