Why is the AC in our homes a sine wave out of all math functions ??

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Why did they choose to make AC change in time based on a sin wave and not any other math function like quadratic or logarithmic

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Think about a ball on a stick. You want to move the ball on the stick from the top to the bottom and the back. There is no way to get the ball from top to bottom, and back up, instantly – it takes time. If you move the ball up and down at a constant speed, and you plot the points the ball is on that pole on a graph with the y axis being location and the x axis being the time it was at that location, guess what you have – something that looks like a sine wave!

Other types of waves are frequencies combined together (we call it convolution). A square wave, for instance, is just a bunch of sine waves placed on top of each other. If you had very sensitive equipment and zoomed in n on that wave, you’d see that a square wave isn’t actually square – it’s very close, especially with high end equipment, but it’s not.

Now, why AC in general? It’s very easy to change the voltage of alternating current without losing much power at all – you just need a transformer, and the electromagnetic fields induced by coiled up wires will allow you to transfer that power to another set of coils, and you can change the voltage by changing amount of coils on that wire on the secondary coil. DC requires something called a switching converter to change its voltage without losing much power – it’s an active, powered converter that can fail much more easily than a transformer.

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