2022 年 88 巻 908 号 p. 21-00324
Ducts are widely used in an industry field. For example, air conditioning ducts, exhaust ducts, smoke elimination ducts and silencers have been used in various ducts. In general, the ducts have a flow and the vortices generated in the duct sometimes cause a resonance phenomenon and a self-sustained tone. Once the resonance occurs, the high level sound is generated and the suppression of this sound is strongly and quickly required. It is necessary to know the natural acoustic frequency of the duct for examination of the cause. The natural acoustic frequency of the straight duct with uniform cross section can be easily obtained but that of varying cross section can’t be obtained immediately. Of cause the natural acoustic frequency of the duct with an arbitrary cross section can be obtained by using the transfer matrix method, FEM and BEM. In our previous studies, many interesting findings of the natural acoustic frequency of ducts with varying cross section were obtained but the understandings of the findings have not been adequate. Then in this paper, in frequency range where plane waves hold, the mode order independent of the ratio of two cross sectional areas is discussed and the table which makes obtaining of the natural acoustic frequency easily is presented. Furthermore, we will show how to understand the relation between the ratio of the cross sectional areas and the natural acoustic frequency for an arbitrary length ratio.
