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Math In The Real World

Image result for headphones clipart
Image result for headphones clipart
Noise Cancelling Headphones
Image result for headphones clipart



What is sound?

Sound is produced when something vibrates. Anybody have any examples of something that vibrates to create sound?
How about guitar strings, a metal bell, speakers?
When one of these vibrates it knocks the molecules in the air back and forth. Those molecules bump into the molecules next to them, which bump into more molecules, etc, until those molecules bump something in our ears. If you were to visualize this bumping, you could draw something like this:
Loudspeaker and Waveform
This is called a wave. The top of the wave is when the molecules were pushed forward, and the bottom of the wave is when the item was vibrating away from your direction. Notice how the wave repeats itself again and again? That's why a sound lasts more than a split second. Even when we are talking and the words are changing, each sound is repeated many times in a wave before it changes to a new sound.
Anybody have an idea of how noise cancelling headphones might work?
If you want to get rid of the noise, you might want to figure out a way to cut off the tops of all the waves, for example. All headphones do this! The over-the-ear headphones are better at this than earbud headphones. They are big because that helps block the high frequency sounds.
High frequency means that the waves look like this:
image.png
Low frequency waves look like this:
image.png
Low frequency waves travel through headphones better than high frequency though, so scientists needed a new way to cancel that noise. The way they did it takes advantage of a very interesting property of waves. If you take two waves that look like this and combine them you get this:
image.png

This is called reinforcement. The peaks of the waves line up and the bottoms line up, making each seem stronger than before. But what happens if you line up the peaks of one wave with the bottoms of the other wave like this:
image.png
They actually end up cancelling each other out! When we're talking about sound, this makes the sound disappear. Noise cancelling headphones have a circuit (though usually not a computer) that samples the low frequency waves and outputs an offsetting wave. No more annoying background noise so you can enjoy your music!

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