Performance of external ear as a sound collector

Abstract

The overall performance of an acoustical antenna system can be expressed in terms of its absorption cross section which, for a diffuse sound field, is defined as the cross-sectional area A of the perfectly absorbing sphere which would absorb the same sound power from the field as the system under study. The limiting value of A is λ2/4π. For the external ear A can be expressed in terms of the eardrum impedance ZA, the impedance looking outward from the eardrum Za, and the radiation efficiency η all of which can be measured or estimated. The analysis shows that the ear is a very inefficient sound collector at low frequencies but performs well at its primary resonance frequency (2.7 kHz) where A attains a peak value of 5 cm2 compared with theoretical limit of 13 cm3. The cross section almost attains the limiting value at 9 kHz and remains within 6 dB of the limit up to 15 kHz. However, when allowance is made for the energy loss in the eardrum and middle ear it is clear that the cochlea receives no more than 10% of the power available in a diffuse field at any frequency.