Mummy, where do harmonics come from?

• Nit Wit
In summary, the conversation is discussing the phenomenon of picking up multiple frequencies using an antenna when a square wave is applied to a purely resistive load. The explanation involves Fourier analysis and the use of sine functions as a basis for expanding the signal. This can result in the observation of harmonics, which can be seen on a spectrum analyzer, but the underlying reason is due to the mathematical representation and choice of basis functions.
Nit Wit
Right, I'm new to this forum but not new to asking daft questions. So here we go.

Just Imagine I'm sat in my shed and I've got a battery hooked up to a purely resistive load with a switch between the two. In adition I've set up a tuneable antenna in close proximity.

If I turn the switch on and off dead fast I'm able to use the antenna to pick up a signal at not only the fundamental frequency but at integer multiples of the fundamental, why?

I know about the theory of Fourier analysis, I'm not interested in that, what I'm interested in where these checky little sinewaves come from when the only thing you're applying is a single square wave.

Is applying a burst of voltage to the electrons in a conductor akin to what goes on inside a guitar string when you twang it?

I've trawled the net for an answer and so far found Fourier all!

So, if I understand this, you're applying a square wave. You don't want to represent that square wave using Fourier series. You want to know why there are sine waves at multiple frequencies. Is this correct?

Here's a quote from Fourier to help:

"The profound study of nature is the most fertile source of mathematical discoveries."

yes please, but I'm a bear of very little brain so keep it simplish if possible.

The integer multiples of the frequency are harmonics, and because you're effectively producing a standing wave in the antenna, that wave can be at any of the given harmonics. Why, because at any other frequency, you won't get a standing wave. I don't know too much about the rest but applying a burst of voltage will produce an EM wave according to Maxwell's equations (in the same way applying a burst of movement to a guitar string would create a sound wave). Why it comes out sinusoidal is beyond me.

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me too, but that's the nugget of info I'm after

But it isn't really "sinusoidal" if it is a square pulse.
The mere fact that you are referring to harmonics means that you are implicitly expanding the waveform using a Fourier theory. Moroever, you are doing using a basis of sine functions. If you expand something in a sine basis you will obviously end up describing your signal as the sum of sines.
There is nothing stopping from using another basis and then your "harmonics" (with a weight which would then use be the prefactors for higher order terms in the expansion) would be different.

We are so used to expanding waveforms using a basis of sine functions that it is easy to forget that this is just a mathematical "trick"; sine functions are used since they are convinent but there are an infinite number of other basis you could use instead.

But harmonics are real, observable and an industry exists based upon eradicating them from the electrical supplies to equipment!

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Nit Wit said:
But harmonics are real, observable and an industry exists based upon eradicating them from the electrical supplies to equipment!

Depends on what you mean by "real". True, if you look at the signal on a spectrum analyzer you will see peaks at frequencies that are multiples of the fundamental.

But -and this is the important bit- what is REALLY happening is that the spectrum analyzer takes the signal and then performs a Fourier transform using a sine functions as a basis; hence if the signal is non-sinusoidal you will end up with a spectrum that contains harmonics for the simple reason that the expansion will contain more than one term. If the spectrum analyzer used another function as a basis the spectrum would not looks the same.

Now, the reason why we tend to use sines in signal analysis (but not always! Wavelets are quite popular nowadays and do NOT use sines as basis functions) is mainly because many things in nature -including the mechanisms we use to generate electricity (which usually involves an axis rotating in e.g. a turbine) are sinusoidal.
But there are plenty of phenomena that are NOT sinusoidal and in some ways we are therefore really trying to push a square peg into a round hole when we try to describe them as a sum of sines.

What are harmonics?

Harmonics are the frequencies that are produced when an object vibrates at a certain frequency. They are multiples of the fundamental frequency and are responsible for the unique sounds of different musical instruments.

How are harmonics created?

Harmonics are created when an object vibrates at a certain frequency, resulting in the generation of multiple frequencies at different amplitudes. These frequencies are called harmonics and are responsible for the unique sound of different objects.

Do all objects produce harmonics?

Yes, all objects produce harmonics when they vibrate at a certain frequency. However, the amplitude and strength of these harmonics vary depending on the object's material, shape, and size.

Can harmonics be controlled?

Yes, harmonics can be controlled by manipulating the object's physical properties such as material, shape, and size. This is why different musical instruments produce different harmonics and have unique sounds.

What is the significance of harmonics in science?

Harmonics play a crucial role in many scientific fields, including acoustics, physics, and engineering. They help us understand the properties of different materials and objects and have various practical applications, such as in music and telecommunications.

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