You are correct. It is two waves canceling each other out.
If you imagine the sound wave as a shape that is flying towards you the noise cancellers generate the anti-shape one that when slammed together turns it into a flat line. (This is an oversimplification but enough)
It does this by using a microphone to pickup sound and play the inverse near instantaneously so they hit your ear at the same moment.
It is not perfect of course. But pretty amazing tech that requires well tuned components.
I don’t know if any headphones do it purely analog but theoretically it should be possible.
Heck you might be able to make a very crude version from off the shelf audio equipment and a custom circuit to make a speaker do active cancelling.
1. You can produce a specific sound wave that cancels out another sound wave at a specific point in space.
2. Electric signals travel faster in wires than sound waves in the air.
With #1, you can cancel out background noise in the environment IF you know what the noise is. With #2, you have enough time to detect and process the noise information before it arrives at your ear (by having microphones a small distance away from your ears).
Sound is a wave of high and low pressure, kind of like [this](https://www.flippingphysics.com/uploads/2/1/1/0/21103672/0327-animated-gif-6_2.gif). Noise cancelling headphones have a microphone that listens to the incoming sound and then makes an opposite sound: high pressure where the incoming sound has low pressure and low pressure where it has high pressure. The low pressure plus the high pressure equals no pressure (other than the undisturbed air pressure).
To play some music or a podcast on top of the noise cancellation it just adds that wave to the noise-cancelling one and plays the sum of the two.
[from 2 weeks ago:](https://www.reddit.com/r/explainlikeimfive/comments/1euodf3/eli5_how_do_noise_canceling_headphones_work/)
“Basically they listen to the world through microphones and add the opposite sounds to the music you listen to. If the sound is +1 the headphones add -1, which results in 0, or no sound. They can’t perfectly capture the sounds in the world, so they can’t perfectly negate them. You also hear sound through your skull and even mouth, and the headphones can’t negate that either. This why they can’t eliminate all sound, but they do make a substantial difference.”
If you hear two sound waves hit the same air, they add their waves together.
If you had two identical waves and they were in sync (both go “up” and “down” across the line at the same times) then playing them at the same time would make it sound like the same thing but twice as loud.
But if the second wave was exactly like the first wave *except* it was mirrored (it goes down when the other goes up), then adding them together would mean the second *subtracts* from the first and instead of sounding twice as loud it would just subtract to zero and be silent.
A noise cancelling headphone is designed to do that. It has a microphone that listens to the sound wave in the outside air that’s about to hit your ear, then it plays an inverted version of that same sound wave in its speakers, but at a lesser volume so it doesn’t completely null out the sound, but just subtracts *some* volume from it.
So the actual anti wave pattern headphones have been explained but there is also a simpler type of noise reduction headphone. It used for shooting ranges and in really loud work environments. Basically they are high noise reduction headphones. But they have microphones and speakers. So with the mics off, they block most sound. With the mics on, they pass through any sounds the mics pick up. They can even amplify it, but what they also do is that if a very loud sound, like gun fire, is picked up by the mic.. it either cuts off the mic for the time that the noise is made OR it simply passes the noise through, but at lower volume.
These are great at the range. You can hear people talking but gunshots are muffled.
I’m pissed off about this. In high school (40 years ago, I’m old) my science teacher drew sines waves on the blackboard and showed us how multiple waves can add together to make complex sound. I looked at it and asked ‘why can’t you have a microphone listen and play back the exact opposite to cancel it out and make a “Cone of Silence” like in Get Smart?’ (a tv show with spy gadgets). The teacher said it wouldn’t work and wouldn’t explain why not. Decades later they come out with noise-cancelling headphones that do exactly what I had imagined.
Oh, well. Maybe I’ll have more luck with Glow-In-The-Dark-Pizza.
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