Re: [Phys-l] Harmonics vs Overtones

[Roger Haar <haar@physics.arizona.edu>]

HI,

	I do not think that it makes physical sense to discuss waves, whose 
wavelengths are shorter than the diameter of a gas molecule.  Although 
one can imagine a square wave (which requires an infinite sum of sine 
waves) in an organ pipe or on a string, I think that it is physically 
impossible.

Sincerely,
 Roger Haar


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Dan Crowe wrote:
> A cutoff frequency implies that there are a finite number of modes, but a series does not have to be an infinite series.
>  
> The sound generated by a musical instrument can be modeled by a mathematical formula that is a sum of terms.  Each term in the sum represents a mode.  The modes themselves form a set, but the sound is represented by a sum.  Is this sum a finite series?  If not, why not?
>  
> I agree that there is a set of modes.  On the other hand, I think that it is useful to talk about representing sound as a modal series, which is a sum over the modes.  The modes are the basis set for the series.  I agree that the modal series is not, in general, a harmonic series.
>  
> Daniel Crowe
> Loudoun County Public Schools
> Academy of Science
> dan.crowe@loudoun.k12.va.us