A relationship between the far field diffraction pattern and the axial pressure radiating from a two-dimensional aperture

作者：Pees Edward H^*

来源：Journal of the Acoustical Society of America, 2010, 127(3): 1381-1390.

DOI：10.1121/1.3291685

The diffraction of an acoustic wave by a two-dimensional aperture produces a sound field that can generally be represented at any point in space as a superposition of a continuum of plane waves. The mathematical formulation that facilitates this representation is known as the angular spectrum of plane waves method. The spectrum, in this representation, is a wavenumber spectrum obtained from a two-dimensional Fourier transform of the acoustic pressure (or velocity) distribution over the surface of the aperture boundary; a quantity which is also known to characterize the Fraunhofer diffraction pattern of the aperture. In this article, the angular spectrum method is used to formulate a mathematical relationship for two-dimensional apertures between the Fraunhofer diffraction pattern and a one-dimensional Fourier transform of the axial pressure. This relationship can be used to rapidly compute the axial pressure profile of the aperture if the boundary condition on the aperture is known and, in some cases, can be used as an inverse method. The approach is demonstrated for the cases of a flat circular piston and a flat rectangular piston undergoing harmonic motion in an infinite, rigid baffle. In the latter case, an analytical solution is also obtained.

• 出版日期2010-3