Why does movement in waves produce harmonics?

[Sea Cow]

Why do strings, etc vibrate in harmonics?

Is it a characteristic of all waves, a consequence of the way energy propagates along a wave? If so, how?

 

[netheril96]

That's just a mathematical way to deal with arbitrary waves called Fourier decomposition

 

[Sea Cow]

But harmonics aren't arbitrary, are they?

 

[eddiemon]

That's just a mathematical way to deal with arbitrary waves called Fourier decomposition

I have to disagree. Harmonics in standing waves is a very real physical phenomena. It is NOT an arbitrary mathematical description.

To answer the OP's question, I think the answer is related to resonance. If you've taken differential equations: Say you have a system that can be described using a non-homogenous second order differential equation for example, and the natural solutions are periodic. If your forcing function is periodic, and the frequency is equal to or is an integer multiple of the natural period, the resulting solution has a larger amplitude. This is called resonance.

If you haven't taken differential equations, you will have to take my word for it, that often a system will have a frequency that if oscillates most naturally. Then oscillations with frequencies that are integer multiples of this "natural" frequency will be more sustainable in the system. For example, if you have a guitar string and you pick the string at t=0, you will be giving the string all sorts of frequencies to begin with, but after a relatively short time, only the harmonic frequencies (including the fundamental frequency of course) will survive. (These harmonic frequencies also correspond to the standing wave solutions.)

I think you should be able to obtain harmonics in the oscillation of water waves by creating 2d standing waves, e.g. water in a round bowl.

Hope this helps

 

[Sea Cow]

Thanks eddiemon. Yes, it did help.:)