Re: [Phys-l] Harmonics vs Overtones

[curtis osterhoudt <flutzpah@yahoo.com>]

  I may be muddying the waters, and John Denker may not have meant this at all, but he does have a point, referring to these "modes" as constituting a set, rather than a series.

    * When I see (or use) "series", I usually think, "Well, there's a relatively simple rule for generating each member of the series, be it arithmetic, geometric, or something more unusual." I also tend to think, "Ah, a series: there are an infinite number of elements." 
    * Each of the preceding thoughts about series can apply to "set", but they very definitely do not have to.

   In this context, "set" seems more appropriate to me, as the frequencies present in a given acoustic signal are often _nearly_, but not quite integer multiples of some sort of "fundamental". Additionally, one often has cutoff frequencies and so on which further complicate matters. 

   Of course, in teaching high schoolers (or even very bright undergraduates), a lot of this worry over nomenclature is wasted, and may be harmful pedagogically. 

                      

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Down with categorical imperative!
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________________________________
From: Dan Crowe <Dan.Crowe@Loudoun.K12.VA.US>
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Wednesday, April 1, 2009 10:12:06 AM
Subject: Re: [Phys-l] Harmonics vs Overtones

John,

I don't understand the distinction that you're making between a set and a series.  In mathematics, a series is a sum, but a set is not a sum, but that doesn't seem to be the distinction you're making.  Are you implying that the elements in a series are defined by a simple mathematical rule, but the elements of a set are not necessarily defined by a simple mathematical rule?  If yes, then how simple does the mathematical rule have to be?

Daniel Crowe
Loudoun County Public Schools
Academy of Science
dan.crowe@loudoun.k12.va.us 

> > > John Denker <jsd@av8n.com> 4/1/2009 10:00 AM >>>
On a related note (if you'll pardon the expression), it is better
to talk about a _set_ of modes rather than a "series" of modes.
In a one-dimensional tube the modes form a nice simple series,
but other systems are more complex.  This includes strings (which
have two transverse polarizations) and drumheads, waveguides, atoms,
and three-dimensional resonant cavities, where it takes two or more
numbers to describe the structure of each mode.
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