Re: prefab for circular modes?

[Jordi Gutiérrez Hermoso]

On 1 June 2011 23:48, xoxos <address@hidden> wrote:
> given the number of diametric and radial nodes, i want to be able to
> determine the frequency (or ratio to fundamental) for the
> vibrational mode of an ideal circular membrane, to a 'fair' number
> of decimal places. examples are here -
> http://hyperphysics.phy-astr.gsu.edu/hbase/music/cirmem.html#c4

This looks like the eigenfunctions of the linear wave equation in a
circular domain. They're built from Bessel functions. I did solve such
a thing with Octave. I'd show you the animation, but you seem to be
tired of it.

I have the work done somewhere, but it will take me a little while to
remember it (i.e. to find my old school notes). Before I do so, I just
want to understand that what you want is a description of the
fundamental vibrating frequencies of an elastic membrane on a circular
domain, e.g. a drum.

> i haven't been able to apply chladni's law, or anything. i am
> comfortable to trig. i have, qunite honestly now, spend solid weeks
> of my life staring at notation for bessel functions et al. without
> understanding or being able to use them to any degree. teh internets
> have yet to realise any sensible to myself expression of methodology
> for doing so, yet there are dozens of matlab and mathematica owners
> who merrily post animations of vibrating circlular modes.

What is your request? You want to understand the partial differential
equation without knowing about derivatives?

> i will pay for the formula, okay?

What formula? What I described above? Also, there's no need to pay for this.

- Jordi G. H.