Theory of the single woodwind tone hole
Theory of the single woodwind tone hole
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单木管音孔理论
DOI：
10.1121/1.388248
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发表时间：
1982
影响因子：
2.4
通讯作者：
D. H. Keefe
中科院分区：
文献类型：
--
作者：
D. H. Keefe
在木管乐器的传输线描述中，单音孔通常可以用T形电路表示。该电路元件由并联和串联阻抗组成，其值取决于孔是打开还是关闭。这些阻抗的虚部已经计算为频率与主孔直径、音孔烟囱高度和直径的函数。求解了通过圆柱形主孔壁的单音孔的无损耗波动方程。主气柱和调孔均进行了绿色功能扩展。在主孔与母孔相交的表面上，这两个展开必须相等，这个条件可以用在该表面上的积分方程来表示。利用Schwinger变分公式得到了积分方程的近似解，并由此计算出T截面的阻抗参数，并以音乐声学家使用的形式显示出来。开孔和闭孔的串联阻抗都是负的惰性。闭孔的分流阻抗是一种顺应性，它只是与闭孔体积有关。裸眼的分流阻抗用裸眼有效长度表示，并表示为音孔比例的函数。
A single tone hole may be generally represented in the transmission‐line description of a woodwind musical instrument by a T‐section circuit. This circuit element is comprised of a shunt and series impedance whose values differ depending on whether the hole is open or closed. The imaginary parts of these impedances have here been calculated as functions of frequency in terms of the main bore diameter, and the tone‐hole chimney height and diameter. The loss‐free wave equation is solved for a single tone hole placed through the wall of a cylindrical main bore. Green function expansions are made in both the main air column and tone hole. These two expansions must be equal on the surface of intersection between the main bore and tone hole, and this condition may be expressed by an integral equation over the surface. An approximate solution to the integral equation is obtained by Schwinger’s variational formulation, and the impedance parameters in the T section are thereby computed and displayed in a form for use by musical acousticians. The series impedance for both open and closed holes is a negative inertance. The shunt impedance of a closed hole is a compliance which is simply related to the closed‐hole volume. The shunt impedance of an open hole is written in terms of the open‐hole effective length and expressed as a function of the tone‐hole proportions.