Stinson M R, Khanna S M
Physics Division, National Research Council, Ottawa, Ontario, Canada.
J Acoust Soc Am. 1989 Jun;85(6):2481-91. doi: 10.1121/1.397743.
A theoretical model of sound propagation in the ear canal is described, which takes into account both the complicated geometry of real ear canals and the distributed acoustical load presented by the eardrum. The geometry of the ear canal enters the theory in the form of a cross-sectional area function relative to a curved axis that follows the center of the ear canal. The tympanic membrane forms part of the ear canal wall and absorbs acoustical energy over its surface. Its motion leads to a driving term that must be added to the horn equation describing the pressure distribution in the ear canal. The sound field within the canal is assumed to be effectively one dimensional, depending only on longitudinal position along the canal. Experiments using model ear canals of uniform cross section were performed to test the ability of the theory to handle distributed loads. Sound-pressure distributions within each model canal were measured using a probe microphone. The behavior of the eardrum was simulated using either a distributed, locally reacting impedance or a mechanically driven piston. The agreement between theory and experiment is good up to a nominal upper frequency limit at which the ratio of canal width to wavelength is 0.25. It is estimated that the theory is applicable in ear canals of cats for frequencies at least as high as 25 kHz and in human ear canals to at least 15 kHz.
描述了一种耳道内声音传播的理论模型，该模型既考虑了真实耳道复杂的几何形状，又考虑了鼓膜呈现的分布声学负载。耳道的几何形状以相对于沿着耳道中心的弯曲轴的横截面积函数的形式进入该理论。鼓膜构成耳道壁的一部分，并在其表面吸收声能。其运动导致一个驱动项，该驱动项必须添加到描述耳道内压力分布的喇叭方程中。假设耳道内的声场有效地是一维的，仅取决于沿耳道的纵向位置。使用均匀横截面的模型耳道进行了实验，以测试该理论处理分布负载的能力。使用探针麦克风测量每个模型耳道内的声压分布。使用分布的局部反应阻抗或机械驱动的活塞来模拟鼓膜的行为。理论与实验之间的一致性在标称上限频率之前都很好，在该上限频率处，耳道宽度与波长之比为0.25。据估计，该理论适用于猫的耳道，频率至少高达25kHz，适用于人的耳道，频率至少为15kHz。
