Acoustic scattering by a sphere with a hemispherically split boundary condition

Bradley Treeby, Jie Pan, Roshun Paurobally

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A general analytical model is developed for the scattering of sound by a sphere with a nonuniform impedance boundary condition that is divided into two uniformly distributed hemispheres. In addition to the overall solution for the time harmonic pressure, the analytical result gives insight into the modal contributions and coupling for different cases of source incidence and boundary impedance. Modal cross coupling is shown to exist between incoming and scattered wave modes of equi-order and nonequal degree when the degrees are opposite in parity (odd-even or even-odd coupling). This cross coupling is strongest between modes of adjacent degree, and decreases as the degrees become dissimilar. The overall magnitude of the cross coupling is dependent on the extent of the impedance mismatch between the two surface hemispheres. Simulation and discussion are given for several specific cases of source incidence and impedance (each hemisphere is given a different constant impedance value). These results are consistent with expectations from the scattering of sound by a sphere with a uniformly distributed surface boundary. The broad scattering characteristics of the hemispherically divided sphere are shown to be analogous to connecting the appropriate sectors from the corresponding uniformly distributed spheres. (c) 2007 Acoustical Society of America.
Original languageEnglish
Pages (from-to)46-57
JournalJournal of the Acoustical Society of America
Volume122
Issue number1
DOIs
Publication statusPublished - 2007

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acoustic scattering
impedance
boundary conditions
cross coupling
hemispheres
incidence
scattering
acoustics
parity
sectors
Split
Acoustics
Boundary Conditions
Hemisphere
harmonics
Sound
simulation

Cite this

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abstract = "A general analytical model is developed for the scattering of sound by a sphere with a nonuniform impedance boundary condition that is divided into two uniformly distributed hemispheres. In addition to the overall solution for the time harmonic pressure, the analytical result gives insight into the modal contributions and coupling for different cases of source incidence and boundary impedance. Modal cross coupling is shown to exist between incoming and scattered wave modes of equi-order and nonequal degree when the degrees are opposite in parity (odd-even or even-odd coupling). This cross coupling is strongest between modes of adjacent degree, and decreases as the degrees become dissimilar. The overall magnitude of the cross coupling is dependent on the extent of the impedance mismatch between the two surface hemispheres. Simulation and discussion are given for several specific cases of source incidence and impedance (each hemisphere is given a different constant impedance value). These results are consistent with expectations from the scattering of sound by a sphere with a uniformly distributed surface boundary. The broad scattering characteristics of the hemispherically divided sphere are shown to be analogous to connecting the appropriate sectors from the corresponding uniformly distributed spheres. (c) 2007 Acoustical Society of America.",
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Acoustic scattering by a sphere with a hemispherically split boundary condition. / Treeby, Bradley; Pan, Jie; Paurobally, Roshun.

In: Journal of the Acoustical Society of America, Vol. 122, No. 1, 2007, p. 46-57.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Acoustic scattering by a sphere with a hemispherically split boundary condition

AU - Treeby, Bradley

AU - Pan, Jie

AU - Paurobally, Roshun

PY - 2007

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AB - A general analytical model is developed for the scattering of sound by a sphere with a nonuniform impedance boundary condition that is divided into two uniformly distributed hemispheres. In addition to the overall solution for the time harmonic pressure, the analytical result gives insight into the modal contributions and coupling for different cases of source incidence and boundary impedance. Modal cross coupling is shown to exist between incoming and scattered wave modes of equi-order and nonequal degree when the degrees are opposite in parity (odd-even or even-odd coupling). This cross coupling is strongest between modes of adjacent degree, and decreases as the degrees become dissimilar. The overall magnitude of the cross coupling is dependent on the extent of the impedance mismatch between the two surface hemispheres. Simulation and discussion are given for several specific cases of source incidence and impedance (each hemisphere is given a different constant impedance value). These results are consistent with expectations from the scattering of sound by a sphere with a uniformly distributed surface boundary. The broad scattering characteristics of the hemispherically divided sphere are shown to be analogous to connecting the appropriate sectors from the corresponding uniformly distributed spheres. (c) 2007 Acoustical Society of America.

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