Abstract
As part of basic research on acoustic transmission systems and their elements, wave theory is applied to acoustic transmission ducts with circular cross section whose radius varies in a stepwise manner. In the present paper we try to deal with three typical types of stepped acoustic transmission ducts with two plane discontinuities as shown in Figs. 1, 4 and 7. These are rather simple acoustic transmission elements, but their characteristics are more complicated than those of acoustic transformers and cavities treated in previous papers. They are widely used in the design of acoustic devices as an acoustic filter-element. They are also expected to play an important role in the analysis of more complicated transmission systems. The purpose of this paper is to investigate the sound field in the stepped ducts and to clarify the transmission characteristics of these elements to the plane incident wave, P_oexp(iωt-ikz). Corresponding to the stepped ducts shown in Figs. 1, 4 and 7, their pressure distributions along the axis are plotted in Figs. 2, 5 and 8, respectively. Relevant acoustic characteristics of the ducts such as transmission and reflection coefficients, transmitted and reflected powers are also given in Figs. 3, 6 and 9. By examining these figures we may be able to understand the effects of higher order modes on a plane wave propagating in the stepped ducts. These higher order modes are excited at the plane discontinuities. At high frequency range they have a great influence upon the sound field as well as acoustic coupling between discontinuities. Moreover We may be able to compare and discuss the acoustic characteristics of each of the stepped ducts by referring to the above figures.
