Application of the Partial Domain Method to the Determination of the Directional Properties of a Finite-Length Cone Horn for a Broadband Acoustic Ear Echo Spectrometer

The paper considers and shows the extension of the partial domain method to the formulation and solution of the problem of forming the spatial selectivity of a radiating acoustic horn of a fixed length, operating in an ideal elastic medium, and which is used in the original device for objective express diagnostics of human hearing – a broadband ear spectrometer. The application of the specified method provides the possibility of avoiding the inaccuracies and conventions of the classical wave approach to the formulation of radiation problems, as well as the use of traditional boundary conditions (Neumann and Dirichlet type) and conjugation conditions at the boundaries of partial domains of canonical forms, or as close as possible to the existing ones. The pressure directivity function is determined by solving the Helmholtz equation in each domain in partial domains, followed by determining the maximum and minimum pressure at the field points of the outer domain because of the interference of acoustic waves emitted by the elements of the horn mouth surface areas. Thus, an angular pressure function is formed, which, after normalization, is converted into a directivity characteristic. In this case, the individual solutions of the pressure field components in the selected partial domains are determined from a system of linear algebraic equations with unknown coefficients recorded for the horn throat, its cavity, mouth, and vicinity. The proposed approach is relevant and up to date because it allows increasing the reliability of the modeling of horns of canonical and complicated geometric shapes using boundary conditions and conjugation conditions of selected partial domains. Calculated and experimental results are presented in the form of directional diagrams, amplitude-frequency characteristics of sound pressure, and phase-frequency characteristics.