Acoustic scattering by an open‐ended hard circular tube of finite length
Journal of the Acoustical Society of America
A boundary value problem for the time-harmonic acoustic field scattered by an open-ended circular tube of finite length is solved by a Galerkin method. The Neumann boundary condition applies on the infinitesimally thin, cylindrical surface of the acoustically hard scatterer. The circular symmetry of this surface of revolution preserves the orthogonality of the azimuthal modes of the obliquely incident plane wave, which serve as the basis for a trigonometric Fourier series in the • coordinate.
... the • coordinate. Spatial Fourier integrals (plane wave spectra) for the scattered field are expressed in terms of the Galerkin coefficients of a Chebyshev series expansion for the discontinuity in surface pressure. Resultant graphs of the interior and near pressure field on the cylinder axis are presented and qualitatively interpreted in terms of traveling wave components that are reflected from the tube ends. An asymptotic evaluation of the far scattered field yields the angular variation of the obstacle scatter diagram, which is compared to a Kirchhoff approximation. Numerical implementation of this finite-dimensional Galerkin projection precludes the practical extension to very high-frequency scattering, but low and intermediate ( resonance region) frequencies are efficiently and accurately accommodated. PACS numbers: 43.20.Fn I. CHEBYSHEV--GALERKIN ANALYSIS OF SURFACE PRESSURE An infinitesimally thin-walled tube of radius a and extent 2L (Fig. 1 ) is insonified by an incident plane wave with pressure field •p i(r) = •p oi exp [ --ik (x sin 0i + z cos 0i ) ] --= 0 øi •, e, ( --i)"J,(kp sin 0i) X cos(n•b)e -•k .... o,