Re: [Phys-l] Harmonics vs Overtones

[Tom Sandin <sandint@ncat.edu>]

You are correct for the simple one-dimensional cases we talk about in 
introductory courses.

I apologize to my students for the two vocabularies, but say we learn 
about both because both are in common use.

The harmonic description is simplest. In our equations for allowed 
wavelengths and frequencies, the integer n is the harmonic number: n 
= 1 is the first harmonic, n = 2 is the second harmonic, and so on.

In the fundamental-overtone description, n = 1 gives the simplest 
pattern of node(s) and antinode(s), the fundamental (lowest) 
frequency, and the longest wavelength. Then the tones over that 
fundamental frequency are called the overtones and so on.

I like to point out that the wavelengths and frequencies are 
quantized (have certain allowed values) to lead to some simple ideas 
of quantum (wave) mechanics.

Tom Sandin


At 9:17 AM -0400 4/1/09, <Tim.Odonnell@CelinaSchools.org> wrote:
> Would people like to elucidate on the difference between harmonics
> vs overtones?
> My current thinking:
> For a closed tube there can only be odd harmonics (1st - the
> fundamental, 3rd, 5th, 7th, etc.), but the overtones are (1st = 3rd
> harmonic, 2nd = 5th harmonic, 3rd = 7th harmonic, etc.)
>
> For open tubes and string instruments there can be all harmonics
> (1st - the fundamental, 2nd, 3rd, 4th, etc.) and for the overtones (1st
> = 2nd harmonic, 2nd = 3th harmonic, 3rd = 4th harmonic, etc.)Tim
> O'Donnell
> Instructor of Physics and Chemistry
> Celina High School
> 715 East Wayne Street
> Celina, Ohio 45822
> (419) 586-8300 Ext 1200 or 1201
> odonnt@celina.k12.oh.us
>
> "Chance only favors the prepared mind." - Louis Pasteur
>
>
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