Free-field Pressure Research Articles

Output Levels of Commercially Available Portable Compact Disc Players and the Potential Risk to Hearing

To measure the sound levels generated by the headphones of commercially available portable compact disc players and provide hearing healthcare providers with safety guidelines based on a theoretical noise dose model. Using a Knowles Electronics Manikin for Acoustical Research and a personal computer, output levels across volume control settings were recorded from headphones driven by a standard signal (white noise) and compared with output levels from music samples of eight different genres. Many commercially available models from different manufacturers were investigated. Several different styles of headphones (insert, supra-aural, vertical, and circumaural) were used to determine if style of headphone influenced output level. Free-field equivalent sound pressure levels measured at maximum volume control setting ranged from 91 dBA to 121 dBA. Output levels varied across manufacturers and style of headphone, although generally the smaller the headphone, the higher the sound level for a given volume control setting. Specifically, in one manufacturer, insert earphones increased output level 7-9 dB, relative to the output from stock headphones included in the purchase of the CD player. In a few headphone-CD player combinations, peak sound pressure levels exceeded 130 dB SPL. Based on measured sound pressure levels across systems and the noise dose model recommended by National Institute for Occupational Safety and Health for protecting the occupational worker, a maximum permissible noise dose would typically be reached within 1 hr of listening with the volume control set to 70% of maximum gain using supra-aural headphones. Using headphones that resulted in boosting the output level (e.g., insert earphones used in this study) would significantly decrease the maximum safe volume control setting; this effect was unpredictable from one manufacturer to another. In the interest of providing a straightforward recommendation that should protect the hearing of the majority of consumers, reasonable guidelines would include a recommendation to limit headphone use to 1 hr or less per day if using supra-aural style headphones at a gain control setting of 60% of maximum.

Lateral Loaded Pile Response in Liquefiable Soil

This paper provides a new analysis procedure for assessing the lateral response of an isolated pile in saturated sands as liquefaction develops in response to dynamic loading such as that generated during earthquake shaking. This new procedure predicts the degradation in pile response and soil resistance due to the free-field excess porewater pressure generated by the earthquake, along with the near-field excess porewater pressure generated by lateral loading from the superstructure. The new procedure involves the integration of the developing (free- and near-field) porewater pressure in the strain wedge (SW) model analysis. The current SW model, developed to evaluate drained response (a nonlinear three-dimensional model) of a flexible pile in soil, has been extended in this paper to incorporate the undrained response of a laterally loaded pile in liquefied sand. This new procedure has the capability of predicting the response of a laterally loaded isolated pile and the associated modulus of subgrade reaction (i.e., the p-y curve) in a mobilized fashion as a result of developing liquefaction in the sand. Current design procedures assume slight or no resistance for the lateral movement of the pile in the liquefied soil which is a conservative practice. Alternatively, if liquefaction is assessed not to occur, some practitioners take no account of the increased free-field porewater pressure, and none consider the additional near-field porewater pressure due to inertial interaction loading from the superstructure; a practice that is unsafe in loose sands.

Lateral Loaded Pile Response in Liquefiable Soil

This paper provides a new analysis procedure for assessing the lateral response of an isolated pile in saturated sands as liquefaction develops in response to dynamic loading such as that generated during earthquake shaking. This new procedure predicts the degradation in pile response and soil resistance due to the free-field excess porewater pressure generated by the earthquake, along with the near-field excess porewater pressure generated by lateral loading from the superstructure. The new procedure involves the integration of the developing (free- and near-field) porewater pressure in the strain wedge (SW) model analysis. The current SW model, developed to evaluate drained response (a nonlinear three-dimensional model) of a flexible pile in soil, has been extended in this paper to incorporate the undrained response of a laterally loaded pile in liquefied sand. This new procedure has the capability of predicting the response of a laterally loaded isolated pile and the associated modulus of subgrade reaction (i.e., the p-y curve) in a mobilized fashion as a result of developing liquefaction in the sand. Current design procedures assume slight or no resistance for the lateral movement of the pile in the liquefied soil which is a conservative practice. Alternatively, if liquefaction is assessed not to occur, some practitioners take no account of the increased free-field porewater pressure, and none consider the additional near-field porewater pressure due to inertial interaction loading from the superstructure; a practice that is unsafe in loose sands.

Patterns of wall pressure on filling a square planform steel silo

This paper reports the filling pressures measured in a rectangular planform silo with flexible walls. Many experiments were conducted on a pilot-scale square unstiffened steel silo with a pyramidal hopper. The stress state in the solid stored in the silo was thoroughly investigated during filling using both wall pressure cells and free field pressure cells. The results show that the pressure distribution at any given depth at the end of filling may be far from uniform, though most existing silo pressure theories and design codes assume uniformity in any horizontal plane. High pressures were found to develop in the corners of the silo, with corresponding lower pressures at the centre of the walls. An explanation is offered for the observed pressure pattern and a design proposal is made.

Foam diagram summation at finite temperature

We show that large- N φ 4 theory is not trivial if one accepts the presence of a tachyon with a truly huge mass, and that it allows exact calculation. We use it to illustrate how to calculate the exact resummed pressure at finite temperature and verify that it is infrared and ultraviolet finite even in the zero-mass case. In three dimensions a residual effect of the resummed infrared divergences is that at low temperature or strong coupling the leading term in the interaction pressure becomes independent of the coupling and is 4 5 of the free-field pressure. In four dimensions the pressure is well defined provided that the temperature is below the tachyon mass. We examine how rapidly this expansion converges and use our analysis to suggest how one might reorganise perturbation theory to improve the calculation of the pressure for the QCD plasma.

Generation and growth of bilayer defects induced by ultrasound.

Transdermal drug delivery is handicapped by the low skin permeability caused by highly ordered structure of lipid bilayers in the outer human skin layer. It has been reported that ultrasound can increase the permeability of human skin. The enhancement was attributed to acoustic cavitation but the underlying physical mechanism is not fully understood. As a model, dipalmitoylphosphatidylcholine (DPPC) lipid bilayers are insonicated by ultrasound of two submegahertz frequencies (168 kHz and 707 kHz). The free-field spatial peak pressure amplitudes of both are measured to be 6×105 Pa. Bilayer defects, which have average diameters of tens to hundreds of nanometers and can be detected by an atomic force microscope, are generated within less than 0.5 min. The number of the defects grows with time. The defect growth rate at the 168-kHz frequency is about 3.5 times that at the 707-kHz frequency.

The effect of polypropylene vials on lithotripter shock waves

In studies to understand the mechanisms responsible for shock wave lithotripsy (SWL) cell injury, we observed that shock waves (SWs) are influenced by the shape of the specimen vial. Lytic injury to kidney cells treated in a Dornier HM3 lithotripter was higher ( p < 0.0001) when SWs entered the vial through the flat end (cap end) compared to the round end. Measurements of the acoustic field within polypropylene vials were carried out using both lithotripter SWs and pulsed ultrasound (US) in the megahertz frequency range. We compared pressure amplitudes inside the round and flat vials and found significant differences. When SWs entered through the round end, the average peak positive pressure was 40% of free-field pressure, due mostly to a dramatic reduction in pressure off axis. The average peak pressure inside the flat vial was twice that of the round vial. Experiments with US demonstrated that sound field focusing was induced by the curved interface of the round vial. Ray analysis for the round vial indicates the presence of “hot spots” on axis and “cold spots” off axis, in qualitative agreement with pressure profiles. We conclude that the shape of the specimen vial is an important factor that should be considered in model systems of SWL cell injury.

Integrated mathematical model of the ear. I. Free-field pressure to basilar membrane displacements

In order to provide insight into the processes operative in the ear, especially at high sound pressure levels, an integrated mathematical model of the ear has been produced. The model’s electroacoustic elements are conformal with the strucure of the ear, which promotes physical insight. For maximum utility the model is menued to allow parameter changes by the user. Mathematically, the model is equations of motion formulated as a system of coupled ordinary differential equations, which allow both linear and nonlinear claculations in the time domain. The ‘‘Q’’ of the basilar membrane is not constant and the range is selectable. The systems are linear, except at very high SPLs (130+dB) where the stapes becomes nonlinear. Input to the model is any 4096-point free-field pressure or pressure at the ear drum. Outputs are standardly numerical files of stapes displacements and basilar membrane displacements at any number of evenly spaced user-selected places. As a final output the model makes a ‘‘movie’’ of the basilar membrane displacements coordinated with the pressure history, which shows the effect of each part of the waveform.

Properties of superresonant systems of spherical scatterers

Systems of identical precisely spaced bubbles or similar monopole scatterers in water-e.g., inflated balloons or thin-walled shells-insonified at frequencies <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{SR}</tex> dose to their fundamental radial resonance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{0}</tex> (bubble) frequency may themselves display resonance modes or superresonances (SR's) [1]. Ordinary single-bubble resonances magnify the local free-field pressure amplitude <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p_{1}</tex> by a factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ka)^{-1}</tex> , <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</tex> being the radius and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> the wavenumber in water: for air bubbles or balloons in water, this factor is of the order of 70. Under SR conditions each member of the system amplifies the local free-field amplitude by a further factor of order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ka)^{-1}</tex> . Depending upon geometry and other constraints, the pressure field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_{SR}</tex> on the surface and in the interior of each scatterer will then be in the range of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10^{3}p_{1}</tex> to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5 \times 10^{3} p_{1}</tex> . This paper investigates the sensitivity of this phenomenon to small departures from the ideal model. In particular, it examines the effect of small differences in scatter positioning and volumes in the context of an SR system consisting of two bubbles/balloons close to the boundary of a thin elastic plate overlying a fluid half-space. It is found that, to observe the SR phenomenon, radii and positions should be controlled to within approximately 1/2 percent. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_{SR}</tex> is also sensitive to the angle of incidence of the plane wave train. For the simple system examined here, this sensitivity is considerable for either flexural wave trains or volume acoustic waves incident upon the bubble/ balloon pair (doublet). Practical uses of the phenomenon may range from the design of passive high- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> acoustical filter/amplifiers and acoustical lenses to improved source efficiencies.

Sound levels from personal cassette players.

Techniques have been devised whereby the levels at which users of personal cassette players listen to tape-recorded sounds through lightweight headphones may be measured and expressed in terms of free-field equivalent continuous A-weighted sound pressure levels. Data have been obtained on over 60 users of such devices who variously listened, in laboratory and field conditions, to music and speech against quiet and noisy backgrounds. The results have been interpreted in terms of noise exposure. Comparison with damage risk criteria indicates that 5% of the sample are listening in such a manner that habitual use would constitute a damage risk to hearing.

Mathematical model of the effect of limited stapes displacement on hazard from intense sounds

As a follow-on to an idea presented earlier [G. R. Price, J. Acoust. Soc. Am. 56, 195–197 (1974)] an integrated mathematical model of the external, middle, and inner ears has been developed for the cat ear. It allows the calculation of stapes displacements (among other values) in response to any free-field sound pressure. An absolute limit to displacement of about 20 μ peak to peak is assumed, based on the dimensions of the annular ligament and in accord with the measurements of Guinan and Peake [J. Acoust Soc. Am. 41, 1237–1261 (1967)]. Where hazard from intense impulses, such as gunfire, are concerned, the effect of this limitation on stapes displacement is profound, producing a spectral bias (higher velocities being transmitted at high frequencies) as well as the blocking of transmission into the cochlea when amplitudes exceed the limiting values. This action may in part explain why low-frequency impulses are much less hazardous than their energy content would seem to indicate as well as why hearing losses are not more severe for very intense sounds (150 dB and up) commonly found around weapons.

Interactive approximations for a cavitating fluid around a floating structure

A method is investigated for determining the response of floating structures to underwater explosions strong enough to cause bulk cavitation. In such problems the difference between the actual and free field pressures on any surface surrounding the structure and cavitated region is related to the corresponding velocity differences by a linear functional relation. In this paper, it is proposed that approximate functionals, called interactive approximations, be applied on these surfaces, called interaction horizons. In the limit, the interaction horizon can be taken as the wet surface of the structures, eliminating the consideration of fluid field equations. The technique is applied to the two-dimensional problem of a rigid rectangular structure, floating on a fluid with a bilinear constitutive relation, subjected to a plane, exponentially decaying wave having an angle of incidence. First the exact solution of the nonlinear, steady state, free field problem, including determination of the cavity, is obtained by the method of characteristics. Then the interaction problem is solved by finite differences, using both plane wave and doubly asymptotic interactive approximations, at interaction horizons and on the wet surface. When an interaction horizon is used, Lax's one-dimensional scheme is modified to discretize the fluid equations. It is found that, for this example, the plane wave approximation applied directly to the wet surface is sufficiently accurate to determine structural response.

An analytical solution for underground structure-country rock dynamic interaction

In this paper according to the results of a great quantity of tests and numerical calculations, it is pointed out that the surrounding rock with thickness of 1/3 span has mechanical characteristics of a thick flexural member in underground rock cave subjected to transverse blast loading. However, it approaches the stress state of free field outside country rock and the equation of thick plate theory under the loading of free field pressure may be applied to the solution of this problem. Therefore, the underground structure-country rock dynamic interaction may be described by dynamic equations of flexural members of thin plate and thick plate, which express linear and country rock respectively. The interaction force between the liner and country rock is expressed as contacting pressure function q(x, l). By solving system of simultaneous equations, the analytical solution for the dynamic analysis of arch-straight liner including elastic half space interaction effect is given and the analytical expression of function q(x, t) is obtained. This analytic solution will contribute to the study of some substantive problems of underground structure-medium dynamic interaction theoretically.

Diffraction constants for pressure gradient transducers

Conventionally the diffraction constant D of a receiving transducer (microphone or hydrophone) is defined as the ratio of the average sound pressure acting on the blocked diaphragm to the free-field sound pressure. This definition is inadequate for transducers that have complex vibration patterns, and, in the absence of ad hoc modifications, it will fail to give the correct results for pressure gradient transducers. A new definition based on the general theory of transducers with fixed velocity distributions is therefore introduced. The diffraction constant is assigned not only the function of accounting for scattered wave effects but also the function of extracting from the surface pressure distribution the component that drives the velocity distribution (or vibration pattern) of the transducer. The diffraction constant depends on the choice of the reference velocity that is associated with the acoustic port of the transducer. A spatial rms reference velocity is defined, and it is shown to be a suitable reference for pressure gradient transducers. Calculation of the diffraction constant is carried out for the following piezoelectric pressure gradient hydrophones: a flexural disk supported inside an annular mass, an end supported flexural bar, a cantilever bar, an oscillating rigid cylinder, and an oscillating rigid sphere. The use of the diffraction constant in conjunction with the electroacoustic circuit of the hydrophone to calculate voltage receiving response is described, and the circuit information needed to illustrate the procedure is given for the flexural disk hydrophone.

Procedure for evaluating a reflection-reduction coating

A new method for utilizing recent new results of the classical solution to the problem of reflection by a two-layer cylindrical shell has been devised for the determination of the material properties of a reflection-reduction coating. In that solution, both layers or either layer may have inherent wave attenuations. A measurement of the incident and reflected free-field pressure amplitudes must be made and elastic constants must be known that define all materials involved except the layer of material whose reflection-reduction properties are sought. A method of least-squares fitting of the exact theory to the measured data will allow determination of the lognitudinal- and shear-wave speeds and their attenuations. Measurements at a given frequency range and cylinder size can be confidently extrapolated to other frequencies or cylindrical curvatures. Defined quantities such as impedance can be determined once the longitudinal- and shear-wave speeds are known.

On the sound pressure transformation by the head and auditory meatus of the cat.

Anesthetized cats were supported by a canvas cradle in a sound-proof chamber and were exposed to a progressive sound wave. A flexible probe microphone was implanted in the external auditory meatus and used to measure the sound pressure in the vicinity of the eardrum. A duplicate probe was used to measure the sound pressure at a point near the center of the cat's head in the absence of the animal. From these measurements the magnitude of the ratio of the sound pressure near the eardrum to that in the free field was determined as a function of frequency. When the ear under study was turned toward the sound source, the sound pressure near the eardrum exceeded the free-field pressure appreciably, except at very low frequencies. By measuring the sound pressure near the tragus, the resonance of the external auditory meatus itself could be determined. The data obtained in this study can be used to compare results of experiments in which the acoustic stimulus is measured in terms of free-field pressures with those in which the stimulus is measured in terms of the sound pressure near the eardrum.

Reverberation Measurements of Narrow-Band Noise Power in a Water Tank

Radiated noise power may be measured in reverberant water tanks by methods analogous to those used in air chambers. In underwater applications, narrow-band noise-power measurements are of particular interest but present a special problem because of difficulty in achieving adequate diffusion of the reverberant field. Consequently, a greater number of field points must be sampled to establish average energy density with good precision. The required number depends upon the statistical distribution of mean-squared pressure. This distribution was measured in a rectangular metal tank 1012×5×512 ft with noise bandwidth, center frequency, and tank absorption as parameters. One finding is that distribution variance diminishes as bandwidth increases toward a critical value. At greater bandwidths, variance is nearly unchanged. These results were applied in related experiments to measure power radiated by an LC32 hydrophone driven with narrow bands of noise. Measured power was used to predict freefield pressure, which was then measured for comparison purposes. [This work was sponsored by the U. S. Navy Bureau of Ships.]

Diffraction Constants of Transducers

The concept of a transducer diffraction constant as the ratio of the blocked diaphragm pressure to the incident free-field pressure is examined for meaning, definition, and application in the general case. The concept is extended to a transmitting transducer, and a transmitting diffraction constant that is equal in value but reciprocal in concept to the conventional or receiving constant is developed from the acoustical reciprocity theorem. The relationship among the diffraction constant D, the radiation resistance R, and the directivity factor δ is given as D2 = Rδ/R0, where R0 is the radiation resistance of a simple source. The electrical analog of the diffraction constant D is found to be an ideal transformer with the turns ratio D:1. The electrical analog of a complete and reciprocal projector medium hydrophone system is presented.

Estimating Structural Response to Noise

Expressions are given for estimating the rms response of a general mechanical structure, vibrating in individual modes, when exposed to noise. The noise field is characterized by the free-field rms sound pressure. Linearity is assumed in air and structure. The principles of reciprocity and superposition are employed. As an extreme case, it is assumed that all damping is due to radiation to the far field. The mean square velocity for a uniform distribution of sources (alternatively, the ensemble average for all angles of incidence) is particularly simple; for given sound spectrum level, it varies inversely with modal stiffness but is independent of the acoustic-mechanical coupling. Under the same assumptions, the mean square dynamic strains in fundamental modes of plates. designed to the same static strain under fixed pressurization, are approximately proportional to spectral density of free-field noise multiplied by mass and divided by the square of surface area. Modifications for other conditions are discussed. (Supported by Wright Air Development Division.)

The Diffraction of Sound by Rigid Disks and Rigid Square Plates

A rigid circular plate was exposed to an essentially plane progressive sound wave, and the sound pressure p at various points on the surface measured relative to the free-field pressure p0 in the undisturbed incident wave by means of a small probe microphone. The diffraction effect |p/p0| was determined as a function of angle of incidence over a range of frequencies beginning with “long” wave-lengths and extending into the region where the radius a of the obstacle approximately equals the wave-length. Expressed in customary notation, 14 &amp;lt; ka &amp;lt; 8, where k is the wave number of the incident wave. Data were obtained for angles of incidence θ = 0, 45, 135, and 180 degrees, where θ is measured with respect to the axis of the obstacle. Similar measurements for θ = 0 and 180° were made for a rigid square plate with side 2a. Approximate contour maps of the quantity |p/p0| in decibels have been prepared from the experimental data portraying the pressure distribution on the surface of the plates. The experimental results are compared with computed values of |p/p0| obtained from an approximate theory in which an attempt is made to solve the problem in terms of a scattered potential calculated as if the face of the obstacle were surrounded by an infinite baffle. The agreement is quite good on the “illuminated” side of the plates, i.e., for θ = 0 and 45° and on the “shadow” side for θ = 180°. The agreement for 135 degree incidence is generally poor, although the computed values show the trends of the experimental data in many instances. At low frequencies the theory gives values which are somewhat too high on the illuminated side and too low on the shaded side. The values of |p/p0| obtained from the exact expression of the diffraction of a plane wave by a disk of zero thickness and for perpendicular incidence are found to be in good agreement with experiment and the approximate theory on the illuminated side (θ = 0) and they agree reasonably well on the shaded side (θ = 180°) for 1⩽ka⩽5. The region near the edge shows discrepancies which are to be expected from the finite thickness of the circular plate (approx. a/12). It is concluded that the approximate theory mentioned above is capable of predicting the diffraction effect |p/p0| on the illuminated side of the obstacles in the frequency range covered by this study for the angles of incidence investigated. On the shadow side the theory can be expected to yield usably approximate answers only for θ = 180°. There are reasonable grounds for the assumption that similar predictions can be made for points on or “near” the surface of “thin” plane obstacles of arbitrary shape and for other acute angles of incidence not too close to θ = 90°.