On Nov 23, 2007 7:15 AM, Mathieu Bouchard <matju@artengine.ca> wrote:
On Sat, 17 Nov 2007, Uur Güney wrote:
> An example of sound producing mechanism is
> plucked and vibrating string (or vibrating membrane) It is a continuum
> and so has infinite dimensions.

It's not because it's a continuum, that it has infinite dimensions. Real
numbers form a continuum, but have only 1 dimension.
 
The set of all possible continuous functions over a given finite interval,
forms a continuum that has infinitely (countably) many dimensions. This
continuum also happens to include some simple (Fourier-compatible)
discontinuities as well. (Including all possible discontinuities is
another story.) Physical sounds can be understood to have no
discontinuities, as several factors tend to "low-pass" the sound enough to
remove discontinuities.

# Ok. I got it. Thanks for clarification.
# Once I asked to my Non-linear Dynamics teacher. "Isn't the shape of a string a 1D function of its length? Why we are calling it as continuum?" And she said that: "A simple harmonic oscillator makes a 1D motion (in time). It goes back and forth. You can approximate a string as N connected harmonic oscillator lying along a line. if N goes to infinity we'll have a SHO at every point in space, which makes a 1D motion in time. And this is a field, and hence it is a continuum."
# This is in accordance with your definition, an ideal string can have any shape, so its possible shapes form "the set of all possible continous functions over its length".