Estimation of the area function of human ear canals by sound pressure measurements

A method to determine the "area function" of a duct, i.e., the variation of the cross section along the middle axis of the duct is described. It is shown that it is sufficient to measure the sound pressure at three locations in the duct to get knowledge of the area function. The calculated approximation fits the true area function the better the broader the bandwidth of the sound pressure signals is chosen. The bandwidth is bounded by the condition that no higher modes of sound propagation must be excited. In principle, the area function can be determined by solving a linear system of equations and executing a simple iterative algorithm. Some more work however is necessary to stabilize the computation against unavoidable small measuring errors. The calculated area function reproduces the acoustical transformation characteristics with good precision. In spite of this the calculated area function may disagree with the real area function in some regions, especially at the edges. Such errors occur, if the deviations of the area function from constant cross section correspond to frequencies outside the range of measurement. The method was applied to determine the area function of human ear canals and the results are presented.