### Abstract

The question concerning the uniqueness of the solution to the problem of the acoustic diffraction by an immersed and isolated thin infinite plate with a finite scatterer is studied. It is shown that, to provide the uniqueness of the solution, the conditions at the scatterer must lead to an energy inequality for a source-free field, which determines the absence of the energy-carrying field components at infinity. A formula that generalizes the Sommerfeld formula is obtained and is used to prove the uniqueness of the solution to the problem of diffraction by a plate immersed in an acoustic medium. For the problem of diffraction of a flexural wave by an irregularity of the plate, the uniqueness theorem is proved only for the case of a fixed or hinged edge. When boundary conditions of a general form are imposed on the scatterer in an isolated plate, the uniqueness of the solution is generally lost, which is also corroborated by an example.

Original language | English |
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Pages (from-to) | 3-9 |

Number of pages | 7 |

Journal | Acoustical Physics |

Volume | 47 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2001 |

### Scopus subject areas

- Acoustics and Ultrasonics

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## Cite this

*Acoustical Physics*,

*47*(1), 3-9. https://doi.org/10.1134/1.1340071