### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 4aMUa3. On the use of Schrodinger's equation in the analytic determination
of horn reflectance.

**David Berners
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**
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*Ctr. for Comput. Res. in Music and Acoust., Dept. of Music, Stanford
Univ., Stanford, CA 94305-8180
*

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The flaring horn has traditionally been modeled in one dimension using
piecewise conical or cylindrical elements. Acoustic properties within each
element are known, and scattering between the elements is computed. Under the
piecewise model, a shape for the wavefront of the acoustic disturbance within
the horn is implicitly assumed (planar for cylindrical elements, spherical for
conical elements). For horns of significant flare, the true wavefront shape
will be neither planar nor spherical. A more general model is thus desirable.
Here an alternate model is presented: The flaring horn is modeled according to
Webster's equation. A change of variables transforms the equation into the form
of the Schrodinger wave equation using in one-dimensional particle scattering.
Boundary conditions can be derived directly from the physical dimensions of the
horn, and the solution of the equation gives estimates of acoustic properties
in terms of frequency dependent reflection and transmission coefficients. Here,
Webster's equation is solved along the entire length of the horn, with no
lumped scattering. Advantages over piecewise modeling techniques include the
ability to specify arbitrary axisymmetric wavefront shapes for the acoustic
disturbance within the horn. Under appropriate assumptions for wavefront
shapes, results converge to those obtained with traditional piecewise models.