Why sine wave is the natural wave, why not something else?
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Most math describes the natural world. A sine wave is the natural response to an object in this universe to a perturbation. If I have a ball hanging from a string and I raise the ball and let it go, we all know, the ball will swing. This is what we observe from every ball and string no matter where we are in this universe. This of course assumes gravity is a constant. The value (y) of the sine function is the velocity of the ball at the position (x). At the top and bottom of the sine wave (maxima and minima) the velocity is zero. If there was no friction from the air or the string, the ball would swing for a very, very long time.
Walter Lewin MIT 802 does a great demo, 802 is a great physics class, it’s worth watching.
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