著者

広根 万里雄 曽根 敏夫 二村 忠元

出版者

一般社団法人 日本音響学会

雑誌

日本音響学会誌 (ISSN:03694232)

巻号頁・発行日

vol.31, no.8, pp.487-495, 1975-08-01 (Released:2017-06-02)

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A theory of the excitation of a clarinet was proposed in case that no performer's lips were applied to the reed of the instrument, by assuming the interaction between the air column and the reed and considering the vibration of reed as a bending vibration of beam. The results of calculation were compared with those of experiment on a model clarinet specially prepared in order to make both experimental condition and theoretical assumption coincide. In Section 2, the method of calculation of the resonance frequency of reed itself is shown ; the calculation was based on the assumption that the reed vibration is well represented by one-dimensional bending vibration of beam. Section 3 depicts the equation (Eq. (14)) of motion of the reed of instrument and the wave equation (Eq. (13)) of air column. These equations were solved simultaneously and from the results of analysis the frequency equation was obtained, which gave the dependence of the excited frequency (including higher order modes) on the physical blowing condition of the instrument. In Section 4, an example of the excited frequency calculated from the frequency equation is first shown (Fig. 7) based on presumable values of the material constants for a standard reed, together with the resonance frequency of the reed. Next, for confirming the above mentioned theoretical results, calculation was performed for the excitation of an instrument with metal reeds of precisely defined material constants and geometrical form. Table 4 and Figs. 8 and 9 show the observed and calculated results of the excited frequency of the model clarinet mentioned above as a function of the pipe length. And for comparison, the resonance frequency of reed itself calculated by the method described in Section 2 is presented in the same table and figures, in which it is shown that the results of calculation and experiment coincide satisfactorily well. It was also made clear that the excited frequency of the clarinet without application of performer's lips is deviated to some extent from the resonance frequency of reed, and that the change of excited frequency due to the pipe length is nearly proportional to the resonance frequency of the air column. In this case, the change of excited frequency was small compared with that of resonance frequency of the air column, and there existed a frequency region in which the clarinet was difficult or perfectly not to be excited according to a certain relation existing between the resonance frequency of reed and that of air column (See Figs. 8 and 9).