Index of content:
Volume 121, Issue 4, April 2007
- GENERAL LINEAR ACOUSTICS 
121(2007); http://dx.doi.org/10.1121/1.2537221View Description Hide Description
A Gaussian beams summation (GBS) algorithm for tracking source excited wave fields in plane stratified media is presented. In the present application the medium is described by layers with constant gradient of the wave speed, and the GB propagators are calculated recursively in a closed form. The algorithm is calibrated for numerical efficacy and accuracy by defining simple physical criteria for choosing the expansion parameters (the beam collimation and the spectral discretization and truncation) that allow for sparse representation of the source-excited angular spectrum of beams. It is validated for a source-excited example in layered media, where it provides a smooth and physically meaningful solution under multipath and caustic conditions and remains accurate for long propagation ranges where phase error tends to accumulate.
121(2007); http://dx.doi.org/10.1121/1.2709407View Description Hide Description
Formulas based on the theory of Weyl are widely used to obtain the average number of modes at or below a given frequency in acoustic and vibrational waveguides. These formulas are valid at asymptotically high frequencies; at finite frequencies they are subject to some error, due to fluctuations in the mode count, which depend on the shape of the waveguide. The periodic orbit theory of semiclassical physics is used to give estimates of the variance of these fluctuations and these results are compared with numerical estimates based on eigenvalues obtained by root-finding. The comparison is good but shows errors that can be related to the nature of the periodic orbit theory. Engineering formulas are provided that give an accurate approximation without significant computational cost. The results are valid for membranes, ducts, and thin plates with clamped and/or simply supported boundary conditions.