Why sine wave is the natural wave, why not something else?
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It so happens that things that repeat in a pattern do so in simple ways or can be decomposed into the summation of simpler patterns. One of the simplest ways of oscillating (i.e. “waving”) can be represented by some value going up and down at a particular rate of repetition. This simple way is also smooth and not erratic (see sawtooth waves). Physical phenomenon tend to be smooth and continuous. It’s therefore easier to use simple and smooth things *to model* physical phenomenon bc they represent reality well when we use them. They are also amazing to work with mathematically and have properties that make it *a lot* better to deal with algebraically.
So really, we have this mathematical object that we call the sine wave and it is perhaps deemed “natural” because it helps in describing so many things. This choice arose mostly out of natural selection bc it’s so simple and useful when we connect the abstract mathematical world to the physical one. We could equivalently use any other periodic function that has similar properties to do the same thing – it so happens that the sine wave is one of the simplest bases to work off of.
I’ll also add that very few things in nature are a single sine wave. Periodic phenomenon, or anything wave-like, are usually better represented as a summation of them, where each individual sine component can have a separate frequency and/or amplitude.
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