角のついた特殊鐘と棒をつけた和鐘の振動 : 固有振動数の連続変化の研究第1報
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概要
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The characteristic frequencies of, a special bell with 34 horns on the upper half(Fig. 1)originated by artist T. Okamoto, and those of an ordinary Japanese bell attached with a brass bar(Fig. 4)are studied. The spectrum of the characteristic frequencies of the special bell(Fig. 2)and the continuous changes of the frequencies of it by the change in the weight on one of the horns are measured(Fig. 3). The frequency spectrum has about 50 lines under 1 kc/s, which are about 10 times as many as that of the bare bell. The frequency spectrum of the special bell is in accordance with the continuous changes of the characteristic frequencies. Since, by the increase in the weight of the horn, the values of the characteristic frequencies generally decrease, those of the bell with horns will decrease below those of the bare bell with the addition of horns. As a simplified model of the special bell, a brass bar (circular in cross section) is attached to an ordinary Japanese bell(Fig. 4), and the continuous changes of characteristic frequencies by the change in the length of the bar are measured(Fig. 4). The steep descending part of the curves is represented by formula (1), approximately. Since the formula for the fundamental frequency of the lateral vibration of the attached brass bar as a canti-lever is represented by (2), the steep descending part of the curve is intimately related to the lateral vibration of the attached bar. On the other hand, the lines parallel to the l axis represent closely the characteristic frequencies of the bare bell. The experimental curves pass close to the above mentioned curve (1) and the parallel lines, which cross each other. However, the experimental curves do not cross each other and these properties are explained by the theorem derived by Neumann and Wingner qualitatively. By the above analysis of the experimental curves of Fig. 4, we arrive at the conclusion that the continuous changes of characteristic frequencies of the special bell with horns and those of the Japanese bell attached with a bar may be interpreted as a coupling phenomenon between the bare bell and the attached horns or bar. As a model of the special bell with horns which allows mathematical analysis we shall next consider the vibrations of the canti-lever attached with a thin bar.
- 1972-12-01
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