### ASA 127th Meeting M.I.T. 1994 June 6-10

## 4aED7. Acoustic resonators with variable nonuniformity.

**Bruce Denardo
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*Dept. of Phys. and Astron., Univ. of Mississippi, University, MS 38677
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The standard method of altering the fundamental frequency of a
one-dimensional resonator is to change the effective length. Another method is
to introduce or alter the nonuniformity (variation in cross-sectional area),
which can be accomplished very simply. If one end of an open-open nonuniform
resonator is slapped by hand, the fundamental frequency of the open-closed
system is heard. If the other end is slapped, the fundamental frequency is in
general different. Furthermore, if the resonator is cut in half along its
length, and one set of ends is placed on a flat surface, the fundamental
frequency is heard if the halves are clapped together. Because the
configuration can be altered by turning either or both halves upside down, as
many as four different frequencies can be generated. The dependence of
frequency upon nonuniformity can be understood and calculated perturbatively by
Rayleigh's energy method, or more generally by the theorem of adiabatic
invariance. For the simplest case of piecewise-uniform resonators, improved
accuracy is obtained by matching solutions of the wave equation in the uniform
regions. With this theory, resonators have been accurately designed to yield
musical intervals. Demonstrations of these ``slappers'' and ``clappers'' will
be given.