## Abstract

Abstract: We study the propagation of waves in a waveguide which is the union of two semi-infinite cylinders connected by a thin rectangular ligament. It is shown that almost complete or even complete transmission of the piston mode at a prescribed frequency can be achieved via fine tuning of the plate sizes, although, of course, almost complete wave reflection occurs in the generic case. The result is obtained by applying an asymptotic analysis of the scattering coefficients of the acoustic wave, in particular, by using the dimension reduction procedure on the thin ligament. Possible generalizations of the problem formulation and related open questions are discussed.

Original language | English |
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Pages (from-to) | 646-663 |

Journal | Computational Mathematics and Mathematical Physics |

Volume | 61 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2021 |

## Scopus subject areas

- Computational Mathematics

## Keywords

- acoustic waveguide
- almost complete reflection and transmission of piston modes
- asymptotics of scattering coefficients
- connecting ligament