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The horn-feed problem: sound waves in a tube joined to a cone, and related problems

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Abstract

A semi-infinite tube is joined to a semi-infinite cone. Waves propagating in the tube towards the join are partly reflected and partly radiated into the cone. The problem is to determine these wave fields. Two modal expansions are used, one in the tube and one in the cone. However, their regions of convergence do not overlap: there is a region \({\mathcal{D}}\) near the join where neither expansion converges. It is shown that the expansions can be connected by judicious applications of Green’s theorem in \({\mathcal{D}}\). The resulting equations are solved asymptotically, for long waves or for narrow cones. Related two-dimensional problems are also solved. Applications to acoustics, electromagnetics and hydrodynamics are considered.

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Martin, P.A. The horn-feed problem: sound waves in a tube joined to a cone, and related problems. J Eng Math 71, 291–304 (2011). https://doi.org/10.1007/s10665-011-9454-8

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  • DOI: https://doi.org/10.1007/s10665-011-9454-8

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