Volume 79, Issue 6, June 1986
Index of content:

Methods of measuring the attenuation of hearing protection devices
View Description Hide DescriptionThe published literature describing three real‐ear‐attenuation‐at‐threshold (REAT), nine above‐threshold, and four objective methods of measuringhearing protector attenuation is reviewed and analyzed with regard to the accuracy, practicality, and applicability of the various techniques. The analysis indicates that the REAT method is one of the most accurate available techniques since it assesses all of the sound paths to the occluded ear and, depending upon the experimenter’s intention, can reflect actual in‐use attenuation as well. An artifact in the REAT paradigm is that masking in the occluded ear due to physiological noise can spuriously increase low‐frequency (≤500 Hz) attenuation, although the error never exceeds approximately 5 dB, regardless of the device, except below 125 Hz. Since the preponderance of available data indicates that attenuation is independent of sound level for intentionally linear protectors, the use of above‐threshold procedures to evaluate attenuation is not a necessity. An exception exists in the case of impulsive noises, for which the existing data are not unequivocal with regard to hearing protector response characteristics. Two of the objective methods (acoustical test fixture and microphone in real ear) are considerable time savers. All objective procedures are lacking in their ability to accurately determine the importance of the flanking bone‐conduction paths, although some authors have incorporated this feature as a post‐measurement correction. The microphone in real‐ear approach is suggested to be one of the most promising for future standardization efforts and research purposes, and the acoustical test fixture technique is recommended (with certain reservations) for quality control and buyer acceptance testing.

Diffraction of Rayleigh waves in a half‐space. II. Inclined edge crack
View Description Hide DescriptionThis paper is concerned with the diffraction of a Rayleigh surface wave by an edge crack included at an arbitrary angle to the free surface of a half‐space. The corresponding problem for a normal edge crack was studied in [B. Q. Vu and V. K. Kinra, J. Acoust. Soc. Am. 7 7, 1425–1430 (1985)]. The scattered field was measured on the free surface both in the vicinity of the crack and far away from it. The nearfield possesses a number of interesting features which can be used to characterize an inclined crack. The farfield transmission and reflection coefficients,A _{ T } and A _{ R }, respectively, were measured under both the steady time‐harmonic motion (tone burst) and the transient motion (spectroscopy) of the half‐space. All three regions of interest were studied: wavelengths large, equal, and small compared to the crack lengths. As expected, in the short‐wavelength limit, A _{ R } asymptotically reaches its frequency‐independent limit which is the reflection coefficient of an infinite wedge. This limit was found to agree very well with the earlier results by Viktorov for a wedge [I. A. Viktorov, R a y l e i g h W a v e s a n d L a m b W a v e s—P h y s i c a l T h e o r y a n d A p p l i c a t i o n (Plenum, New York, 1964)]. The transmission coefficient exhibits an oscillatory dependence on frequency; this is attributed to a resonance between the crack tip and the free surface. The spacing between the peaks of A _{ T } was found to satisfy the following simple kinematic condition: wavelength equals twice the crack length. Furthermore, A _{ T } was found to be measurably identical for two complementary cracks of inclination θ and π−θ, where θ is measured from the free surface.

Sound scattering from a thin rod in a viscous medium
View Description Hide DescriptionSoundwaves incident on a thin elastic rod whose radius is smaller than the wavelength of the incident sound induce flexural and uniform compressional oscillations in the rod. These elastic oscillations, in turn, radiate soundwaves into the fluid medium and affect the scatteredwaves. This paper deals with an analytic study on sound scattering by, and acoustoelastic vibrations of, a thin elastic unbound rod in a viscous fluid. The shear viscosity of the fluid is considered in the solutions to boundary value problems concerning the sound scattering and the elastic response of the rod. Results show that the scattered compressional waves consist of the rigid‐rod scattering of compressional waves, monopolar waves due to the uniform pulsating of the rod, and dipolar waves due to the flexural vibration of the rod. The scatteredviscouswaves consist of the rigid‐rod scattering of viscouswaves and dipolar waves due to the flexural vibration of the rod. Acoustic resonances occur when the effective inertia force of the rod balances the stiffness force of the rod. The fluid viscosity and the scattering of sound give rise to damping effects for the rod vibrations and signficantly affect the acoustic resonances.

Synthesis of backscattering from an elastic sphere using the Sommerfeld–Watson transformation and giving a Fabry–Perot analysis of resonances
View Description Hide DescriptionThe Sommerfeld–Watson transformation (SWT) was recently applied to the acoustic backscattering from elastic spheres in water having k a≫1 [K. L. Williams and P. L. Marston, J. Acoust. Soc. Am. 7 8, 1093–1102 (1985)]. Expressions for the scattering due to each class of elasticsurface wave (e.g., the Rayleigh wave) were interpreted in terms of contributions from repeated circumnavigations. In the present paper, these expressions are summed in closed form as in the analysis of Fabry–Perot resonators. The form function is synthesized by adding this sum to the specular reflection. The procedure is confirmed by comparison with the exact form function f for a tungsten carbide sphere in the range 10≤k a≤80. In this case, the interference of the specular and Rayleigh contributions produces the underlying structure in ‖f(k a)‖, while the whispering gallery wave resonances produce a finer superposed structure. Phase shifts and coupling coefficients are identified which affect the signatures in ‖f(k a)‖ of the Rayleigh waveresonances.

Acoustic attenuation in fluid‐saturated porous cylinders at low frequencies
View Description Hide DescriptionLaboratory measurements on the elastic moduli and the acoustic attenuation of fluid‐saturated porous rock cylinders are frequently affected by the boundary conditions of the rock sample, i.e., whether the curved surface of the cylindrical sample is exposed to air or properly sealed. In this paper, the analytical solutions of these problems for the extensional, torsional, and flexural modes are derived, and several numerical examples are computed. It was found that there exists an ‘‘artificial’’ attenuation caused by the open‐pore boundary condition, whose relaxation frequency, in the case of extensional mode, is directly proportional to the permeability of the rock and inversely proportional to the viscosity of the pore fluid and the square of the sample radius. This attenuation exists in both the extensional and the flexural modes but not in the torsional mode.

On the mode‐splitting of Love waves in a rough layer
View Description Hide DescriptionUsing the technique of mean‐field renormalization, it is shown that the general effect of surface roughness on Love waves is to cause not only a splitting of the mode frequency but also an effective attenuation because of multiple scattering from the rough surface. The precise amounts of splitting and attenuation are shown to be dependent on the power spectrum of the surface roughness as well as on the normal mode. The calculation is restricted to the two‐dimensional problem where the roughness varies in one spatial direction only so that coupling of the Love modes to P–S V waves is strictly forbidden. For surface roughness, of rms amplitude 〈 f ^{2}〉^{1} ^{/} ^{2}, occurring on a scale that is long when compared to the Love mode wavelength, both the frequency splitting and effective attenuation are of fractional order ω〈 f ^{2}〉^{1} ^{/} ^{2}(s ^{2} _{1}−s ^{2} _{2})^{1} ^{2}/^{2}, where ω is the angular frequency and s _{1} and s _{2} are the slowness on either side of the rough boundary. For a surface roughness dominating the evaluation of certain basic integrals occurring in the mean‐field dispersion relation, it is shown that the modes couple nonlinearly to the rough fluctuations so that both resonant scattering of the modes amongst themselves, as well as nonresonant scattering to ‘‘background’’ oscillations, takes place. These analytic calculations have been done to both illustrate the broad range of diverse phenomena that can arise as well as to provide formulas for later comparison against numerical experiments and synthetic seismograms.

Acoustical properties of partially reticulated foams with high and medium flow resistance
View Description Hide DescriptionA new method for measuring impedance has been used for evaluating the normal surface impedance of three foams in free field. The results have been interpreted using the Biot theory, the two dilatational waves being taken into account. It has been pointed out from the theory that, for high flow resistance, the ratio of the acoustical velocities of the frame and the air is close to 1 at the surface of the foam. This ratio decreases with flow resistance but is never negligible for the studied foams. For foams with high flow resistance, the contributions of the two waves must be taken into account when calculating the impedance, and a description with only one wave would not be realistic. For foams with medium flow resistance, the one‐wave approximation for calculating the surface impedance is a good approximation in the whole range of acoustical frequencies.

The existence of caustics and cusps in a rigorous ray tracing representation
View Description Hide DescriptionWith rigorous ray tracing, caustics and their associated cusps in addition to those of classical ray tracing are encountered. These additional caustics are associated with classical (WKB) vertex points. Rigorous ray tracing also confirms those caustics that exist under a classical ray tracing representation, albeit both displaced from the classical locations into the classical shadow zone and perhaps deformed with additional cusps.

Applications of multifold Kirchhoff–Helmholtz path integrals to sound propagation in the ocean. Part I: Theory
View Description Hide DescriptionKirchhoff–Helmholtz theory is used to derive a generalized ray theory, called the multifold path integral (MFPI) method, that enables the calculation of frequency‐dependent ray theoretical amplitudes at caustics and shadows where ordinary ray theory (geometrical acoustics) fails. The method is then applied to some problems of acoustic propagation in an ocean whose sound‐speed profile, bathymetry, and bottom characteristics are all range dependent. Specifically, considered are: (a) rays with multiple bounces between the surface and a bottom that is rough on a scale much larger than a wavelength of the signal; (b) rays in a sound‐speed channel whose axis height varies with range; and (c) rays around an obstacle such as a seamount. Modeling examples will be presented in a subsequent paper but included here is a discussion of various methods for evaluating the multifold integrals.

Simulation of bottom interacting waveforms
View Description Hide DescriptionCurrent understanding of the acoustic processes occurring in the seafloor is used to develop a detailed ray approach for simulating the received time series of a broadband acoustical signal interacting once with the seafloor. The environment is assumed to be horizontally stratified, and the seafloor is described in terms of a geoacoustic profile. The frequency response is constructed from the superposition of the individual responses of each of the eigenrays. The ray approach includes the effects of reflection from the water–sediment interface, penetration into the sediment, refraction due to a constant compressional sound‐speed gradient in the sediment, absorption within the sediment, phase shifts due to caustics, and multipaths. The one‐bounce time series is constructed from the inverse Fourier transform of the product of the source spectrum and the eigenray frequency response. As an example application, the one‐bounce time series for an explosive source in a deep water environment is calculated and analyzed in terms of acoustical processes. Excellent agreement with measuredtime series is demonstrated.

Rough surface elastic wave scattering in a horizontally stratified ocean
View Description Hide DescriptionA previously developed boundary perturbation method [W. A. Kuperman, J. Acoust. Soc. Am. 5 8, 365–370 (1975)] is extended to treat scattering at a randomly rough interface which separates viscoelastic media. This method is then combined with a full wave treatment of sound propagating in a stratified ocean described by a system of fluid and elastic layers [H. Schmidt and F. B. Jensen, J. Acoust. Soc. Am. 7 7, 813–825 (1985)]. The net result of combining the extended boundary perturbation method with the full wave solution technique is to define a set of effective potentials which, when inserted in the full wave solution algorithm, yield the coherent components of the compressional and shear wave fields which decay with range due to boundary roughness scattering into incoherent compressional and shear waves. A natural outcome of this model is also the option to calculate the coherent reflection coefficient for an arbitrarily arranged layered system of fluid/solid media separated by randomly rough interfaces. Numerical examples of reflection coefficients and sound propagation in an ocean described by a stratified waveguide are presented.

Surface velocity, shadowing, multiple scattering, and curvature on a sinusoid
View Description Hide DescriptionThe Kirchhoff approximation is frequently invoked in the solution of scattering problems because it greatly reduces the computational complexity. This paper compares the actual surface velocity distribution on a sinusoidal pressure release surface to that assumed by the Kirchhoff approximation and examines more closely the reasons for its successes and failures. Corrections designed to improve the result by including the effects of shadowing, surface curvature, and multiple scattering are also investigated. In the cases examined, curvature correction appears to offer the most improvement while the multiple scattering contribution is practically negligible.

Real‐time study of frequency dependence of attenuation and velocity of ultrasonic waves during the curing reaction of epoxy resin
View Description Hide DescriptionThe frequency dependence of the phase velocity and attenuation of ultrasonic waves were measured as a function of time during the polymerization (curing) reaction of epoxy resins. The phase velocity and attenuation were evaluated from the amplitude and phase spectra of ultrasonic signals transmitted through a layer of curing epoxy resin. The measurements were made in the frequency range of 2–20 MHz. From the experimental data follows an important conclusion: The attenuation coefficient increases linearly with frequency at all stages of the curing reaction from the viscousliquid to the solid state. The slope of the attenuation coefficient as a function of frequency is strongly dependent on the time of cure (degree of cure). The linear behavior of attenuation versus frequency suggests that the attenuation effect cannot be explained by classical viscothermal absorption or relaxation theory. This type of behavior (so‐called hysteresis behavior) is poorly understood on the molecular level and was found previously for some highly viscousliquids, for solid polymers, and for biological tissue. The phase velocity data were evaluated from the phase spectrum of the transmitted signal. The ultrasonic velocity changes with time according to an S‐shaped curve. It is also moderately dependent on the frequency.

Diffraction correction for a radiation force measurement on an infinite plane target
View Description Hide DescriptionA discussion is given of a rigorous diffraction correction for acoustic dosimetry by a radiation force measurement on an infinite plane target. As an example, analytical results are presented for circular radiators of different velocity distributions and diameter‐to‐wavelength ratios, including baffled rigid piston, simply supported piston, clamped piston, and Gaussian radiators.

The response of a semi‐infinite fiber to a pulse applied asymmetrically to its end
View Description Hide DescriptionMcKenna and Simpkins [J. Acoust. Soc. Am. 7 8, 1675–1683 (1985)] have developed a normal modetheory concerning wave propagation down a semi‐infinite or finite elastic cylinder due to a time‐dependent load applied at one or both ends. To test the practicality of applying this theory, a nontrivial model problem concerning the dynamic response of a glass fiber to a certain pulse applied at its end representing tensile fracture is studied. After considerable analytical effort, the expansion coefficients for the modes are computed. Calculations concerning displacements and strains of the dominant modes are presented. When necessary, additional asymptotic analyses are done. It is possible to obtain a comprehensive description of the fiber’s response to the pulse. However, the effort required to apply the theory to a general problem is extensive. If the problem formulation admits considerable simplification of the expressions for the modal expansion coefficients, the theory is probably both elegant and meaningful.

An analysis of doubly rotated quartz resonators utilizing essentially thickness modes with transverse variation
View Description Hide DescriptionClosed‐form asymptotic expressions for the frequency–wavenumber dispersion relations in doubly rotated quartz plates vibrating in the vicinity of the odd pure thickness frequencies are derived from the equations of linear piezoelectricity and the associated boundary conditions on the major surfaces. The usual assumptions of small piezoelectric coupling and small wavenumbers along the plate are made and it is supposed that the pure thickness frequencies are sufficiently different that one pure thickness wave is dominant at a time. In the treatment the mechanical displacement is decomposed along the eigenvector triad of the pure thickness solution to facilitate the asymptotic analysis. The fact that the wavenumbers along the plate are restricted to be small significantly reduces the complexity of the equations without neglecting any transformed elastic constants. The resulting asymptotic dispersion equation enables the construction of a scalar differential equation describing the transverse behavior of essentially thickness modes of vibration in doubly rotated quartz plates. The scalar equation is applied in the analysis of both trapped energy resonators with rectangular electrodes and contoured crystal resonators using established procedures. In particular, calculations performed for the contoured SC cut and a number of other doubly rotated orientations are shown to be in excellent agreement with experiment. Since the differential equation for each harmonic family depends on the order of the harmonic and in the general doubly rotated case contains mixed derivatives in the plane of the plate, a different transformation is required for each harmonic family to obtain the coordinate system in which the mixed derivatives do not appear and, hence, the equation is separable. An interesting consequence of this transformation is that since the nodal planes of the anharmonics of each harmonic family of the contoured SC‐cut quartz resonator are oriented along the transformed coordinate system for that harmonic family, they are oriented differently for each harmonic family.

Acoustical comparison of three theaters
View Description Hide DescriptionThree theaters, including both thrust stage and proscenium arch designs, are evaluated using acoustical measures not yet in common use. The unique characteristics of each theater are considered and include a partially covered orchestra pit and a music shell. A computer model is used to estimate the detrimental effects of excessive ceiling lighting holes.

Transmission loss optimization in acoustic sandwich panels
View Description Hide DescriptionConsidering the sound transmission loss (TL) of a sandwich panel as the single objective, different optimization techniques are examined and a sophisticated computer program is used to find the optimum TL. Also, for one of the possible case studies such as core optimization, closed‐form expressions are given between TL and the core‐design variables for different sets of skins. The significance of these functional relationships lies in the fact that the panel designer can bypass the necessity of using a sophisticated software package in order to assess explicitly the dependence of the TL on core thickness and density.

High‐resolution beamforming by fitting a plane‐wave model to acoustic data
View Description Hide DescriptionThe problem addressed in this paper is the representation of the acoustic field at an array of hydrophones as a background plus a small number of plane waves. As data, assume that a narrow‐band covariance matrix has been observed. The covariance matrix implied by the model (i.e., background plus small number of plane waves) is adjusted to obtain the least‐squares fit to the observed covariance matrix. Since the number of plane waves is not known, one plane wave is initially assumed and others added in succession until the error is no longer reduced. Each plane wave is described by two parameters: power and bearing. However, the power may be eliminated formally. The problem remaining is one of multidimensional optimization with bearings as unknowns.

Representation of system response using expansions of Hermite and Beranek functions
View Description Hide DescriptionA new representation of system functions in the time and frequency domains using Hermite functions is introduced. The properties of such a representation are compared and contrasted with the well‐known Laguerre expansion of system temporal response introduced by Y. W. Lee [S t a t i s t i c a l C o m p u t a t i o n T h e o r y (Wiley, New York, 1960), Chap. 19]. It is argued that the Hermite functions are more relevant representations of systems with many degrees of freedom, and offer other mathematical and conceptual advantages as well. A new set of functions related to Hermite functions by the Hilbert transform are introduced, and are named Beranek functions. The use of these representations is illustrated by an application to the transfer function for a lossy acoustical pipe.