The spatial distribution of sound pressure within the human ear canal

Abstract

The sound field inside a human ear canal has been computed using 2 approaches. A simple model, a modified Webster horn equation approach, can accommodate the curvature and varying cross section of the ear canal. Calculations using the horn equation demonstrate the formation of standing waves within the canal. The pressure may be interpreted as either the pressure along the center axis of the canal or the average pressure within a cross-sectional slab. To investigate possible spatial variation through a cross section, the sound field has also been computed using the boundary element method (BEM). Over 2000 triangular mesh elements, 1 mm or less in size, were used to represent the canal geometry. For a plane piston source at the canal entrance and both a rigid and a resistive impedance condition at the eardrum position, the computed sound pressures along the center axis of the ear canal are in good agreement with the horn equation calculations, up to 15 kHz. The BEM approach, though, reveals spatial variations of sound pressure through each canal cross section, increasingly significant as frequency increases. Further, for source configurations that are more realistic than a simple piston, large transverse variations in sound pressure are anticipated.