Reflectance of acoustic horns and solution of the inverse problem

Daniel M. Rasetshwane, Stephen T. Neely, Jont B. Allen, Christopher A. Shera

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


A method is described for solving the inverse problem of determining the profile of an acoustic horn when time-domain reflectance (TDR) is known only at the entrance. The method involves recasting Webster's horn equation in terms of forward and backward propagating wave variables. An essential feature of this method is a requirement that the backward propagating wave be continuous at the wave-front at all locations beyond the entrance. Derivation of the inverse solution raises questions about the meaning of causality in the context of wave propagation in non-uniform tubes. Exact reflectance expressions are presented for infinite exponential, conical and parabolic horns based on exact solutions of the horn equation. Diameter functions obtained with the inverse solution are a good match to all three horn profiles.

Original languageEnglish (US)
Pages (from-to)1863-1873
Number of pages11
JournalJournal of the Acoustical Society of America
Issue number3
StatePublished - Mar 2012

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics


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