Gibbons, John wrote:
Barry said
"If only pipes were so simple"
The formula for strings:
f = (1/2L) * sqrt (T/mu)
neglects all sorts of effects, such as the bow or the finger, the rigidity of
the string, the speed of tension waves in the string, etc. And we haven't
thought of the motion of the fiddle's bridge and body yet.
I believe that of all the approximations in acoustics this one works
pretty well for strings under the conditions we find in musical
instruments. However, it does assume that the string is uniform and
stretched between two fixed points - nut and bridge. There again, that
is the normal arrangement for tuning.
Similarly, the analogous formula for a one-open-ended pipe:
f = (1/4L) * sqrt (gamma P/rho)
neglects the effects of the reed at the 'closed' end or the hole at the other.
Or the bore, or the 'dead' bore below the open hole, the vibration of the wood,
etc...
This may be a good starting point but I believe that for NSP in
particular it is very approximate. Wall effects which are generally
negligible in other instruments become significant at the bore sizes we
use. The effective reed length is a whole can of worms.
Barry
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