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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.