A threshold resonance generated by an almost standing wave occurring at a threshold — a solution of the problem that do not decay at infinity, but rather stabilizes there — brings about various anomalies in the diffraction pattern at near-threshold frequencies. Examples when a simple threshold resonance occurs or does not occur are trivial. For the first time an acoustic waveguide (the Neumann spectral problem for the Laplace operator) of a special shape is constructed in which there is a maximum possible number (namely two) of linearly independent almost standing waves at a threshold (equal to a simple eigenvalue of the model problem on the cross-section of the cylindrical outlets to infinity). Effects in the scattering problem for acoustic waves, which are caused by these standing waves are discussed. Bibliography: 54 titles.

中文翻译：

---

在简单阈值处具有双阈值共振的波导

由在阈值处发生的几乎驻波所产生的阈值共振（该问题不会在无穷远处衰减，而是在那里稳定）的解决方案会在接近阈值频率处引起衍射图样的各种异常。简单的阈值共振发生或不发生的例子很简单。首次构造特殊形状的声波导管（拉普拉斯算子的诺伊曼光谱问题），其中在阈值（等于简单特征值）处存在最大可能数目（即两个）的线性独立几乎驻波模型问题在圆柱出口到无穷大的横截面上的解析）。讨论了由这些驻波对声波的散射问题的影响。参考书目：54种。