As part of basic research on acoustic transmission systems and their elements , wave theory is applied to acoustic transmission ducts with circular cross sectiQn 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 , 4and 7. These are rather simple acou3tic transrnission ele 皿 ents , but their characteristics are more complicated than those of acoustic

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... sformers and cavities treated in previous papers7 )8)9 ) . They are widely used in the design of acoustic devices as an acQust 三 c filter − element . They are alsQ expected to play an important role in the analysis of more co 皿 ・ plicated transmission systems2 )io) . The purpose of this paper is to investigate the sound 丘eld in the stepped ducts and to clarify the transmission characteristics of these elements to the plane incident wave , P 。 exp ( iwt − ikz ) . Corresp nding to the stepped ducts shown in F 三 gs .ユ,4and 7, their pressure distributions along the axis are plotted in Figs .2 , 5and 8 , respectively . Rele ・ vant acoustic characteristics of the ducts such as transm 三 ssion and refiection coe 飾 cients , transmitted and reflected powers are also given in Figs、3,6and 9. By examining these figures we may be able to understand the effects of higher order rnodes on a plane wave propagating i【1 the stepped ducts . These higher order modes are excited at the plane discontinuit 三 es . At high frequency range they have a great 三 nfluence upon the s 。 und 丘eld as well as acoustic coupling between discontinuit 三 es . Moreover We may be able to compare and discuss the acoustic characterist 三 cs of each of the stepped ducts by referring to the above figures .