Sound is a wave that travels through the air that alternates between peaks (high points) and valleys (low points). The nature of waves is that when multiple of them are traveling though the air at the same time, their effects are added together to create a new wave. That’s why when you listen to two speakers playing the exact same music, it’s louder than if you were just listening to a single speaker.
The cool thing about this is just like how you can add two identical waves together to create something louder, you can add two waves that are the exact opposite of each other together and they’ll cancel each other out. Noise cancelling headphones have microphones in them that listen for the sound waves traveling to your ear, then the headphones instantly create the inverse of that wave (so that the peaks become valleys and the valleys become peaks) and they play the resulting inverse wave through your headphones. The result is that you have two sound waves hitting your ear at the same time (the original sound from your surroundings and that inverse from the headphones), they cancel each other out, and you effectively hear nothing as a result.
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