Michael R. Stinson

The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross-sectional shape

The general Kirchhoff theory of sound propagation in a circular tube is shown to take a considerably simpler form in a regime that includes both narrow and wide tubes. For tube radii greater than rw=10−3 cm and sound frequencies f such that rwf3/2<106 cm s−3/2, the Kirchhoff solution reduces to the approximate solution suggested by Zwikker and Kosten. In this regime, viscosity and thermal conductivity effects are treated separately, within complex density and complex compressibility functions. The sound pressure is essentially constant through each cross section, and the excess density and sound pressure (when scaled by the equilibrium density and pressure of air, respectively) are comparable in magnitude. These last two observations are assumed to apply to uniform tubes having arbitrary cross‐sectional shape, and a generalized theory of sound propagation in narrow and wide tubes is derived. The two‐dimensional wave equation that results can be used to describe the variation of either particle velocity or...

Propagation of sound and the assignment of shape factors in model porous materials having simple pore geometries

The acoustical properties of a class of simple porous materials have been studied experimentally and theoretically. Rigid‐frame materials containing air‐filled pores of uniform cross section were investigated. Two model porous materials were constructed, one with pores of rectangular cross section (0.0146×0.0172 cm) and one with pores of triangular cross section (0.037‐cm sides). The characteristic impedance and propagation constant were measured for frequencies between 50 and 4500 Hz and good agreement with exact theoretical predictions was obtained. The exact theoretical expressions for specific pore shapes (e.g., slitlike, square, and triangular) can be used to investigate the assignment of shape factors by various general but approximate theoretical models. It is demonstrated that the model introduced by Attenborough requires a shape factor that is frequency dependent. A theoretical model, appropriate for materials containing pores of uniform cross section, that correctly treats the low‐ and high‐freq...

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.

On acoustical models for sound propagation in rigid frame porous materials and the influence of shape factors

The propagation of sound in rigid‐frame porous materials saturated with air is studied experimentally and theoretically. Two existing theoretical models, the Attenborough and the Biot–Allard models, are first evaluated using measured characteristic impedances and propagation constants for samples of ceramic material. The Biot–Allard model is found to give good agreement to the measured data if a single, frequency‐independent shape factor is introduced. The Attenborough model, though, requires a shape factor that has a significant frequency dependence. To provide a more stringent test, we have constructed a model porous material that has large variations in pore cross‐sectional area. This sample contains 373 straight cylindrical pores whose diameters alternate between 0.025 and 0.154 cm along their lengths. Both the Biot–Allard and Attenborough models are unable to describe the measured acoustical properties for this sample. A simple theoretical model is proposed that describes the propagation of sound thr...

Air‐based system for the measurement of porosity

An experimental system for the measurement of porosity, the volume fraction of air contained in a material, is described. Porosity is important as one of several parameters required by acoustical theory to characterize a porous material. As with the technique described by Beranek [J. Acoust. Soc. Am. 13, 248–260 (1942)], the isothermal pressure change in a closed volume containing a sample material is measured for a known change in the volume. The volume of air contained in the sample, and hence the porosity, is inferred from these two quantities. The new system, though, avoids the use of liquids, either directly in the technique or for temperature stabilization. Instead, a piston of accurately known diameter is used to produce the change in volume, and the change in pressure is measured with an electronic pressure transducer. Model calculations and measurements on real materials confirm that porosity can be measured rapidly and conveniently with this apparatus, with an accuracy of better than 1% over a b...

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.

Porous road pavements: Acoustical characterization and propagation effects

Measurements of the acoustical properties of some porous road pavements are presented here and an acoustical method for monitoring the performance of these surfaces is presented. Porous road pavements have been used previously because of their driving qualities and drainage capacities during rainy days (i.e., the elimination of water splash and spray) but they have also been found to reduce traffic noise substantially. Reductions in A-weighted sound levels of 3–5 dB, compared to a dense pavement structure, have been measured. To study further their acoustical performance, measurements over real road surfaces have been carried out and the results compared to theoretical predictions based upon models describing the surface impedance and sound propagation. For the impedance characterization, both a phenomenological and a microstructural model were used. Both approaches introduce a viscous and a thermal dependence to account for the different phenomena inside the porous structure. By incorporating these model...

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.

Electronic system for the measurement of flow resistance

A measurement system has been developed that can determine flow resistances quickly and accurately and can be used to complement acoustical measurements on the same samples. The use of electronic components permits measurements to be made 20–50 times faster than with the commonly used Leonard apparatus. Variable‐capacitance pressure transducers are used to measure pressure differences across both the test sample and a laminar flow element with known flow resistance (these two in series): For steady nonpulsating flow, the ratio of flow resistances equals the ratio of measured pressure differences. The rate of air flow through the sample is adjusted using a mass flow controller; flows of 10−3–1 cm3 s−1 can be controlled to better than 1%. Flow resistances between 1 and 105 g cm−4 s−1 can be determined with an accuracy of better than 1.6%. The corresponding range of flow resistivities of porous materials that can be determined with the present sample holder is 1–106 cgs‐rayl cm−1. Initial measurements have b...

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.