Ear canal cross-sectional pressure distributions: Mathematical analysis and computation

Cross-sectional pressure distributions, natural acoustic modes, and associated cutoff frequencies are determined for real ear-canal geometries using an asymptotic theory in combination with a numerical method. The technique is particularly well suited to obtain the higher modes, which are trapped near both ends of the ear canal. Results detail the influence of the canal geometry and frequency on the spatial distribution of the pressure. Adult ear-canal geometries are determined near the concha from ear-mold sections using a light microscope interfaced to a video-data-acquisition system. Computed results compare favorably to the exact solutions for circular and square acoustic waveguides. The cutoff frequency of the two adult ear canals studied averaged 20% less than the cutoff frequency of a circular tube of identical cross-sectional area. Inserting a probe microphone into the canal decreases the rate of decay of circumferential nonplanar modes while increasing the rate of decay of radial modes. Relative to the pressure beyond the tube, insertion increases the plane-wave component of the pressure around the tube by a multiplicative factor approximately equal to the square root of the original area divided by the occluded area. Eccentric placement of the probe tube has a relatively small influence on the cutoff frequency. The transition of the pressure distribution at the entrance to a simple plane wave in the core region of the canal is calculated and shown graphically for the actual geometry of two adult subjects.