Transverse pressure distributions in a simple model ear canal occluded by a hearing aid test fixture.

The sound field in a model ear canal with a hearing aid test fixture has been investigated experimentally and theoretically. Large transverse variations of sound pressure level, as much as 20 dB at 8 kHz, were found across the inner face of the hearing aid. Variations are greatest near the outlet port of the receiver and the vent port. Deeper into the canal, the transverse variations are less significant and, at depths greater than 4 mm, only a longitudinal variation remains. The model canal was cylindrical, 7.5 mm diameter, and terminated with a Zwislocki coupler to represent absorption by the human middle ear. The outer end of the canal was driven by the receiver in the hearing aid test fixture, with the acoustic output entering the canal through a 1 mm port. The hearing aid was provided with a 20-mm-long vent, either 1 or 2 mm in diameter. The sound field inside the canal was measured using a specially designed 0.2-mm-diam probe microphone [Daigle and Stinson, J. Acoust. Soc. Am. 116, 2618 (2004)]. In parallel, calculations of the interior sound field were performed using a boundary element technique and found to agree well with measurements.

Spatial distribution of sound pressure and energy flow in the ear canals of cats.

Spatial pressure distributions have been measured in the ear canals of ten cats and analyzed to obtain the energy reflection properties of the middle ear over a 10- to 25-kHz range of frequencies. Considerable intersubject variability is observed, much of which can be correlated with the condition of the tympanic membrane. For ears judged to be in good condition, reflection coefficients typically take values of about 0.2 between 15 and 25 kHz, indicating good matching of the dynamical properties of the auditory system to the ear canal sound field. At lower frequencies, the reflection coefficients tend to be somewhat higher and at higher frequencies the reflection coefficients increase quite rapidly with frequency. For ears judged to be in poorer condition, energy reflection coefficients of 0.5 and 0.9 were determined for the 15- to 25-kHz range. The variations of sound pressure along the canal (about 10 dB, even in well-coupled systems) confirm that single point pressure measurements may be inappropriate for defining the acoustical input at higher frequencies and new measures for specifying the input should be investigated. The net flow of acoustic energy into the auditory system, the sound power, is one possibility. Some initial measurements of sound power, obtained from analysis of the spatial pressure distributions, are presented.

Revision of estimates of acoustic energy reflectance at the human eardrum.

An improved analysis procedure has been applied to standing wave patterns measured previously [B. W. Lawton and M. R. Stinson, J. Acoust. Soc. Am. 79, 1003-1009 (1986)] in human ear canals. Revised acoustic energy reflection coefficients, at the eardrum, are obtained for 20 ears for frequencies between 3 and 13 kHz. The new analysis addresses anomalous features of the standing wave patterns, apparent at frequencies above 8 kHz, due primarily to the curvature of the ear canal. Much better agreement is now found, at these higher frequencies, between the theoretical form assumed for the standing wave patterns and the experimental data. The revised values of eardrum reflectance are somewhat smaller, especially for frequencies above 11 kHz. The reflectance rises from about 0.25 at 4 kHz up to 0.7 at 8 kHz, falls to a minimum of 0.5 at 11 kHz, then rises to 0.6 at 13 kHz. Considerable intersubject variability in the results is noted.

Sound propagation in the ear canal and coupling to the eardrum, with measurements on model systems.

A theoretical model of sound propagation in the ear canal is described, which takes into account both the complicated geometry of real ear canals and the distributed acoustical load presented by the eardrum. The geometry of the ear canal enters the theory in the form of a cross-sectional area function relative to a curved axis that follows the center of the ear canal. The tympanic membrane forms part of the ear canal wall and absorbs acoustical energy over its surface. Its motion leads to a driving term that must be added to the horn equation describing the pressure distribution in the ear canal. The sound field within the canal is assumed to be effectively one dimensional, depending only on longitudinal position along the canal. Experiments using model ear canals of uniform cross section were performed to test the ability of the theory to handle distributed loads. Sound-pressure distributions within each model canal were measured using a probe microphone. The behavior of the eardrum was simulated using either a distributed, locally reacting impedance or a mechanically driven piston. The agreement between theory and experiment is good up to a nominal upper frequency limit at which the ratio of canal width to wavelength is 0.25. It is estimated that the theory is applicable in ear canals of cats for frequencies at least as high as 25 kHz and in human ear canals to at least 15 kHz.

Specification of the geometry of the human ear canal for the prediction of sound-pressure level distribution.

The geometry of 15 human ear canals has been studied. Silicone rubber molds were made of the ear canals of human cadavers, and a mechanical probe system was used to obtain approximately 1000 coordinate points over the surface of each mold. The data points were accurate to about 0.03 mm in each of the three space directions, allowing ample resolution of surface detail. The measurements have been summarized as individual ear canal area functions, the area of cross-sectional slices normal to a curved central axis following the bends of the canal. Large intersubject differences were found, but several overall trends were evident in the area functions. Accurate specification of the canal geometry has lead to improved predictions of the sound-pressure distribution along the human ear canal at frequencies greater than 8 kHz. Such predictions are relevant to the development of high-frequency audiometric methods, high-fidelity hearing aids, and to the interpretation of experiments in physiological and psychological acoustics.

Standing wave patterns in the human ear canal used for estimation of acoustic energy reflectance at the eardrum.

Standing wave patterns were measured in the unoccluded ear canals of 13 human subjects, for applied pure tones of 3 to 13 kHz. Measurements were made, using a probe microphone technique, over a region which could be approximated as a duct of constant cross-sectional area. Analysis of the patterns allowed the reflective properties of the middle ear to be determined in terms of an acoustic energy reflection coefficient, or reflectance, at the eardrum. Over all subjects the trend of the results was for the energy reflection coefficient to rise from about 0.3 at 4 kHz up to 0.8 at 8 kHz, and continue at this value to 13 kHz. There was, however, significant intersubject variation, especially at frequencies greater than 7 kHz.

The spatial distribution of sound pressure within scaled replicas of the human ear canal.

A theoretical model for calculating the variation of sound pressure within the ear canal is presented. The theory is an extension of the horn equation approach, and accounts for the variation of cross-sectional area and curvature of the ear canal along its length. Absorption of acoustic energy at the eardrum is included empirically through an effective eardrum impedance that acts at a single location in the canal. For comparison, measurements of the distribution of sound pressure have been made in two replica ear canals. Both replicas have geometries that duplicate, as nearly as possible, that of a real human ear canal, except that they have been scaled up in size to increase the precision of measurements. One of the replicas explicitly contains a load impedance to provide acoustical absorption at a single eardrum position. Agreement between theory and experiment was good. It is clear that at higher frequencies (above about 6 kHz in human ear canals), this theoretical approach is preferable to the more usual "uniform cylinder" approximation for the ear canal. At higher frequencies, there is no unique eardrum pressure; rather, very large variations of sound pressure are found over the tympanic membrane surface.

Specification of the acoustical input to the ear at high frequencies.

The sound fields that arise in the auditory canals of cats have been examined both experimentally and theoretically. Of particular interest was the spatial variation of sound pressure near the eardrum, where reference probes are typically located. Using a computer controlled data acquisition system, sound pressure was measured between 100 Hz and 33 kHz for constant driver input at 14 different locations in the ear canal of a cat, and the standing wave patterns formed. The shape of the patterns could be predicted quite well above 12 kHz using a theory that requires specification of only the geometry of the ear canal. This theory, an extension of the one-dimensional horn equation, applies to three-dimensional, rigid-walled tubes that have both variable cross section and curvature along their lengths. Large variations of sound pressure along the ear canal and over the surface of the eardrum are found above about 10 kHz. As a consequence it is not possible to define the acoustical input to the ear from sound pressure level measured at any single location. Even in comparative experiments, in which only the constancy of the acoustical input is important, any uncertainty in reference probe location would lead to an uncertainty in sound pressure level when different sets of measurements are compared. This error, calculated for various probe locations and frequencies, is especially large when the probe is near a minimum of the sound field. Spatial variations in pressure can also introduce anomalous features into the measured frequency response of other auditory quantities when eardrum sound pressure is used as a reference. This is illustrated with measurements of the round window cochlear microphonic.

Estimation of acoustical energy reflectance at the eardrum from measurements of pressure distribution in the human ear canal.

At frequencies greater than 2 kHz the acoustic impedance at the human eardrum is an unreliable indicator of the behavior of the middle ear system because of the complicated configuration of the ear canal and tympanic membrane. The energy reflectance at the eardrum, however, when obtained from measurement of the standing wave ratio (SWR) in the canal, is relatively insensitive to irregularities in the anatomical layout at the higher frequencies. Measurements of sound pressure distribution in 13 normal ear canals have been analyzed in a critical manner to provide new values of SWR, with estimates of error, between 5 and 10 kHz. At the higher frequencies these values tend to be appreciably greater than those previously reported. At 8 kHz, for example, the new values of SWR range between 18 and 24 dB as compared with earlier values which are in the vicinity of 13 dB. The correspondingly greater values of energy reflectance (60%-78%, as compared with 40%) are more consistent with known properties (mass, size, vibrational patterns) of the human eardrum. These results are applicable to the development of network models representing the middle ear system.