On the calculation of reflectance in non-uniform ear canals

Ear-canal reflectance is useful for quantifying the conductive status of the middle ear because it can be measured non-invasively at a distance from the tympanic membrane. Deriving the ear-canal reflectance requires decomposing the total acoustic pressure into its forward- and reverse-propagating components. This decomposition is conveniently achieved using formulas that involve the input and characteristic impedances of the ear canal. The characteristic impedance is defined as the ratio of sound pressure to volume flow of a propagating wave and, for uniform waveguides, the plane-wave characteristic impedance is a real-valued constant. However, in non-uniform waveguides, the characteristic impedances are complex-valued quantities, depend on the direction of propagation, and more accurately characterize a propagating wave in a non-uniform ear canal. In this paper, relevant properties of the plane-wave and spherical-wave characteristic impedances are reviewed. In addition, the utility of the plane-wave and spherical-wave reflectances in representing the reflection occurring due to the middle ear, calibrating stimulus levels, and characterizing the emitted pressure in simulated non-uniform ear canals is investigated and compared.