Acoustic scattering on spheroidal shapes near boundaries

Touvia Miloh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A new expression for the Lamé product of prolate spheroidal wave functions is presented in terms of a distribution of multipoles along the axis of the spheroid between its foci (generalizing a corresponding theorem for spheroidal harmonics). Such an “ultimate” singularity system can be effectively used for solving various linear boundary-value problems governed by the Helmholtz equation involving prolate spheroidal bodies near planar or other boundaries. The general methodology is formally demonstrated for the axisymmetric acoustic scattering problem of a rigid (hard) spheroid placed near a hard/soft wall or inside a cylindrical duct under an axial incidence of a plane acoustic wave.

Original languageEnglish
Pages (from-to)663-671
Number of pages9
JournalAcoustical Physics
Issue number6
StatePublished - 1 Nov 2016


  • Green’s function and integral representation
  • Linear acoustics and Helmholtz equation
  • multipole expansions and ultimate singularity system
  • planar boundaries and cylindrical duct
  • spheroidal wave functions


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