Modeling acoustic propagation in tubes including the effects of thermoviscous losses at the tube walls is important in applications such as thermoacoustics, hearing aids, and wind musical instruments. Frequency dependent impedances for a tube transmission line model in terms of the so-called thermal and viscous functions are well established, and form the basis for frequency domain analysis of systems that include tubes. However, frequency domain models cannot be used for systems in which significant nonlinearities are important, as is the case with the pressure-flow relationship through the reed in a woodwind instrument. This paper describes a cylindrical tube model based on a continued fraction expansion of the thermal and viscous functions. The model can be represented as an analog circuit model which allows its use in time domain system modeling. This model avoids problems with fractional derivatives in the time domain.

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The ratio of Bessel functions J1(z)/J0(z) often occurs in the calculation of impedance of lossy components in electroacoustic devices. In particular, the electric impedance of hearing aid receivers or loudspeakers has a term proportional to a Bessel function ratio of this form when losses due to eddy currents are taken into account. This so-called semi-inductance has been notoriously difficult to model in simple lumped-parameter circuit calculation tools such as SPICE. This paper presents a simple ladder network derived from the Bessel function ratio expressed as a continuous fraction. The same transformation has been used to model the acoustic impedance of small cavities with losses at the thermal boundary layer.

Results are presented of an analysis and characterization of the mechanical vibration of hearing aid receivers, a key electroacoustic component of hearing aids. The function of a receiver in a hearing aid is to provide an amplified sound signal into the ear canal. Unfortunately, as the receiver produces sound, it also undergoes vibration which can be transmitted through the hearing aid package to the microphones, resulting in undesirable feedback oscillations. To better understand and control this important source of feedback in hearing aids, a rigid body model is proposed to describe the essential dynamic features of the system. The receiver is represented by two hinged rigid bodies, under an equal and opposite dynamic moment load, and connected to each other by a torsional spring and damper. A method is presented to estimate the parameters for the proposed model using experimental data. The data were collected from translational velocity measurements using a scanning laser vibrometer of a Knowles ED-series receiver supported on a complaint foundation. Excellent agreement is shown between results obtained using the analytical model and the measured translation and rotation of an independent receiver. It is concluded that a dynamic model of the receiver must account for both rotation and translation of the structure in order to properly describe its motion due to an input current.

Active noise cancellation (ANC) technologies have been successfully applied in headsets to reduce ambient noise in the ear canal. The performance of such a technology depends on the characteristics of the secondary path (SP). In this paper, two different systems are studied: one system utilizes a moving-coil speaker as the secondary source and forms a closed cavity over the ear, while the other one uses a balanced-armature receiver inside the ear canal as the secondary source. The differences in the SP responses of these two systems are investigated both experimentally and theoretically. The implications for designing an effective ANC solution will be discussed based on numerical simulations.