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

154 views

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

In: Physics

Spinning generators produce a sine wave naturally. It’s hard to explain in words but simple if you get a picture of a generator.

That’s the only thing that oscillates, i.e. goes back and forth between two values.

Literally everything that does that can be modelled with sine waves. Some are complicated, really complicated, but at the end of the day it’s all sine waves (even cosine waves are just sine waves that showed up to work late).

So it’s less that they chose to make it a sin wave and more they chose to make it oscillate.

You also mention “[why] not any other math function like quadratic or logarithmic”

A quadratic function grows faster and faster with time and logarithmic equations grow slower and slower with time. but both of them Keep growing forever eventually reaching infinity.

I assume it’s clear why voltage can’t increase over time and go to infinity.

Its the shape a circle makes when it rolls/spins if you follow 1 point on the circumference.

And our generators are big coiled, circles of wire, which spin.

AC electricity is generated by spinning a generator. [Sin waves are linked to circular motion](https://i.stack.imgur.com/pQ377.gif).

So the AC coming out of a spinning generator is naturally a sin wave.

Now AC doesn’t *have* to be a sin wave, cheap DC to AC converters use a square wave but the sudden change from positive to negative tends to cause transformers in electronics to make a buzzing sound that you don’t get from a smooth sin wave.

It’s not necessarily. It’s can be a square wave, a triangular wave, or a sinusoidal wave, depending on where you live.

What’s necessary to be AC is that it oscillates back and forth.

A sinusoid is the natural form of an oscilation because it’s the smoothest transition back and forth between two maximums.

Take a circle, track the vertical (or horizontal) position of a point on that circle over time, and you will get a sinusoid.

When you look at how quickly the value of a sine wave changes, you’ll notice that this is also a sine wave. This simple fact makes sine waves natural for electricity in a ton of ways.

The first thing we noticed about it was that, since the change is also a sine wave, passing a sine wave through a transformer produced another sine wave. There are a lot of transformers between your power company and your home, so this alone is a big deal.

More broadly, in differential equations (big hard math problems that involve change over time) a single sine wave behaves very nicely. Stacking multiple sine waves on top of eachother also behaves very nicely. If we analyze *any*thing as a stack of sine waves, we can look at each sine wave separately, and this property makes sine waves the “just one single piece” of signal processing.

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.