Re: About Harmonics
- From: Terry Given <my_name@xxxxxxxx>
- Date: Fri, 27 May 2005 17:57:12 +1200
Rich Grise wrote:
On Mon, 23 May 2005 11:27:28 -0700, Jack// ani wrote:
How is harmonics generated? Why are they integral multiple of the fundamental frequency?
The way I understand it, the harmonics are generated by different vibration modes of the string happening simultaneously. In this case, they're called "overtones". The same thing happens with an air column in a woodwind, and so on.
Why they occur in electronic stuff like oscillators and amplifiers
is because of nonlinearities that "distort" the signal, and make it
be something other than a pure sine wave. If you put a pure sine
wave through a speaker, it's a very boring sound, like, "oooooooo....".
The overtones, or harmonics, give it tone coloring, or timbre, like "eeeeeee" or "ahhhhhh" and so on. Say "errrr" into a mic on a
spectrum analyzer sometime, and I can guar-awn-tee that you will be surprised.
I can't answer "why are they ..." any more than I can answer, "why is the sky blue?". They just are. It probably has something to do with phase relationships and Laplace transforms and Fourier transforms and heavy arithmetical stuff like that. But suffice it to say, when a signal is distorted, the distortion can be seen on a spectrum analyzer as other frequencies that just plain happen to be integral multiples of the fundamental.
Maybe it's just that the ones at integral multiples don't get cancelled
out with the ones that _aren't_ integral multiples, but that's just as much of a non-answer as saying "The sky is blue because it isn't red."
Hope this helps!
read "the cuckoos egg" by Clifford Stoll. Apparently the sky is blue because of a PhD thesis involving dipole moments.
Cheers Terry .