Radiation impedance for baffled rectangular pistons of arbitrary aspect ratio at any frequency

Abstract

An algorithm has been developed for calculating the complex farfield radiation impedance of a plane rectangular piston vibrating at any frequency in a coplanar infinite baffle for any ratio of length to width. The method is based on previously published expressions for the radiation from an infinite strip [J. W. Miles, J. Acoust. Soc. Am. 20, 652–1664 (1948)] and for the radiation from a long strip [O. A. Lindemann, J. Acoust. Soc. Am. 52, 1045–1048 (1972)], as well as on the expressions and calculated values found in the thesis [D. S. Burnett, “Radiation Impedance Functions of Rectangular Pistons and Their Application to Sound Transmission Through Finite Depth Apertures,” Ph.D. dissertation, University of California, Berkeley, CA (1969)]. Six different power and asymptotic series (some believed new) in combination with three empirically derived algebraic expressions are shown to be valid for each of four contiguous regions in the dimensionless length and width parameters, kl and kw. The boundaries of the regions are slightly different for the real and the imaginary parts. The algorithms are amenable to very fast computer calculation and produce results that are usually accurate to within a few percent.