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.     

Acoustics of ear canal measurement of eardrum SPL in simulators

The effect of standing waves on the ear canal measurement of eardrum sound pressure level (SPL) was determined by both calculation and measurement. Transmission line calculations of the standing wave were made using the dimensions of the ANSI S3.25-1979 ear simulator and three different eardrum impedances. Standing wave curves have been obtained for the standard eardrum impedance at 1-kHz intervals in the range of 1-8 kHz. The changes in standing wave position due to each of the three eardrum impedances and their effects on ear canal measurements of SPL were computed for each of the eardrum impedances. Ear canal SPL measurements conducted on simulators modified to correspond to the eardrum impedances used in the calculations were compared to the computed values. Differences between eardrum SPLs and those measured at different locations in the ear canal approached a standing wave ratio (SWR) of 10-12 dB as the position of the measuring probe approached the standing wave minimum at each frequency. These maximum differences compared favorably with data developed by other investigators from real ears. Differences due to the eardrum impedance were found to be significant only in the frequency region of 2-5 kHz. Calibration of probes in a standard or modified ANSI simulator at the same distance from the eardrum as in the real ear reduces the eardrum SPL measurement errors to those resulting from differences in eardrum impedance.     

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.     

Sound pressure distribution and power flow within the gerbil ear canal from 100 Hz to 80 kHz

Sound pressure was mapped in the bony ear canal of gerbils during closed-field sound stimulation at frequencies from 0.1 to 80 kHz. A 1.27-mm-diam probe-tube microphone or a 0.17-mm-diam fiber-optic miniature microphone was positioned along approximately longitudinal trajectories within the 2.3-mm-diam ear canal. Substantial spatial variations in sound pressure, sharp minima in magnitude, and half-cycle phase changes occurred at frequencies >30 kHz. The sound frequencies of these transitions increased with decreasing distance from the tympanic membrane (TM). Sound pressure measured orthogonally across the surface of the TM showed only small variations at frequencies below 60 kHz. Hence, the ear canal sound field can be described fairly well as a one-dimensional standing wave pattern. Ear-canal power reflectance estimated from longitudinal spatial variations was roughly constant at 0.2-0.5 at frequencies between 30 and 45 kHz. In contrast, reflectance increased at higher frequencies to at least 0.8 above 60 kHz. Sound pressure was also mapped in a microphone-terminated uniform tube-an "artificial ear." Comparison with ear canal sound fields suggests that an artificial ear or "artificial cavity calibration" technique may underestimate the in situ sound pressure by 5-15 dB between 40 and 60 kHz.     

Estimation of eardrum acoustic pressure and of ear canal length from remote points in the canal

Sound pressure distributions in the human ear canal, whether unoccluded or occluded with ear molds, were studied using a probe tube technique. On average, for frequencies below 6 kHz, the measuring probe tube had to be placed within 8 mm of the vertical plane containing the top of the eardrum (TOD), determined optically, in order to obtain sound pressure magnitudes within 6 dB of "eardrum pressure." To obtain that accuracy in all of the eight subjects studied, the probe had to be within 6 mm of the TOD. Since probe location relative to the drum has to be known, a purely acoustic method was developed which can be conveniently used to localize the probe-tip position, utilizing the standing wave property of the sound pressure in the ear canal. The acoustically estimated "drum location" generally lay between the optically determined vertical planes containing the TOD and the umbo. On average, the "drum location" fell 1 mm medial to the TOD. Of the 32 estimates made acoustically in various occluded and unoccluded conditions in 14 subjects, 30 estimates lay within a +/- 2-mm range of this average.     

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.     

High-frequency plane waves in the ear canal: application of a simple asymptotic theory

An asymptotic theory describing the propagation of plane waves in a variable cross-section ear canal is combined with pressure measurements in order to determine the energy reflection coefficient at the eardrum and the standing wave patterns along the length of the canal. The relative phase of the reflected wave, and the cross-sectional area function of the ear canal, are also determined from the noninvasive pressure measurements. The theory is based on a high-frequency multiscale solution of the one-dimensional horn equation and is shown to agree well with the phase and amplitude of experimental measurements in human replica ear canals.     

Wideband reflectance tympanometry in normal adults.

Acoustic impedance/reflectance measurements were made at various ear-canal pressures in 20 subjects with a clinical acoustic immittance instrument and an experimental impedance/reflectance system. Measurements were made over a frequency range of 226-2000 Hz with the clinical system and 125-11,310 Hz with the experimental system. For frequencies < or = 2.0 kHz, tympanograms obtained with the two systems are similar, with patterns that progress through the same orderly sequence with increasing frequency. Eardrum impedance measurements were also similar. There are small gender differences in middle-ear impedance. Reflectance patterns (reflectance versus frequency) at ambient ear-canal air pressure are characterized by high reflectance at low frequencies, two district minima at 1.2 and 3.5 kHz, increasing reflectance to 8.0 kHz, and decreasing reflectance above that frequency. Ear-canal pressure increases reflectance at low frequencies, decreases reflectance in the region of the minimum, and increases reflectance slightly at high frequencies. Reflectance tympanograms (reflectance versus ear-canal pressure) progress through a sequence of three patterns. At low frequencies, reflectance tympanograms are "V" shaped, indicating that pressure increases reflectance. At frequencies near the minimum reflectance, the pattern inverts, indicating that pressure decreases reflectance. At high frequencies, the patterns are flat, indicating that ear-canal pressure has little effect. Results presented for one patient suggest that reflectance tympanometry may be useful for detecting middle-ear pathology.     

Frequency characteristics of sound transmission in middle ears from Norwegian cattle, and the effect of static pressure differences across the tympanic membrane and the footplate

For 23 cadaver ears from Norwegian cattle, frequency characteristics for the round-window volume displacement relative to the sound pressure at the eardrum have been measured, and are compared to earlier results for human ears [M. Kringlebotn and T. Gundersen, J. Acoust. Soc. Am. 77(1), 159-164 (1985)]. For human as well as for cattle ears, mean amplitude curves have peaks at about 0.7 kHz. At lower frequencies, the mean amplitude for cattle ears is about 5 dB smaller than for human ears. The amplitude curves cross at about 2 kHz, and toward higher frequencies the amplitude for cattle ears becomes increasingly larger. If amplitude curves are roughly approximated by straight lines above 1 kHz, the slope for cattle ears is about -5 dB/octave as compared to about -15 dB/octave for human ears. The phase of the round-window volume displacement lags behind the phase of the sound pressure at the tympanic membrane. The phase lag is close to zero below 0.2 kHz, but increases to about 3.5 pi at 20 kHz for cattle ears, as compared to less than 2 pi for human ears. Further investigations are needed in order to explain the observed differences. Sound transmission in the ear decreases with an increasing static pressure difference across the tympanic membrane, especially at frequencies below 1 kHz, where pressure differences of 10 and 60 cm water cause mean transmission losses of about 10 and 26 dB, respectively, the losses being somewhat larger for overpressures than for underpressures in the ear canal. At higher frequencies, the transmission losses are smaller. For small overpressures, and in a limited frequency range near 3 kHz, even some transmission enhancement may occur. Static pressure variations in the inner ear have only a minor influence on sound transmission. Static pressures relative to the middle ear in the range 0-60 cm water cause mean sound transmission losses less than 5 dB below 1 kHz, and negligible losses at higher frequencies.     

Stable multibubble sonoluminescence bubble patterns

Multibubble standing wave patterns can be generated from a flat piezoceramic transducer element radiating into water. By adding a second transducer positioned at 90 degrees from the transducer generating the standing wave, a 3-dimensional volume of stable single bubbles can be established. Further, the addition of the second transducer stabilizes the bubble pattern so that individual bubbles may be studied. The size of the bubbles and the separation of the standing waves depend on the frequency of operation. Two transducers, operating at frequencies above 500 kHz, provided the most graphic results for the configuration used in this study. At these frequencies stable bubbles exhibit a bright sonoluminescence pattern. Whereas stable SBSL is well-known, stable MBSL has not been previously reported. This paper includes discussions of the acoustic responses, standing wave patterns, and pictorial results of the separation of individual bubble sonoluminescence in a multibubble sonoluminescence environment.     

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 absorbed-sound power in the ear canal: application to suppression of stimulus frequency otoacoustic emissions

An insert ear-canal probe including sound source and microphone can deliver a calibrated sound power level to the ear. The aural power absorbed is proportional to the product of mean-squared forward pressure, ear-canal area, and absorbance, in which the sound field is represented using forward (reverse) waves traveling toward (away from) the eardrum. Forward pressure is composed of incident pressure and its multiple internal reflections between eardrum and probe. Based on a database of measurements in normal-hearing adults from 0.22 to 8 kHz, the transfer-function level of forward relative to incident pressure is boosted below 0.7 kHz and within 4 dB above. The level of forward relative to total pressure is maximal close to 4 kHz with wide variability across ears. A spectrally flat incident-pressure level across frequency produces a nearly flat absorbed power level, in contrast to 19 dB changes in pressure level. Calibrating an ear-canal sound source based on absorbed power may be useful in audiological and research applications. Specifying the tip-to-tail level difference of the suppression tuning curve of stimulus frequency otoacoustic emissions in terms of absorbed power reveals increased cochlear gain at 8 kHz relative to the level difference measured using total pressure.     

Development of an electroacoustic analogue model of the middle ear and acoustic reflex

Experimental measurements of changes in the acoustic admittance of the eardrum caused by stapedius muscle contractions in human subjects are used to develop and electroacoustic analogue model of the middle ear. In this model the stapedius muscle is included as an explicit functional unit. The acoustical characteristics of the external ear canal are also included. The model is extensively evaluated by comparing its properties with the known characteristics of real ears of humans and other animals. Subsequently, the model is used to predict the effects of the acoustic reflex on middle ear sound transmission, which cannot easily be measured in humans. The model predicts attenuation of potentially hazardous high level sounds at frequencies below 1 kHz of up to about 10 dB, but very little effect at higher frequencies unless the reflex-eliciting stimulus is of sufficient intensity to cause partial disarticulation of the incudo-stapedial joint by stapedius muscle contraction. Overall attenuation for typical industrial noises is unlikely to be greater than approximately 3 dB(A) and will probably be even less in practice, resulting in little effective protection from the harmful effects of high intensity noise. It is considered that the model will be of benefit in the analysis of middle ear function, including the interpretation of audiological measurements of eardrum impedance and acoustic reflex response. This should lead to more versatile diagnosis of peripheral auditory dysfunction than has been possible hitherto.     

Wave model of the cat tympanic membrane

In order to better understand signal propagation in the ear, a time-domain model of the tympanic membrane (TM) and of the ossicular chain (OC) is derived for the cat. Ossicles are represented by a two-port network and the TM is discretized into a series of transmission lines, each one characterized by its own delay and reflection coefficient. Volume velocity samples are distributed along the ear canal, the eardrum, and the middle ear, and are updated periodically to simulate wave propagation. The interest of the study resides in its time-domain implementation--while most previous related works remain in the frequency domain--which provides not only a direct observation of the propagating wave at each location, but also insight about how the wave behaves at the ear canal/TM interface. The model is designed to match a typical impedance behavior and is compared to previously published measurements of the middle ear (the canal, the TM, the ossicles and the annular ligament). The model matches the experimental data up to 15 kHz.     

High-frequency audiometric assessment of a young adult population

The hearing thresholds of 37 young adults (18-26 years) were measured at 13 frequencies (8, 9,10,...,20 kHz) using a newly developed high-frequency audiometer. All subjects were screened at 15 dB HL at the low audiometric frequencies, had tympanometry within normal limits, and had no history of significant hearing problems. The audiometer delivers sound from a driver unit to the ear canal through a lossy tube and earpiece providing a source impedance essentially equal to the characteristic impedance of the tube. A small microphone located within the earpiece is used to measure the response of the ear canal when an impulse is applied at the driver unit. From this response, a gain function is calculated relating the equivalent sound-pressure level of the source to the SPL at the medial end of the ear canal. For the subjects tested, this gain function showed a gradual increase from 2 to 12 dB over the frequency range. The standard deviation of the gain function was about 2.5 dB across subjects in the lower frequency region (8-14 kHz) and about 4 dB at the higher frequencies. Cross modes and poor fit of the earpiece to the ear canal prevented accurate calibration for some subjects at the highest frequencies. The average SPL at threshold was 23 dB at 8 kHz, 30 dB at 12 kHz, and 87 dB at 18 kHz. Despite the homogeneous nature of the sample, the younger subjects in the sample had reliably better thresholds than the older subjects. Repeated measurements of threshold over an interval as long as 1 month showed a standard deviation of 2.5 dB at the lower frequencies (8-14 kHz) and 4.5 dB at the higher frequencies.     

Frequency characteristics of the middle ear

For 68 temporal bones, frequency curves for the round window volume displacement have been measured for a constant sound pressure at the eardrum. Phase curves were measured for 33 of the specimens. The levels averaged amplitude curve is approximately flat below 1 kHz, where the round window volume displacement per unit sound pressure at the eardrum is 6.8 X 10(-5) mm3/Pa, and falls off by about 15 dB/oct at higher frequencies. For the 20 ears having the largest sound transmission magnitude at low frequencies, the corresponding amplitude curve is displaced about 5 dB towards higher levels. The phase of the round window volume displacement lags the eardrum sound pressure phase. In average for 33 temporal bones, the phase lag increases from zero at the lowest frequencies to pi near 2 kHz and to about 1.5 pi at 10 kHz.     

Distribution of standing-wave errors in real-ear sound-level measurements

Standing waves can cause measurement errors when sound-pressure level (SPL) measurements are performed in a closed ear canal, e.g., during probe-microphone system calibration for distortion-product otoacoustic emission (DPOAE) testing. Alternative calibration methods, such as forward-pressure level (FPL), minimize the influence of standing waves by calculating the forward-going sound waves separate from the reflections that cause errors. Previous research compared test performance (Burke et al., 2010) and threshold prediction (Rogers et al., 2010) using SPL and multiple FPL calibration conditions, and surprisingly found no significant improvements when using FPL relative to SPL, except at 8 kHz. The present study examined the calibration data collected by Burke et al. and Rogers et al. from 155 human subjects in order to describe the frequency location and magnitude of standing-wave pressure minima to see if these errors might explain trends in test performance. Results indicate that while individual results varied widely, pressure variability was larger around 4 kHz and smaller at 8 kHz, consistent with the dimensions of the adult ear canal. The present data suggest that standing-wave errors are not responsible for the historically poor (8 kHz) or good (4 kHz) performance of DPOAE measures at specific test frequencies.     

Boundary element modeling of the external human auditory system

In this paper the response of the external auditory system to acoustical waves of varying frequencies and angles of incidence is computed using a boundary element method. The resonance patterns of both the ear canal and the concha are computed and compared with experimental data. Specialized numerical algorithms are developed that allow for the efficient computation of the eardrum pressures. In contrast to previous results in the literature that consider only the "blocked meatus" configuration, in this work the simulations are conducted on a boundary element mesh that includes both the external head/ear geometry, as well as the ear canal and eardrum. The simulation technology developed in this work is intended to demonstrate the utility of numerical analysis in studying physical phenomena related to the external auditory system. Later work could extend this towards simulating in situ hearing aids, and possibly using the simulations as a tool for optimizing hearing aid technologies for particular individuals.     

On the undamped natural frequencies and mode shapes of a finite-element model of the cat eardrum

This paper presents a three-dimensional finite-element model of the cat eardrum which includes inertial effects. The model is implemented using a hierarchical modeling scheme which permits the mesh resolution to be varied. The static behavior of the model is calculated as a function of mesh resolution in order to check the validity of an earlier model. The first six undamped natural frequencies, and the corresponding modal vibration patterns, are then calculated. They are found to lie between about 1.8 and 3.2 kHz for the standard values chosen for the model parameters. The effects on the natural frequencies of varying seven parameters of the model are described.     

Influence of in situ, sound-level calibration on distortion-product otoacoustic emission variability

Standing waves can cause errors during in-the-ear calibration of sound pressure level (SPL), affecting both stimulus magnitude and distortion-product otoacoustic emission (DPOAE) level. Sound intensity level (SIL) and forward pressure level (FPL) are two measurements theoretically unaffected by standing waves. SPL, SIL, and FPL in situ calibrations were compared by determining sensitivity of DPOAE level to probe-insertion depth (deep and "shallow") for a range of stimulus frequencies (1-8 kHz) and levels (20-60 dB). Probe-insertion depth was manipulated with the intent to shift the frequencies with standing-wave minima at the emission probe, introducing variability during SPL calibration. The absolute difference in DPOAE level between insertions was evaluated after correcting for an incidental change caused by the effect of ear-canal impedance on the emission traveling from the cochlea. A three-way analysis of variance found significant main effects for stimulus level, stimulus frequency, and calibration method, as well as significant interactions involving calibration method. All calibration methods exhibited changes in DPOAE level due to the insertion depth, especially above 4 kHz. However, SPL demonstrated the greatest changes across all stimulus levels for frequencies above 2 kHz, suggesting that SIL and FPL provide more consistent measurements of DPOAEs for frequencies susceptible to standing-wave calibration errors.