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Journal of the Acoustical Society of America

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Jun 1981

Volume 69, Issue 6, pp. 1545-1867

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On the theory of stress‐constrained optimum compliant tubes and uniform tube arrays

Gerald A. Brigham

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1545-1556 (1981); (12 pages)

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A low‐frequency model for the plane‐wave transmissitivity of a planar uniform grating of compliant tubes is combined with a tube stress model to determine maximum array resonant reflectivity and maximum resonant bandwidth. The study shows tubes of intermediate roundness are optimum in compliance, size, weight, and resonant bandwidth. A comparison is made of various materials and concludes that composite tubes made of S glass fiber and epoxy resin have maximum compliance and generate the optimum grating acoustics.
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43.20.Hq Velocity and attenuation of acoustic waves
43.20.Ks Standing waves, resonance, normal modes
43.20.Fn Scattering of acoustic waves
43.40.Ey Vibrations of shells

Acoustic signals of nonthermal origin from high energy protons in water

S. D. Hunter, W. V. Jones, D. J. Malbrough, A. L. Van Buren, A. Liboff, T. Bowen, J. J. Jones, J. G. Learned, H. Bradner, L. Pfeffer, R. March, and U. Camerini

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1557-1562 (1981); (6 pages) | Cited 3 times

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Acoustic pulses generated by the passage of 30‐GeV protons through water show evidence for the presence of a nonthermal source. In addition to the bipolar leading‐compression signal expected from thermal shock, a tripolar leading‐rarefaction component is observed. The component is dominant at 4°C, where the thermal signal should vanish. A space‐charge effect may be the source of this component, since other proposed mechanisms leading to tripolar pulses should give a leading‐compression signal.
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43.20.Px Transient radiation and scattering
43.30.Lz Underwater applications of nonlinear acoustics; explosions

Nonthermal acoustic signals from absorption of a cylindrical laser beam in water

S. D. Hunter, W. V. Jones, and D. J. Malbrough

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1563-1567 (1981); (5 pages) | Cited 1 time

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A Q‐switched ruby laser has been used to study the generation of acoustic signals in water. The presence of a predominant thermal expansion mechanism is verified by the dependence of the signal amplitude on the ambient temperature. Qualitative agreement with the theory for a cylindrical source is implied by the amplitude dependence on the distance from the source. An additional nonthermal mechanism is evident from the existence of a leading compression, tripolar pulse at 4°C, where the thermal signal must vanish. This pulse may indicate microbubble production by the laser beam.
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43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods
43.20.Px Transient radiation and scattering
43.35.Sx Acoustooptical effects, optoacoustics, acoustical visualization, acoustical microscopy, and acoustical holography

Rayleigh scattering by compressible, movable bodies of revolution

M. C. Junger

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1568-1572 (1981); (5 pages)

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Rayleigh’s solution for the scattered field of an acoustically small sphere of finite bulk modulus and density is extended to finite cylinders and other bodies of revolution. The analysis has applications to scattering by elastic spherical and cylindrical shells and by zooplankton.
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43.20.Fn Scattering of acoustic waves
43.20.Bi Mathematical theory of wave propagation

Dilatational waves in an elastic solid containing lined, gas‐filled spherical cavities

M. C. Junger

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1573-1576 (1981); (4 pages) | Cited 1 time

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The real and imaginary wavenumber components describing dilatational wave propagation in a porous medium are computed. The acoustically small cavities are spherical in shape and characterized by a statistical size distribution. They are gas‐filled and lined with an elastic shell. It is shown that marked dispersion and resonance‐enhanced absorption requires that the Poisson’s ratio of the solid matrix lie between 1/3 and 1/2.
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43.20.Bi Mathematical theory of wave propagation
43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants

Acoustic transmission matrix of a variable area duct or nozzle carrying a compressible subsonic flow

J. H. Miles

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1577-1586 (1981); (10 pages) | Cited 8 times

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The differential equations governing the propagation of sound in a variable area duct or nozzle carrying a one‐dimensional subsonic compressible fluid flow are derived and put in state variable form using acoustic pressure and particle velocity as the state variables. The duct or nozzle is divided into a number of regions. The region size is selected so that in each region the Mach number can be assumed constant and the area variation can be approximated by an exponential area variation. Consequently, the state variable equation in each region has constant coefficients. The transmission matrix for each region is obtained by solving the constant coefficient acoustic state variable differential equation. The transmission matrix for the duct or nozzle is the product of the individual transmission matrices of each region. Solutions are presented for several geometries with and without mean flow.
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43.20.Mv Waveguides, wave propagation in tubes and ducts
43.20.Bi Mathematical theory of wave propagation

Acoustic coupling between two finite‐sized spheres; n = 2 mode

J. Mark Reese and William Thompson, Jr.

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1587-1590 (1981); (4 pages)

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The modification of the radiation impedance load on a spherical source vibrating in the third or n = 2 axisymmetric mode, caused by the nearby presence of another equal sized sphere which is either vibrating in that same mode (in‐phase or 180° out‐of‐phase) or is a perfect scatterer (rigid or soft), has been calculated. Plots of the normalized resistive and reactive components of the modified radiation impedance are presented as a function of the wavelength separation distance between the two spheres.
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43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods

Spectral analysis of elastic pulses backscattered from two cylindrical cavities in a solid. Part I

Selcuk Sancar and Yih–Hsing Pao

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1591-1596 (1981); (6 pages) | Cited 1 time

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A series solution for the scattering of plane harmonic pressure waves from two cylindrical cavities in an elastic solid is derived in terms of cylindrical wavefunctions. The scattered waves are expressed as an infinite sum of various orders of scattering, the first order being the scattering of the incident wave by each of the two cavities, and each successive order being expressed in terms of the single cylinder scattering coefficients. The exact steady‐state solution for the scattered radial stress is derived, which is also the power spectra of the scattered pulse due to an incident pulse of delta function in time. These results are simplified further for the case of backscattering at farfields.
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43.20.Fn Scattering of acoustic waves
43.20.Bi Mathematical theory of wave propagation

Spectral analysis of elastic pulses backscattered from two cylindrical cavities in a solid. Part II

Selcuk Sancar and Wolfgang Sachse

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1597-1609 (1981); (13 pages) | Cited 1 time

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The eigenfunction solutions in Part I for the scattering of plane harmonic waves from two cylindrical cavities in an elastic solid is numerically evaluated for incident wave frequencies ranging from 0–10 MHz, and the power spectrum of the backscattered radial‐stress pulse is calculated. These theoretical spectra, computed for a wide range of cavity radii, center‐to‐center separations, and incidence directions, are analyzed and interpreted. Spectral features are explained by the interference of various reflected and diffracted rays. Experimental backscattering spectra are obtained and compared with the theoretical results. Simple expressions which explain the major details of the spectra are derived for applications to quantitative flaw characterization in ultrasonic nondestructive testing.
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43.20.Fn Scattering of acoustic waves
43.20.Ks Standing waves, resonance, normal modes

Experimental verification of the impulse response method to evaluate transient acoustic fields

Peter R. Stepanishen and George Fisher

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1610-1617 (1981); (8 pages)

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An experimental verification of the impulse‐response method to evaluate the transient acoustic field of pulsed ultrasonic radiators is presented. Several piezoelectric disk radiators were constructed for the experiments. Transient pressure measurements were obtained at several field points for pulsed wide bandwidth electrical excitations of the radiators. The pressure data were processed via an iterative deconvolution method to obtain experimental impulse responses. The method ideally eliminates the effects of the dynamic response of the transmit and receive system on the impulse responses. A comparison of the experimental and theoretical impulse responses shows the responses to be in general agreement.
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43.20.Px Transient radiation and scattering
43.20.Bi Mathematical theory of wave propagation

Frequency dependence of the acoustic radiation force function (Yp) for spherical targets for a wide range of materials

L. W. Anson and R. C. Chivers

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1618-1623 (1981); (6 pages) | Cited 2 times

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In a previous communication the authors reported a procedure for calculating Yp for spherical radiometer targets over wide ranges of ka, identifying the importance of fine steps in ka for accurate representations. The present paper summarizes the results of the calculation Yp, over the ka range 0–20, for over 50 different materials which are assumed to be immersed in water. A primary grouping according to material shear velocity and density is proposed. Material density has a substantial effect upon the form of the maxima and minima of the Yp curves, a low density producing higher maxima, deeper minima, and increasing the width of these features. The present calculations do not give a shear indication of the effect of the Poisson’s ratio of the material, nor explain the extremely high maxima at low wave velocities.
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43.25.Qp Radiation pressure
62.65.+k Acoustical properties of solids

Acoustic cavitation prediction

R. E. Apfel

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1624-1633 (1981); (10 pages) | Cited 7 times

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We have derived an approximate expression for the threshold pressure for transient acoustic cavitation and have used this result with published expressions for the thresholds for gas bubble nucleation and for rectified diffusion in synthesizing cavitation prediction charts for water covering a frequency range from 10 kHz to 2.5 MHz, and for gas saturation percentages 10%, 50%, and 100%. This synthesis, which is applicable to other liquids, may provide guidance about the phenomena associated with acoustic cavitation to those who are either trying to minimize or to optimize its effects.
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43.25.Yw Nonlinear acoustics of bubbly liquids

Torque generated by orthogonal acoustic waves—Theory

F. H. Busse and T. G. Wang

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1634-1638 (1981); (5 pages) | Cited 12 times

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An analytical calculation of the torque generated by orthogonal waves is reported. This torque is a result of a viscous effect, rather than the Bernoulli effect as in Rayleigh’s torque. The agreement between the reported experimental values and this calculation is excellent.
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43.25.Gf Standing waves; resonance
43.25.Cb Macrosonic propagation, finite amplitude sound; shock waves
43.28.Py Interaction of fluid motion and sound, Doppler effect, and sound in flow ducts
43.58.Pw Rayleigh disks

Sound velocities and B/A in fluorocarbon fluids and in several low density solids

Walter M. Madigosky, Ira Rosenbaum, and R. Lucas

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1639-1643 (1981); (5 pages) | Cited 6 times

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Sound velocities were obtained in six fluorocarbon fluids, two syntactic foams, and two low density solids. Temperature and pressure ranges considered were 0 °–30 °C and 1–700 kg/cm2. An equation was fit to the data. This equation was then differentiated to permit the calculation of the nonlinear parameter, B/A, and Rao’s constant. Comparisons of these data with those obtained by other authors are made wherever possible. Very low sound velocities are observed in fluorocarbon fluids and these fluids have the highest values of B/A reported thus far.
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43.25.Ba Parameters of nonlinearity of the medium
62.60.+v Acoustical properties of liquids
62.65.+k Acoustical properties of solids
43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions

Nonlinear equations of acoustics, with application to parametric acoustic arrays

Jacqueline Naze Tjøtta and Sigve Tjøtta

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1644-1652 (1981); (9 pages) | Cited 8 times

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The propagation and interaction of finite amplitude sound waves produced by a baffled piston source in a thermoviscous fluid are considered. Basic equations are derived and their ranges of validity established. This is used to relate some earlier works by others on nonlinear model equations in acoustics. Applications are made to the theory of parametric acoustic arrays, where the effects of nonlinear attenuation are discussed.
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43.25.Cb Macrosonic propagation, finite amplitude sound; shock waves
43.25.Lj Parametric arrays, interaction of sound with sound, virtual sources

The influence of wind‐induced bubbles on echo integration surveys

John Dalen and Arne Løvik

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1653-1659 (1981); (7 pages) | Cited 1 time

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An investigation of attenuation of acoustic energy caused by gas bubbles in the surface layers has been carried out. This was done primarily to study the effect on echo integration of fish abundance when using hull‐mounted transducers. Two different approaches have been used. The first examines the variation of the echo intensity from an acoustically stable bottom layer and the second measures the total volume reverberation as a function of depths. The bubble density, size distribution, and the attenuation caused by the bubbles is estimated from the measurements done under different weather conditions. The results show that the acoustic attenuation caused by wind‐induced gas bubbles in the surface layers appear at a lower wind force and at a greater magnitude than earlier reported and expected. The attenuation is found to increase rapidly with increasing frequency. The results are also used to find the minimum towing depths of a transducer as a function of the wind speed necessary in order to keep the attenuation due to the bubbles below a given number.
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43.30.Bp Normal mode propagation of sound in water
43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries
43.30.Dr Hybrid and asymptotic propagation theories, related experiments

Investigation of chemical sound absorption in sea water: Part II

R. H. Mellen, D. G. Browning, and V. P. Simmons

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1660-1662 (1981); (3 pages) | Cited 1 time

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Resonator measurements of relaxational sound absorption by boric acid in artificial sea water exhibit pH anomalies similar to that observed in aqueous solution. Discrepencies between theory and experiment indicate that the simple two‐step relaxation model is inadequate. However, the results are in good agreement with sea measurements in the sea water pH range.
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43.30.Bp Normal mode propagation of sound in water
43.35.Fj Ultrasonic relaxation processes in gases, liquids, and solids
43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions

The hybrid algorithm: A solution to acquisition and tracking

José M. F. Moura

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1663-1672 (1981); (10 pages)

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The paper discusses a solution for platform location in underwater acoustics. The work is relevant to several fields such as the passive detection and tracking of underwater mobiles, the navigation of platforms relative to bottom‐moored sources, the coherent synthesis of acoustic apertures, etc. This paper proposes the design of efficient algorithms that recover position and dynamics information by processing the radiated signature of nonfixed sources. There are conflicting requirements: Global location, e.g., the global recovery of the source/receiver separation, and minimization of the associated computational effort. A compromise is a receiver structure, herein referred to as the hybrid algorithm, that exhibits two basic modes of behavior. In the acquisition mode, the hybrid algorithm is globally observable, but nonrecursive. In the tracking mode, the hybrid algorithm, being recursive, is locally observable. The irregularities of the source path impose a maximum time for the acquisition mode, while the tracking mode is time‐limited by the unbounded time behavior of the error variance at the output of the recursive algorithm. For the underwater problem, the paper discusses compromises between these time constraints, as well as the consequences on the error performance of operating the acquisition and tracking modes for longer or shorter periods. It establishes strategies to follow in practical acoustic problems, quantifying the relation between the hybrid algorithm behavior and the parameters characterizing the geometry and the statistical noise environment.
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43.30.Bp Normal mode propagation of sound in water
43.30.Vh Active sonar systems
43.60.Gk Space-time signal processing, other than matched field processing

Application of Ludwig’s uniform progressing wave ansatz to a smooth caustic

D. C. Stickler, D. S. Ahluwalia, and L. Ting

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1673-1681 (1981); (9 pages) | Cited 1 time

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It is well known that the usual harmonic ansatz of geometrical acoustics fails at a caustic and that uniform expansions can be found which remain valid in the neighborhood of the caustic and reduce asymptotically into the usual geometrical acoustic ansatz far from the caustic. A similar uniform ansatz can be constructed for transient acoustic fields using the so‐called progressing wave ansatz. In this paper some of the details of this construction are considered for a point source in a time independent, refracting medium in which a smooth caustic is formed. The time dependence at the source is taken to be a rather general function of time. Particular attention is given to the nature of the leading term of the uniform progressing wave expansion and its construction from the nonuniform harmonic ansatz. Explicit expressions are obtained for times near the direct arrival time and the caustic arrival time as well as for large time. An analytic example is examined when the squared refractive index is linear and some numerical results for this case are presented.
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43.30.Bp Normal mode propagation of sound in water
43.20.Bi Mathematical theory of wave propagation
43.20.Dk Ray acoustics

Secondary states of vibrating plates

Leonard J. Putnick, Bernard J. Matkowsky, and Edward L. Reiss

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1682-1687 (1981); (6 pages)

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A perturbation method is used to obtain a new class of periodic motions for the nonlinear vibrations of rectangular, elastic plates. The dynamic von Kármán plate theory is used in the analysis. Periodic solutions bifurcate at the natural frequencies of free vibration of the linearized plate theory. The new solutions bifurcate from these periodic solutions. Thus they are states of secondary bifurcation.
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43.40.Dx Vibrations of membranes and plates
43.40.Ga Nonlinear vibration

Dynamic stability of orthotropic annular plates under pulsating torsion

J. Tani

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1688-1694 (1981); (7 pages) | Cited 1 time

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The dynamic stability of clamped, polar orthotropic annular plates under pulsating torsion is theoretically analyzed with the effect of the static torsion taken into consideration. The Galerkin method is used to reduce the problem to that for a finite degree‐of‐freedom system, the stability boundaries of which are determined by utilizing Hsu’s result [J. Appl. Mech. 30, 367–371 (1963)] for coupled Hill’s equations. The instability regions of both principal and combination resonances are determined for a wide range of exciting frequencies. The variation in the polar orthotropic material property is found to change significantly the wavenumber dependence of the dynamic stability.
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43.40.Dx Vibrations of membranes and plates
43.40.At Experimental and theoretical studies of vibrating systems

An approach to the theoretical background of statistical energy analysis applied to structural vibration

J. Woodhouse

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1695-1709 (1981); (15 pages) | Cited 7 times

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Rayleigh’s classical approach to the study of vibration of systems having a finite number of degrees of freedom is applied to the problem of coupling of subsystems in a complicated structure, in order to probe the regions of applicability of the approach to vibration analysis usually known as statistical energy analysis (SEA). The classical method has advantages of simplicity and rigor over previous approaches to the background of SEA in certain cases, and provides extensions and simplifications in several areas of the theory. It also suggests modifications to SEA modeling strategy depending on the type of coupling involved, even when that coupling is weak, so that earlier analyses might be thought to apply.
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43.55.Cs Stationary response of rooms to noise; spatial statistics of room response; random testing
43.55.Ka Computer simulation of acoustics in enclosures, modeling
43.40.At Experimental and theoretical studies of vibrating systems

Comments on the coherent and incoherent nature of a reverberant sound field

W. T. Chu

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1710-1715 (1981); (6 pages) | Cited 3 times

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Is is proposed that reverberant sound fields should be classified with better‐defined characteristics in terms of coherence and incoherence. Their exact nature created under different types of signal excitation and room condition are explored with the object of clarifying the conditions for which various results from the statistical theory apply.
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43.55.Br Room acoustics: theory and experiment; reverberation, normal modes, diffusion, transient and steady-state response
43.55.Cs Stationary response of rooms to noise; spatial statistics of room response; random testing

Sound decay in reverberation chambers with diffusing elements

K. Heinrich Kuttruff

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1716-1723 (1981); (8 pages) | Cited 4 times

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Sound scattering bodies are frequently used to improve diffusion in reverberation chambers and generally produce reverberation on their own. This effect is negligible at relatively low diffuser densities; in this range the effect of increasing diffusion prevails. At high densities of the scattering bodies, however, reverberation caused by the latter makes the usual reverberation formulae unapplicable. Between both limiting cases there is an optimum range of diffuser density. This is calculated theoretically as well as determined by Monte‐Carlo simulations.
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43.55.Br Room acoustics: theory and experiment; reverberation, normal modes, diffusion, transient and steady-state response
43.55.Nd Reverberation room design: theory, applications to measurements of sound absorption, transmission loss, sound power

New models on the ocean acoustic detection process

Harilaos N. Psaraftis, Anastassios N. Perakis, and Peter N. Mikhalevsky

J. Acoust. Soc. Am. Volume 69, Issue 6, pp. 1724-1734 (1981); (11 pages)

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The basic problem of the ocean acoustic detection process is formulated analytically under the assumption of fully developed saturated phase random multipath acoustic fluctuations. Detection is defined as occurring whenever ρ, the root‐mean‐square pressure at the receiver, exceeds a specified threshold level ρ0. Two models, one exact and one approximate, are developed for obtaining the probability density functions of the time between two successive detections and of the time ρ is above ρ0 (holding time). The two models are compared with one another and with the extensively used (λ, σ) model. One of the reasons that the latter model has a limited success in practice is the inability to estimate the appropriate value for λ, a parameter which is determined empirically. In this paper we have derived an appropriate value for λ, in terms of ν (the single path root‐mean‐square phase rate), σ21 (half the long time average mean‐square pressure at the receiver) and ρ0 (the threshold level). Using this equivalent value for λ, we observe that our exact and approximate detection models exhibit similar long‐term behavior but markedly different short‐term characteristics as compared with the (λ,σ) model. This is due to the memory of the process, a property that cannot be accounted for in the (λ,σ) model. A comparison of these models with data obtained from various field experiments demonstrates, in most cases, an improved capability over the (λ,σ) model.
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43.60.Cg Statistical properties of signals and noise
43.30.Vh Active sonar systems
92.10.Vz Underwater sound
43.30.Bp Normal mode propagation of sound in water
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