Nelson,
Thanks for the explanation,
>
> Karl,
>
> >It occurs to me that the rules you give
> > here suggest that the there's a cross sectional area or volume effect at
> > play here (i.e. that scaling for consistent timbre must be somewhat
> > dependent on one or the other of those quantities rather than just bore
> > diameter) i.e. that the scaling is more than a simple linear scaling.
>
> The reason to scale with a bore factor other than 2 when doubling has to do
> with energy loss in the pipe. The loss at the end of the pipe involves
> cross-sectional area. And the loss to the walls involves total wall area.
> Both calculations are computed using bore radius. Both are second degree
> functions--that is functions of area. The bore scaling factor comes from the
> ratio of these two functions. Thus no function survives which is second
> degree (or greater) which would make it non-linear.
>
> If the two loss amounts (end and wall) were equal when doubling that'd be
> the end of the story--but they aren't, they're slightly different.
>
> Because of this difference we need a bore scaling factor slightly smaller
> than 2 (in this case 1.78) when doubling to keep the energy losses
> equalized.
>
> Nelson
>
> ____________________________________________________
>
-- Karl Young kyoung@slac.stanford.edu SLAC M/S 71 PO Box 20450 Stanford, CA 94309 650-926-3380 (voice) 650-926-2923 (FAX) ____________________________________________________
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