Simple approximate formulas for backscattering of sound by spherical and elongated objects

The scattering of sound by objects is a complex process and is dealt with both analytically and numerically. Regardless of method, calculation of the exact scattered field is quite laborious and may require much computer time as well as human time to program the computer. In order to simplify calculations of the backscattering by a fluid sphere, Johnson combined low- and high-frequency limits in a heuristic manner to obtain a simple closed-form solution (named the ‘‘high-pass’’ solution) [J. Acoust. Soc. Am. 61, 375–377 (1977)]. In this present article, his approach is refined and generalized so that the backscattering by bodies of other shapes can be described. The general model is evaluated for the sphere, prolate spheroid, straight finite cylinder, and bent finite cylinder. The scattering geometries for these specific examples are limited to normal and near-normal incidence for the elongated objects, although the general model can accommodate other geometries provided the exact solutions exist. Comparisons are made of the scattering of these objects using both modal series solutions and the high-pass solutions for fluid, elastic, rigid and fixed, and gaseous materials over a wide range of frequencies. The high-pass solutions are formulated in a general way so as to describe scattering by idealized objects where their shape is simple (i.e., sphere, spheroid, etc.) and their material is lossless, and by nonideal more realistic objects where their shape may be irregular and their material lossy. Calculations of both ‘‘ideal’’ models and ‘‘nonideal’’ models are compared with the modal solutions by using converged modal series for the ideal cases and truncated (keeping just the first two terms) as approximations for (irregular only) nonideal cases. In addition to the numerical simulations, some of the high-pass solutions and corresponding modal series solutions are compared with data involving ideal objects (machined Dural) and nonideal objects (marine organisms: shrimp, euphausiids, and fish). The numerical and experimental results show promise for use of the high-pass models for quick estimates of backscattered sound of many types of objects.