## 5aMU10. The discontinuous conical bore as a Sturm--Liouville problem.

### Session: Friday Morning, December 6

### Time: 10:50

**Author: David P. Berners**

**Location: CCRMA, Dept. of Music, Stanford Univ., Stanford, CA 94305-8180**

**Abstract:**

In some cases the reflection functions associated with the discontinuities
in conical bores are growing exponentials [J. Martinez and J. Agul-lo, J.
Acoust. Soc. Am. 84, 1613--1619 (1988)]. It is shown that discontinuities can be
modeled by a Sturm--Liouville system using a pressurelike quantity as the
dependent variable. For the subset of discontinuities exhibiting the growing
exponential reflection function, the Sturm--Liouville potential function is an
energy well. This well is shown to support exactly one trapped energy mode which
corresponds to the growing exponential. It is shown that in the region
surrounding the discontinuity for these systems, traveling Fourier components
taken together with their reflected waves do not constitute a complete set and
that the trapped mode is required to complete the set. On the other hand, for
systems which do not exhibit the growing exponential, the Sturm--Liouville
potential is an energy barrier with no trapped modes, and the Fourier components
compose a complete set within the conical regions. Furthermore, a change of
dependent variable can be used to go from a Sturm--Liouville description
involving an energy well to one involving a barrier, thus eliminating the
trapped mode.

ASA 132nd meeting - Hawaii, December 1996