STATIONARY-PHASE FOR SUMMATIONS

Authors
Citation
Wr. Graham, STATIONARY-PHASE FOR SUMMATIONS, The Journal of the Acoustical Society of America, 99(5), 1996, pp. 3233-3235
Citations number
6
Categorie Soggetti
Acoustics
ISSN journal
00014966
Volume
99
Issue
5
Year of publication
1996
Pages
3233 - 3235
Database
ISI
SICI code
0001-4966(1996)99:5<3233:SFS>2.0.ZU;2-B
Abstract
The geometrical, or ''ray'' approach to high-frequency wave fields is well known. Using the method of stationary phase, the ray terms can be shown to arise as the leading-order solution of an exact integral for mulation for the wave field. However, this analysis cannot be applied directly when the problem geometry is cylindrical or circular, and the integral is replaced by a summation. Instead the sum must first be co nverted into an integral by the rather cumbersome means of a Watson tr ansformation. Here an intuitive and concise extension of the method of stationary phase, which may be applied directly to summations, is pre sented, and the validity of the approach is confirmed using the Watson transformation. (C) 1996 Acoustical Society of America.