Facultad de Física, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna, 4860 Santiago, Chile.
J Acoust Soc Am. 2012 Jan;131(1):146-55. doi: 10.1121/1.3658440.
The extended boundary condition technique of Waterman [J. Acoust. Soc. Am. 45, 1417-1429 (1969)] has been used to make accurate studies of the frequency and azimuthal scattering distributions from extended axisymmetric acoustic objects. These objects are formed using the mathematical function for a "superellipse" [i.e., (x/a)(s) + z/b)(s) = 1, where s = 2n, n = 1,2,[ellipsis (horizontal)]], and revolving around the z-axis. For s = 2, the object is a spheroid with aspect ratio α = b/a. As s increases, the shape of the object approaches a right circular cylinder of diameter 2a and length 2b. The method is applied to the case of prolate (i.e., α > 1) air-filled objects in water, which has importance for the interpretation of acoustic scattering from oceanic objects such as air-bubbles, the swim bladders of some fish, and zooplankton. It is found that the resonance frequency increases with α, essentially as predicted using a different method by Weston, and increases in a relatively minor way with s. The resonance peak amplitude, and Q, are also more sensitive to changes in α, than s. The method shows that the monopole resonance continues to dominate low frequency scattering, leading to an almost spherically symmetric azimuthal scattering distribution, even for elongated, cylindrical, air-filled, objects with an aspect ratio up to α = 20, and s = 32.
沃特曼[J. Acoust. Soc. Am. 45, 1417-1429 (1969)]提出的扩展边界条件技术已被用于对轴对称扩展声学物体的频率和方位散射分布进行精确研究。这些物体是使用数学函数“超椭圆”[即(x/a)(s) + z/b)(s) = 1，其中 s = 2n，n = 1,2,[省略号（水平）]形成的，并绕 z 轴旋转。当 s = 2 时，物体是一个长半轴为 b/a 的旋转椭球体。随着 s 的增加，物体的形状趋近于直径为 2a 且长度为 2b 的圆柱体。该方法适用于充空气的长轴（即 α > 1）物体在水中的情况，这对于解释海洋物体（如气泡、某些鱼类的鳔和浮游动物）的声散射具有重要意义。研究发现，共振频率随 α 增加，基本上与 Weston 用不同方法预测的结果一致，并且随 s 的增加而略有增加。共振峰幅度和 Q 值也对 α 的变化比 s 更敏感。该方法表明，单极共振继续主导低频散射，导致即使对于长径比高达 α = 20 且 s = 32 的圆柱形充空气物体，方位散射分布仍然几乎呈球形对称。
