A noisy flight can make it difficult to enjoy a podcast or listen to music without turning up your volume super high.

Much of that disturbance comes from the steady rumble of the engines, which continues throughout the journey. Noise-cancelling headphones can reduce this background noise, making your listening experience more comfortable without requiring the surrounding environment to become any quieter.

This is possible because these headphones do more than physically cover your ears. They use microphones to capture surrounding sounds, electronic circuits to process the signals, and speakers to produce additional sound waves that counteract some of the incoming noise. The process happens continuously, allowing the headphones to respond to changes in the sound around you.

But how can one sound reduce another and how do headphones calculate the right signal quickly enough to make it work?…