caa a22 4500 397499833 CHVBK 20180308164530.0 cr unu---uuuuu 161202e199505 xx s 000 0 eng 10.1093/qjmam/48.2.211 doi (NATIONALLICENCE)oxford-10.1093/qjmam/48.2.211 LINTON C. M. Department of Mathematical Sciences, Loughborough University of Technology, Leicestershire LE11 3TU ACOUSTIC SCATTERING BY A SPHERE IN A CIRCULAR CYLINDRICAL WAVEGUIDE [Elektronische Daten] [C. M. LINTON] Multipole expansions are used to solve the problem of the acoustic scattering of an arbitrary mode in a circular cylindrical waveguide by a sphere situated on its axis. Both hard and soft boundary conditions for both the guide and the sphere are considered. The multipole method considered here, although only being appropriate to the above geometry, provides fairly simple equations from which accurate results can be obtained without much computational effort. These results, whilst being interesting in their own right, can be used as a check for more complicated numerical schemes that solve problems for arbitrary geometries. The multipole formulation also enables simple approximate formulae for the reflection and transmission coefficients to be obtained in the low-frequency and small-sphere limits. The same method, with a different set of multipoles, can be used to solve the problem of potential flow past a sphere in a circular tube, and this is done in an Appendix. © Oxford University Press Articles nationallicence The Quarterly Journal of Mechanics and Applied Mathematics Oxford University Press 48/2(1995-05), 211-235 0033-5614 48:2<211 1995 48 qjmamj https://doi.org/10.1093/qjmam/48.2.211 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1093/qjmam/48.2.211 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- LINTON C. M. Department of Mathematical Sciences, Loughborough University of Technology, Leicestershire LE11 3TU NATIONALLICENCE 773 0- The Quarterly Journal of Mechanics and Applied Mathematics Oxford University Press 48/2(1995-05), 211-235 0033-5614 48:2<211 1995 48 qjmamj Metadata rights reserved CC BY-NC-4.0 http://creativecommons.org/licenses/by-nc/4.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-oxford