The paper is concerned with a partly analytical, partly numerical study of acoustic trapped modes in a cylindrical cavity (expansion chamber), placed in between two semi-infinite pipes acting as a waveguide. Trapped mode solutions are expressed in terms of Fourier–Bessel series, with the expansion coefficients determined from a determinant condition. The roots of the determinant, expressed in terms of the real wavenumber k, correspond to trapped modes. For a shallow cavity and for low values of the circumferential mode number it is found that there is just one trapped mode in the allowable wave number domain, and this mode is symmetric about a radial axis in the center of the cavity. As the circumferential mode number is increased, more and more trapped modes, placed between two cutoff frequencies, come into play, and they alternate between symmetric and antisymmetric modes. An analytical explanation of the mechanism behind the mode increasing and mode alternation is given via asymptotic expressions of the determinant condition. Numerical computations are done for verification of the analytical results and for consideration of less shallow cavities. Also for these cases, similar phenomena of an increasing number of trapped modes, and alternation between symmetric and antisymmetric modes, are found.

本文涉及对位于两个用作波导的半无限管之间的圆柱腔（扩展室）中的声陷波模式的部分分析，部分数值研究。陷获模式解用傅立叶－贝塞尔级数表示，其膨胀系数由行列式条件确定。行列式的根，以实波数k表示，对应于陷阱模式。对于较浅的腔并且对于较低的圆周模式数值，发现在允许波数域中仅存在一个陷波模式，并且该模式关于腔中心的径向轴对称。随着圆周模式数的增加，越来越多的陷波模式（位于两个截止频率之间）开始发挥作用，并且它们在对称模式和反对称模式之间交替。通过行列式条件的渐近表达式，对模式增加和模式交替背后的机理进行了分析性解释。进行了数值计算，以验证分析结果并考虑到较小的浅腔。同样在这些情况下，类似的现象就是陷波模式越来越多，