Why sine wave is the natural wave, why not something else?
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The main way a sine wave is usually defined is that it’s what you get when you measure the height of a point as it travels around the edge of a circle. However, there is another way to get a sine wave:
A sine wave is the pattern of motion you get when you dangle an object from the end of a spring and it bounces up and down.
The force that the spring exerts on the object is linearly proportional to the distance that the spring has been stretched, (AKA the longer the spring stretches the harder it pulls) and that’s really the only thing going on here. A sine wave naturally emerges whenever you have a system where a parameter’s acceleration is inversely linearly proportional to its distance from some equilibrium value (inversely because the pull is back towards the center). In other words, the only requirement for a sine wave is you have some system that pulls some parameter towards a resting value and pulls harder the further away that parameter is.
That’s really not an uncommon scenario, so it pops up literally everywhere in nature from electromagnetic waves to sound waves to chemical reactions.
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