円形断面が不連続的に拡大する音響変成器

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The effect of a plane discontinuity on a plane wave propagating in a tube of arbitrary cross section has been discussed on the basis of various points of view. In a previous paper the authors regarded the effect as an acoustic element analogous to a transformer in electrical circuits, and devoted their attention to the element with discontinuous reduction in cross section. In this paper, therefore, another important type of an acoustic transformer with circular cross section, as shown in Fig. 1, is studied by making use of the same theoretical treatment as before and the results are compared with the previous ones in order to clarify their points of difference as well as those of similarity. The sound field in a tube is rigorously evaluated by a quantitative analysis, and several examples of pressure amplitude distribution along the axis are plotted in Fig. 3. By examining this figure, we may be able to appreciate the effects of higher order modes in the vicinity of the discontinuity. Fig. 4 shows the manner in which the incident power subject to (0, 0) mode is divided into transmitted and reflected powers. Examples of transmission and reflection coefficients of (0, 0) mode are shown in Fig. 5, and input impedances of the acoustic transformer under consideration are shown in Fig. 6. Investigations based on a simple plane-wave approximation and a plane-piston approximation are also made and the results are compared with exact solution in order to obtain the limitation of each of the approximate methods. Moreover, the propagation of sound in a circular cylindrical tube with infinite rigid baffle is quantitatively analyzed as a special case of the acoustic trans-former and the results are shown in Figs. 8-10. The above investigation of the acoustic transformer leads us to a better understanding of its characteristics. Both simple plane-wave approximation and plane-piston approximation have superior merits, but it is undesirable to use these approximate methods beyond the limitations which depend on the frequency parameter ka and diameter ratio ξ of the tube. We should, further, give attention to the fact that the sound field is more sensitive to the method of approximation than the global quantities such as input impedance and transmission coefficient which are less dependent on the method of approximation.
社団法人日本音響学会の論文
1969-07-20

円形断面が不連続的に拡大する音響変成器

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