[Destructive Interference](https://en.wikipedia.org/wiki/Wave_interference). Sound waves are pressure waves in a medium. As waves obey the [superposition principle](https://en.wikipedia.org/wiki/Superposition_principle) – that is, the amplitudes of waves add arithmetically – we can create a second wave with opposing amplitudes, thereby canceling out the original wave.
Noise canceling headphones have microphones that measure incoming sound waves and create artificial sound waves canceling out the the incoming waves in the area around your ear.
Imagine a tug of war, with a long stick (instead of rope) with a ribbon tied in the center to see movement. Each side can push or pull. Lets say left side is pushing, right is also pushing, making the ribbon stand still. Same with pull, if other side is countering the same force, the ribbon in the center does not move. For an observer, ribbon stands still.
So that ribbon barely moving is sound wave, by doing a counter wave(cancel wave), you stopped it.
This is what i told my kids when they were five. There were a few digressions for some of the vocabulary like “membrane”. I mentioned “destructive interference” to them, but only in passing.
Sound is the action of waves of motion in the air or other things around you. When someone talks, their throat releases little puffs of air by turning airflow on and off really fast. Each little puff of air goes out their mouth. The air that is already there has to get out of the way. But then that air has to go somewhere, which makes some more air get out of the way … all the way to your ear. The last bit of air pushes slightly against your eardrum and moves it a little. Pushing your eardrum back and forth makes you hear sound.
The sound pushes on everything else too. If you cover your ears you can still hear sound. That’s because sound waves from around you push on the outer layer of your hand, which pushes on the middle of your hand, which pushes on the part of your hand over your ear. So some of the sound gets through.
Headphones work by pushing back and forth on the air right next to your ear, which shakes your eardrum without shaking the surrounding air very much (because they’re so small). There’s a little membrane (sort of the size and shape of your eardrum, actually) that gets shaken back and forth by the electronics in the headphone.
Noise canceling headphones work by actively measuring how much sound is getting through — in early ones, there’s a little microphone on the inside that measures the sound right next to your ear canal. Newer noise canceling headphones use clever electronics to measure the sound using the same membrane that makes the headphones’ sound.
The headphones can push the membrane around really fast, so they push it in the opposite direction from whatever sound they detect in there. Some people like to say that causes “destructive interference”, which is a pair of really big words you’ll learn later. Other folks like to say that it makes the headphones act like a near-perfect strong wall that doesn’t move when sound hits it (or even moves *against* the sound to make u for sound that leaks around the headphones).
The reason you can’t have noise canceling loudspeakers is that the noise canceling effect only works over a very small region. The region has to be small compared to the length of the sound waves. High pitched sound waves are about the size of a whistle, so you can’t cancel sound easily in a space much bigger than that.
Fortunately, the inside of your ear would totally fit inside a whistle — so it’s small enough for the noise canceling headphones to work.
Noise canceling headphones play music into your ears a really interesting way. They’re using something called “feedback” to measure how to push the membrane around. The headphone senses the pressure near your ear, and adjusts the membrane to keep it constant (blocking out sound). That is called “feedback” because the headphone *feeds* the measurement *back* into its membrane. To play music or something, you inject a fake signal into the feedback device, and the headphones compensate for it. As far as the headphone knows, it’s keeping your ear as silent as possible. But you’re messing with its senses, telling it there’s “anti-music” coming in. It compensates by generating music to try and block the anti-music. Since the anti-music isn’t real, you hear the music in your ear.
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