Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] Harmonics vs Overtones



I think a series is, e.g. 1, 2, 3, ... While a set is e.g. TE 0,1; 0,2 ... and 1,0; 1,1; 1,2 ... and 2,0; 2,1; 2,2; ... plus the TM modes. x,y both types x/=y/=0, etc.

Obviously rectangular wave guide modes.

http://web.mit.edu/6.013_book/www/chapter13/13.4.html


bc thinks yes, unless one is a musician, modes only.

p.s. like string vs. drum head, circular wave guide modes are not simple. They both use Bessel functions!

http://www.rfcafe.com/references/electrical/circular-waveguide-modes.htm



On 2009, Apr 01, , at 09:12, Dan Crowe wrote:

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.
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l