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Journal of the Acoustical Society of America

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Mar 1978

Volume 63, Issue 3, pp. 661-978

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Asymptotic theory of ducted propagation

S. Choudhary and L. B. Felsen

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 661-666 (1978); (6 pages)

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A new high‐frequency asymptotic theory of propagation in ducts with continuously varying refractive index is presented. The theory is based on local wave fields with complex phase and constitutes a special application of the evanescent wave tracking theory developed by the authors. It is shown, for analytic profiles and for refractive indexes that vary only transversely to the duct direction, how the coefficients in the asymptotic expansion are evaluated explicitly. When the method is applied to parabolic and hyperbolic secant profiles for which exact solutions of the wave equation are available, the asymptotic expansions so generated agree term by term with the asymptotically expanded exact results. The method is then applied to a class of polynomial profiles for which exact results in terms of known functions are not available.
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43.20.Mv Waveguides, wave propagation in tubes and ducts
43.20.Bi Mathematical theory of wave propagation

Effect of an expansion chamber on the propagation of sound in circular ducts

A. I. El‐Sharkawy and Ali H. Nayfeh

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 667-674 (1978); (8 pages) | Cited 4 times

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An analytical and experimental study is presented of sound propagation through a circular duct in the presence of an expansion chamber. Results are presented for various sound frequencies, expansion ratios, and chamber lengths. It is found that the analytical results are in good agreement with the experimental results.
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43.20.Mv Waveguides, wave propagation in tubes and ducts

Reflection of elastic waves by a cylindrical cavity in an absorptive medium

Lawrence Flax and Werner G. Neubauer

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 675-680 (1978); (6 pages) | Cited 2 times

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The analytical formulation for the total scattering cross section of a cylindrical cavity in an elastic medium is given for the case of inclusion of compressional and shear wave attenuations. Examples are computed of relatively small attenuations exemplified by the material polymethacrylate and relatively large attenuations exemplified by polyethylene. The inclusion of wave attenuations known to exist in these materials cause the scattering cross section to diminish significantly for wave‐number cylindrical‐cavity‐radius product up to 10.
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43.20.Fn Scattering of acoustic waves
43.40.Ey Vibrations of shells

Propagation of sound in a curved bend containing a curved axial partition

Christopher R. Fuller and David A. Bies

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 681-686 (1978); (6 pages) | Cited 3 times

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Sound transmission in a 180° bend containing a curved partition positioned on the axial center line is investigated theoretically and experimentally using equations for sound propagation in straight and curved ducts. Good agreement is obtained and small discrepancies are discussed. The partition is found to significantly alter the sound propagation through the bend and reasons for the different acoustic behavior are given.
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43.20.Mv Waveguides, wave propagation in tubes and ducts
43.20.Bi Mathematical theory of wave propagation

Collinear interaction of noise with a finite‐amplitude tone

Don A. Webster and David T. Blackstock

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 687-693 (1978); (7 pages)

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The interaction between a low‐level band of noise and a finite‐amplitude tone has been measured in air in a plane progressive wave tube. Noise bands generally 1–3 octaves wide with center frequencies in the range 0.7–1.2 kHz were used. At the source the tone SPL was in the range 140–151 dB (re 20 μPa); the frequency was either within the noise band or somewhat above. The data show the following. When the tone is absent, the noise propagates as a small‐signal wave. When the tone is turned on, however, a strong modulation takes place. After a propagation distance of only a few meters, not necessarily beyond the point of shock formation for the tone, the noise spectrum extends many octaves above the original noise band and, moreover, becomes nearly flat. The energy required to extend the noise apparently comes from the tone and its harmonics, not the original noise band. Theoretical predictions have also been obtained. A computer algorithm based on the Earnshaw solution, with corrections for tube wall absorption added, was used. The input waveform of the noise was constructed from the measured source power spectrum, the components of which were assigned random phase. The computed results agree well with the experimental data.
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43.25.Ed Effect of nonlinearity on velocity and attenuation
43.25.Lj Parametric arrays, interaction of sound with sound, virtual sources
43.25.Cb Macrosonic propagation, finite amplitude sound; shock waves

Echosonde interferometer for atmospheric research

Edmund H. Brown, C. Gordon Little, and Wayne M. Wright

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 694-699 (1978); (6 pages)

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A preliminary version of an echosonde interferometer is described and some of the first results obtained with it are presented. The results demonstrate that the formation of an acoustic interference pattern from a pair of coherent sources extends to the sound field scattered by turbulent fluctuation and that an echosonde interferometer is practicable. Possible applications to the remote sensing of atmospheric temperature profiles are discussed.
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43.28.Fp Outdoor sound propagation through a stationary atmosphere, meteorological factors
43.20.Fn Scattering of acoustic waves

Model experiments on surface waves

R. J. Donato

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 700-703 (1978); (4 pages) | Cited 9 times

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Experiments are described in which exponential attenuation factors for surface waves both in the direction of propagation along a complex impedance surface and perpendicular to the surface are measured. The surface impedance calculated from these attenuations is then compared to that measured in an impedance tube.
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43.28.Fp Outdoor sound propagation through a stationary atmosphere, meteorological factors
43.35.Pt Surface waves in solids and liquids
43.20.Fn Scattering of acoustic waves
43.58.Bh Acoustic impedance measurement

Underwater acoustic backscattering and echo structure characteristics for a thin stiffened plate

K. W. Alkier

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 704-708 (1978); (5 pages)

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Underwater acoustic reflection characteristics for a thin stiffened aluminum plate were investigated. The thin stiffening rib extends parallel to the edge across the entire width of the plate. A plain plate without the stiffening rib was used as a control. The targets were sequentially suspended in water during the experiments. The stiffening rib on the experimental target was positioned in the acoustic shadow of the plate to avoid specular returns from its edges. Internally guided longitudinal stress waves were detected in both targets for a critical angle of incidence of 15.8°, at a frequency of 60 kHz and a 30‐μsec pulse width. Based on ray theory and the assumption that these stress waves were reflected at the reinforcing rib, theoretical travel times, and pulse‐reflection periods were calculated. Good agreement between theoretical and experimental results was achieved. Pulse decay rates in the form of logarithmic decrement of internally guided longitudinal stress waves are shown to be a significant clue to the presence and location of a reinforcing rib in thin plates.
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43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries
43.20.Fn Scattering of acoustic waves
43.40.Dx Vibrations of membranes and plates
43.30.Dr Hybrid and asymptotic propagation theories, related experiments

Propagation of sound in underwater surface channels with rough boundaries

G. R. Barnard and R. L. Deavenport

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 709-714 (1978); (6 pages)

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A study is made of sound propagation in surface channels with rough boundaries. A generalized phase integral approach is formulated for calculating the complex eigenvalues due to leakage and surface roughness. Calculations of propagation loss versus range are given for the bilinear profile and compared with experimental data.
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43.30.Bp Normal mode propagation of sound in water
43.30.Dr Hybrid and asymptotic propagation theories, related experiments

Effect of line‐discontinuity admittance on sound scattered by plate vibration

K. L. Chandiramani

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 715-722 (1978); (8 pages)

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We investigate how the force and moment impedance of a line discontinuity on a plate influences the sound scattered by impingement of plate flexural waves on the line discontinuity. Effects of fluid loading are accounted for. For a specific high‐frequency situation, we numerically evaluate three line‐discontinuity models: a simple support, a clamped support, and a support whose force and moment susceptances cancel out the corresponding susceptances of the plate driving‐point admittances. Calculated are total acoustic powers radiated and farfield pressure patterns. We also calculate, for two angular locations, contours of constant radiated pressure in the line‐discontinuity force‐admittance–moment‐admittance plane. It is shown that under certain circumstances slight changes in the line‐discontinuity admittance can cause relatively large changes in the radiated pressure.
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43.30.Jx Radiation from objects vibrating under water, acoustic and mechanical impedance
43.40.Dx Vibrations of membranes and plates

Theory of elastic resonance excitation by sound scattering

L. Flax, L. R. Dragonette, and H. Überall

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 723-731 (1978); (9 pages) | Cited 49 times

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The resonance formalism of nuclear‐reaction theory is applied to the problem of sound scattering from submerged elastic bodies (illustrated here by circular cylinders and spheres). It is demonstrated that the strongly fluctuating behavior of, e.g., the backscattering cross section is caused by a superposition of generally narrow resonances in the individual normal modes (partial waves), which move up in frequency from one partial wave to the next, corresponding to a series of creeping waves (’’Regge poles’’), and which are superimposed on a background of rigid‐body (potential) scattering. This fact, together with a resonance representation of the elastic field in the interior, indicates that the elastic body is relatively impenetrable to the incident wave except in the vicinity of the resonances, which occur at the eigenfrequencies of the elastic vibrations of the body. Various types of interference between resonance and background are analyzed, and the phase of the partial wave is shown to undergo a jump of π at each resonance. Decay times (ringing) of the excited resonances are found to depend inversely on their width, and the appearance of nulls in the scattering angular distribution at certain resonances is related to the cross section of the rigid body.
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43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries
43.30.Jx Radiation from objects vibrating under water, acoustic and mechanical impedance
43.40.Ey Vibrations of shells

Approximations to distant shipping noise statistics

Peter N. Mikhalevsky and Ira Dyer

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 732-738 (1978); (7 pages)

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Distant shipping noise modeled by multiple phase‐random line components has a probability density and statistics easy to state in generality but difficult to compute in particular. To obtain numerical results with reasonable effort, previous computations have been based on Gaussian approximations to the densities. Here we show that an Edgeworth‐series approximation to the density greatly improves the quality of the result, without adding much to the computational effort. Also, to justify adoption of the Edgeworth series, and to further develop the theoretical framework for distant shipping noise, exact analytical results are presented for several new cases of multiple line components.
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43.30.Nb Noise in water; generation mechanisms and characteristics of the field
43.30.Bp Normal mode propagation of sound in water

Adiabatic mode theory of underwater sound propagation in a range‐dependent environment

Anton Nagl, H. Überall, Anton J. Haug, and G. L. Zarur

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 739-749 (1978); (11 pages) | Cited 2 times

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For an ocean sound channel whose environmental parameters depend not only on depth, but in a gradual fashion also on range, the wave equation may be separated by the adiabatic range variation method of Pierce [J. Acoust. Soc. Am. 37, 19 (1965)]. This method is used here to calculate underwater sound propagation in a channel with arbitrary (but gradual) range dependence, and also with arbitrary depth dependence of the sound velocity profile, by employing Airy function solutions of segmentwise linearized problems. Our results are illustrated for a realistic deep‐water propagation case with profile data collected in the western North Atlantic, as well as a shallow‐water example from the Norwegian Sea, and compared against the experimental transmission loss data, and the results of calculations using other methods for the same cases.
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43.30.Bp Normal mode propagation of sound in water
92.10.Vz Underwater sound
43.30.Jx Radiation from objects vibrating under water, acoustic and mechanical impedance
43.20.Bi Mathematical theory of wave propagation

Effects of density gradients on bottom reflection loss for a class of marine sediments

Steven R. Rutherford and Kenneth E. Hawker

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 750-757 (1978); (8 pages) | Cited 7 times

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The sensitivity of bottom reflection loss to a density gradient is examined within the context of a physically meaningful model consisting of a fluid sediment layer having depth‐dependent density and sound speed overlying a substrate having solid properties. The bottom grazing‐angle range is divided into two regions, the low‐angle and the high‐angle regions. In the low‐angle region sediment sound‐speed gradients refract incident energy upward before it encounters the substrate. In the high‐grazing‐angle region, energy impinges on the substrate. Through the use of a numerical plane‐wave reflection coefficient model it is shown that the effect of a density gradient on low‐angle bottom loss is small. An expression indicating this effect is derived and is shown to agree with numerical bottom‐loss calculations. The high‐angle bottom loss is more influenced by a density gradient because of the impedance changes at the sediment–substrate interface which accompany a density gradient. It is shown that introduction of density gradient of 0.002 g/cm3/m can cause the high‐angle bottom loss to change on the average by 12.5%, 7%, and 3% in 100‐m clay, silt, and sand layers, respectively.
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43.30.Bp Normal mode propagation of sound in water
43.30.Dr Hybrid and asymptotic propagation theories, related experiments
92.10.Vz Underwater sound

Bistatic surface scattering strength measured at short wavelengths

John G. Zornig

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 758-767 (1978); (10 pages)

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A series of measurements of the scattering strength of wind‐driven water surfaces at short wavelengths (circa 1 mm) have been performed. Bistatic azimuthal configurations ranging from 0° (backscatter) to 180° (specular direction) were used at three grazing angles and two conditions of roughness. Orientations with respect to the wind over a range of 180° were also studied. The experiments were conducted with short, relatively narrow‐band probing signals under computer control. The data were converted to scattering strength using a flat‐surface reference and a computed compensation for beam patterns and source and receiver time gating. The results of these measurements indicate that wind direction is an important factor in determining reverberation from the surface. Wind speed, hence roughness was confirmed to be an equally important factor, but Rayleigh parameter, an often used scalar index of effective roughness, was shown to be insufficient to predict reverberation. At short wavelengths, scattering strength was found to be insensitive to small changes in wavelength as expected. Backscatter strengths measured at 8.3 m/s at crosswind were found to agree closely with a relation proposed by Marsh [J. Acoust. Soc. Am. 35, 240–244 (1963)] relating backscattering strength to grazing angle. No satisfactory predictive theory, however, seems to be available for the general case of bistatic scattering.
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43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries

Sensitivity of the schlieren method for the visualization of low‐frequency ultrasonic waves

J. A. Bucaro and H. D. Dardy

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 768-773 (1978); (6 pages) | Cited 2 times

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Schlieren visualization of ultrasonic waves is usually carried out at megahertz frequencies since it is generally realized that lower‐frequency waves are much more difficult to observe. This paper considers the factors involved in the frequency dependence of the sensitivity of an ideal diffraction‐limited schlieren system. The results indicate that relatively low‐amplitude sound waves can be visualized even at low‐kilohertz frequencies. A techique is suggested which would make the sensitivity at these low frequencies comparable to that at the higher frequencies.
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43.35.Sx Acoustooptical effects, optoacoustics, acoustical visualization, acoustical microscopy, and acoustical holography
43.35.Yb Ultrasonic instrumentation and measurement techniques

Sound dispersion in a quasi‐Lorentz gas

L. Monchick

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 774-776 (1978); (3 pages)

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It is shown that some well‐known formulas connecting viscous drag and thermal transfer in the continuum to the free molecular flow regime can be used to extend the Temkin–Dobbins formulas for sound dispersion in a dusty gas to very small particle sizes.
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43.35.Ae Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in gases
43.20.Hq Velocity and attenuation of acoustic waves

Method for the measurement of the sound velocity in metastable liquids, with an application to water

Eugene Trinh and Robert E. Apfel

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 777-780 (1978); (4 pages) | Cited 9 times

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A standard optical Schlieren method has been adapted to the problem of measuring the speed of sound in moderately supercooled and in superheated liquids under atmospheric pressure. The estimated accuracy is ±3 m/s. Results in supercooled water down to −16.75 °C and in superheated water up to 176.5 °C are reported.
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43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions
43.30.Cq Ray propagation of sound in water
62.60.+v Acoustical properties of liquids
43.35.Sx Acoustooptical effects, optoacoustics, acoustical visualization, acoustical microscopy, and acoustical holography

Wave propagation in a piezoelectric two‐layered cylindrical shell with hexagonal symmetry: Some implications for long bone

Ashok Ambardar and Clifford D. Ferris

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 781-792 (1978); (12 pages)

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Harmonic wave propagation is considered in a two‐layered cylinder of dissimilar but transversely isotropic materials such as bone. The model includes the approximate piezoelectric behavior of long bone and the frequency equation is shown to constitute a 16th‐order determinant. A frequency equation is also derived for the nonpiezoelectric case. Though the frequency equations are much too complicated to be treated analytically, they are shown to lead to simpler forms for the special cases of axial symmetry, very long and very short wavelengths. In the absence of established values for the piezoelectric moduli of bone and of the elastic constants of the inner spongy layer, a numerical solution to the model does not seem worthwhile at present.
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43.40.Ey Vibrations of shells
43.20.Bi Mathematical theory of wave propagation
43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants
43.80.Cs Acoustical characteristics of biological media: molecular species, cellular level tissues

Frequency analysis of two types of simulated acoustic emissions

W. J. Pardee and L. J. Graham

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 793-799 (1978); (7 pages) | Cited 1 time

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It has been suggested that the frequency spectrum of an acoustic emission burst may be a partial ’’signature,’’ identifying the source. To explore this possibility we have studied in some detail, theoretically and experimentally, two qualitatively different simulated acoustic emissions. The first is the fracture of small (20–40 μm) silicon carbide grains on a steel slab. The second is the impact of a small elastic sphere of various materials on the same slab. Our primary objective has been to test our understanding of the medium response, and, consequently, the extent to which we can determine the source spectrum from the observed spectrum.
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43.40.Le Techniques for nondestructive evaluation and monitoring, acoustic emission

Large‐amplitude vibration of oblique panels

R. S. Srinivasan and S. V. Ramachandran

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 800-805 (1978); (6 pages)

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This paper deals with the large‐amplitude free vibration of skew plates having variable thickness. Two governing nonlinear differential equations in terms of the lateral deflection and ’’force function’’ are derived in the oblique coordinates. The edges of the plate are assumed to be clamped and free to move in the plane of the plate. The differential equations together with the boundary conditions are transformed into nonlinear algebraic equations by using the integral equation for beams along the oblique directions. These algebraic equations are then solved by the Newton–Raphson procedure. Numerical work has been done and graphs showing period versus amplitude are presented for different values of thickness parameter, skew angle, and aspect ratio.
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43.40.Dx Vibrations of membranes and plates

Application of a quartz crystal with electrode‐tab configuration for simultaneous mass and temperature determination

E. C. van Ballegooijen, F. Boersma, and C. van der Steen

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 806-814 (1978); (9 pages) | Cited 1 time

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In this paper the possibility of using a quartz crystal coated with electrodes and a tab for simultaneous mass and temperature determinations is investigated. The practical applicability of the recently introduced method, based on the properties of the resonant frequencies of an electrode‐tab system, strongly depends on the accuracy by which mass and temperature can be determined. It is shown from the experiments presented in the paper that the accuracy of the method is strongly improved by measuring the temperature with the help of the higher‐order harmonic overtones related to the electrodes, and by measuring the mass with the help of the fundamental resonant frequency related to the tab. An analysis to determine the error in the mass and temperature, resulting from calibration and experimental errors, is given. The results from the analysis show that a mass change of 10 Å (copper) and a temperature change of 0.01 °C can be determined within 3% and 18%, respectively. Some suggestions are given for further improvement of the method in order to make it useful for practical applications.
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43.40.At Experimental and theoretical studies of vibrating systems
43.40.Dx Vibrations of membranes and plates
43.20.Ks Standing waves, resonance, normal modes
43.38.Fx Piezoelectric and ferroelectric transducers

Psychological Assessment of Aircraft Noise Index

Chikio Hayashi, Susumu Kondo, and Habuku Kodama

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 815-822 (1978); (8 pages)

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The aim of this paper is to describe the nature and development of a new index called Psychological Assessment of Aircraft Noise Index (PAANI). An intervening variable UFR (Unfavorableness Ratio) is used without setting directly the relation between psychological measurements and psychological reaction of the inhabitants to aircraft noise as is done for  Weighted Equivalent Continuous Perceived Noise Level  and  Noise and Number Index.  UFR is made for an aircraft by using the  Theory of Quantification,  which evaluates the physical measurements (maximum A‐weighted noise level, duration of noise above 70 dB, and frequency spectra of the noise). The characteristic I (r) of the noise at the rth location is defined as the number of aircraft over fixed value of UFR on the distribution of UFR calculated from the aircraft passing over the location. While the psychological reaction to noise of the inhabitants in the rth location is estimated from data obtained by a social survey, the PAANI is determined from the distribution of Guttman scores of noise reaction shown by the inhabitants in the location. The characteristics of I30(r), which is the number of aircraft over 30% of UFR at the rth location, correlates well with the index of psychological reaction of the inhabitants of the rth location for all r locations.
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43.50.Ba Noisiness: rating methods and criteria
43.50.Lj Transportation noise sources: air, road, rail, and marine vehicles
43.50.Qp Effects of noise on man and society

Insulating buildings from aircraft noise

J. D. Quirt

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 823-831 (1978); (9 pages)

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Field measurements of insulation against aircraft noise were made for a wide range of building components. Single‐figure ratings of noise insulation were derived, and a design procedure for use of these ratings is presented. The dependence of the effective sound insulation on the spectral balance of aircraft noise is examined.
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43.55.Ti Sound-isolating structures, values of transmission coefficients
43.50.Lj Transportation noise sources: air, road, rail, and marine vehicles

Studies of acoustical parameters in open‐plan offices

A. C. C. Warnock

J. Acoust. Soc. Am. Volume 63, Issue 3, pp. 832-840 (1978); (9 pages)

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The major acoustical elements of open‐plan offices—windows, walls, ceilings, and partial‐height screens—have been studied in laboratory simulations of open‐office acoustical problems. The basic test environment is an anechoic room with a carpet‐covered plywood floor over which the test elements are deployed. Measurements of attenuation provided by various configurations were made in one‐third‐octave bands and the data processed to permit study of seven single‐figure ratings for attenuation between work stations (the ’’interzone attenuation’’). Of the ratings tested the A‐weighted level and the Noise Isolation Class correlated best with Articulation Index, which is taken as the ’’true’’ measure of performance. For testing ceiling systems it is confirmed that the commonly used test arrangement is insensitive to significant changes in the ceiling system. A simple modification of the procedure is proposed.
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43.55.Gx Studies of existing auditoria and enclosures
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