Comparison and analysis of different acoustic calculation methods for predicting sound radiated from a pulsating sphere

Abstract

The radiated sound from a pulsating spherical source is a classical acoustic problem, which can be solved either by the classical acoustic method or by the aeroacoustics method. In this paper, an example of sound radiated by a small sphere in the air is designed, and the formulas for determining the surface pressure are derived using the classical acoustic method and the Kirchhoff method, respectively. In the derivation of Kirchhoff method, toroidal strip integrals are used. For the radiated sound field with different frequencies, sphere radius, the two methods are used to solve the problem. It is found that the results obtained by the two methods are very close to each other in the scope of actual engineering concern. Then, this paper discusses the applicability of the Kirchhoff method and points out that the main reason for the result deviation between the two ways is that the Kirchhoff method is derived from the point source Green function. For the more general equation of FW-H, the equivalent relation with the Kirchhoff method is introduced. Through the research of this paper, the characteristics and consistency of different acoustic theories in calculating the radiated sound from the pulsating sphere are explained in depth.