Limitations of the asymptotic equations for exterior sound waves

Abstract

The determination of exterior sound field due to incident plane waves on a cylinder may be of importance in many areas of acoustics. Applications in acoustics include detecting, locating and classifying objects that generate a scattered sound field excited by the incident sound waves. The exterior sound field in the acoustic domain due to incident plane waves on a cylinder can be determined analytically and numerically. However, it has been observed that for convergence the asymptotic expressions of the analytical models used in the literature required infinite number of terms in the series calculations or are seldom restricted either by low or high frequency limit or the requirement of near-field and far-field approximations. This paper investigates the reasons that caused the nonconformity of the asymptotic analytical expressions. The investigation thus carried out based on the numerically determined exterior sound field using the boundary element method (BEM) and compared with the results obtained using the governing expressions. The comparisons showed good agreement when the governing expressions are not restricted, but nonconformity occurs when they are restricted.