Department of Physics and Astronomy, Bowling Green State University, Bowling Green, Ohio 43403, USA.
J Acoust Soc Am. 2011 Sep;130(3):1597-605. doi: 10.1121/1.3605672.
In an important paper on the physics of small amplitude oscillations, Titze showed that the essence of the vertical phase difference, which allows energy to be transferred from the flowing air to the motion of the vocal folds, could be captured in a surface wave model, and he derived a formula for the phonation threshold pressure with an explicit dependence on the geometrical and biomechanical properties of the vocal folds. The formula inspired a series of experiments [e.g., R. Chan and I. Titze, J. Acoust. Soc. Am 119, 2351-2362 (2006)]. Although the experiments support many aspects of Titze's formula, including a linear dependence on the glottal half-width, the behavior of the experiments at the smallest values of this parameter is not consistent with the formula. It is shown that a key element for removing this discrepancy lies in a careful examination of the properties of the entrance loss coefficient. In particular, measurements of the entrance loss coefficient at small widths done with a physical model of the glottis (M5) show that this coefficient varies inversely with the glottal width. A numerical solution of the time-dependent equations of the surface wave model shows that adding a supraglottal vocal tract lowers the phonation threshold pressure by an amount approximately consistent with Chan and Titze's experiments.
在一篇关于小振幅振动物理学的重要论文中，Titze 表明，垂直相位差的本质——它允许能量从流动的空气中传递到声带的运动——可以用表面波模型来捕捉，并且他推导出了一个关于声门开启压力的公式，该公式明确依赖于声带的几何和生物力学特性。该公式激发了一系列实验[例如，R. Chan 和 I. Titze，J. Acoust. Soc. Am 119, 2351-2362 (2006)]。尽管这些实验支持了 Titze 公式的许多方面，包括与声门半宽的线性关系，但该公式在该参数最小的值时的实验行为与公式不一致。结果表明，消除这种差异的一个关键因素在于仔细检查入口损耗系数的特性。特别是，使用声门的物理模型（M5）对小宽度的入口损耗系数进行的测量表明，该系数与声门宽度成反比。表面波模型的时变方程的数值解表明，在声门上增加一个声道会降低声门开启压力，其降低量与 Chan 和 Titze 的实验大致一致。
