Volume 75, Issue 2, February 1984
Index of content:

Reflection and transmission of obliquely incident Rayleigh waves by a surface‐breaking crack
View Description Hide DescriptionReflection, transmission, and scattering of Rayleigh waves that are obliquely incident on a surface‐breaking crack are investigated. The formulation of the problem has been reduced to two systems of singular integral equations of the first kind for the dislocation densities across the crack faces. The systems of integral equations are solved numerically. Substitution of the dislocation densities into appropriate representation integrals yields the reflected and transmitted surface waves. Reflection and transmission coefficients are plotted versus the angle of incidence for various values of the frequency and versus the frequency for various values of the angle of incidence. A critical angle of incidence, which depends on the material properties of the solid, has been observed. Beyond this angle no mechanical energy is radiated into the solid by body waves.

Scattering by a cylinder: A fast exact numerical solution
View Description Hide DescriptionThe known exact analytic solutions to the problem of (acoustic and electromagnetic)scattering by a two‐dimensional infinite right circular cylinder are not in closed form, but consist of infinite series, each term of which contains Hankel and Bessel functions of increasing order, and the convergence rate of which decreases rapidly with increasing (k a) numbers. For a given numerical solution, it is thus necessary to compute many Hankel and Bessel functions in high order for each spatial datum point for which the scattered field need be calculated. Presented is an exact numerical method of solution, which is in closed form, and requires the computation of only one Hankel function of order unity per spatial datum point for which the fields need be calculated. The method consists of a closed form numerical deconvolutionsolution of the scatteringintegral equation, executed efficiently with the aid of the fast Fourier transform algorithm, thus requiring only ( (3)/(2) N log_{2} N) complex arithmetic multiply–add operations, and the computation of only N Hankel functions of order unity, where N is the number of spatial datum points for which a solution is required. Because of the extreme simplicity of the method of solution, a computer program listing for the algorithm is presented. Numerico‐experimental results verifying the speed and accuracy of the method are also presented.

Elements of a geoacoustic model of the upper crust
View Description Hide DescriptionElements of a geoacoustic model of the geologically young (< 10 million years) upper crust, the top few hundred meters of the basalt subbottom, are described. The model is based on analysis of low‐frequency reflectivity versus angle data at a 1 million‐year‐old sediment‐free site, as well as limited Deep Sea Drilling Project downhole logging results, and extrapolated seismic refraction measurements. The upper crust at this site, which is in close proximity to the crest of the East Pacific Rise, may be characterized by low interfacial velocities (V _{ p }∼2800 m/s and V _{ s }∼800 m/s), large gradients (3–5 s^{−} ^{1}), and substantial rms roughness (∼5 m). The low‐inferred shear speed implies no shear critical angle. Hence, low‐frequency energy incident on the bottom at small grazing angles is in large part transmitted into the rock, refracted by the gradient, and reradiated into the water. Scattering loss occurs at both the initial incidence and the interaction of the refracted energy at the boundary. Low interfacial shear speeds lead to large grazing angles at the boundary for the transmitted shear waves, large wavenumbers and, hence, large boundary‐scattering losses; small changes in interfacial shear speed produce large changes in subsurface boundary‐scattering loss, and hence in the reflection coefficient. A summary of logging and extrapolated seismic refraction measurements in the young crust, below 10 million years, suggests that the range of interfacial shear speeds is between about 800 and 2400 m/s. In older crust, the range of shear speeds is projected to be significantly different. Ramifications of the site dependence of upper crustal properties, particularly shear speed, on sound propagation are discussed.

Application of Twersky’s multiple scattering formalism to a dense suspension of elastic particles in water
View Description Hide DescriptionAcoustic wave propagation through a dense suspension of solid elastic particles in water is studied. The particles in suspension have a size distribution and their relative positions are described by a pair‐correlation function. Twersky’s multiple scattering formalism is employed to obtain new analytical expressions for the phase velocity and coherent attenuation of a wide range of concentrations. Numerical results presented are of interest in the study of marine sediments.

Scattering of sound from hard and soft eggcrate surfaces
View Description Hide DescriptionThe problem of scattering of a plane sonic wave from hard and soft eggcrate surfaces, composed of tridimensional protuberances distributed periodically on a plane along two orthogonal directions, is examined by means of the Rayleigh plane wave expansion method, numerically implemented by Fourier base projection of the boundary conditions. The Kirchhoff approximation solution, which predicts that the intensity specularly reflected from a surface of the form x _{3}=f(x _{1})+f(x _{2}) is the square of the intensity specularly reflected from a simple periodic surface of the form x _{3}=f(x _{1}), is shown, by means of the Rayleigh solutions, to be well‐verified for surfaces with small‐amplitude irregularities.

Linear inviscid wave propagation in a waveguide having a single boundary discontinuity: Part I: Theory
View Description Hide DescriptionAn examination of wave propagation in waveguides of rectangular cross section having a single boundary discontinuity is presented. Special attention is paid to waveguides with heights that are small compared to an acoustic wavelength. It is shown that the dynamic behavior of the enclosed fluid can be parametrized by the value of a single small parameter ε, where ε is the ratio of the typical duct height H _{0} to the wall wavelength L _{0}. The influence of planar discontinuities of zero and small but finite thickness on wave propagation is determined using the method of matched asymptotic expansions. Junction conditions, impedance across the junction, and uniformly valid composite expansions for the pressure in the duct are presented.

Linear inviscid wave propagation in a waveguide having a single boundary discontinuity: Part II: Application
View Description Hide DescriptionThe method of match asymptotic expansions MMAE, is used to analyze wave propagation in two problem geometries. The acoustic pressure is evaluated for a waveguide having a single discontinuity in wall slope and a waveguide having a right‐angle bend. A two‐port representation of the fluid motion across the discontinuity for each problem is tabulated. A uniformly valid expression for the pressure for each problem is given.

Acoustic radiation from vibrating surfaces at characteristic frequencies
View Description Hide DescriptionThe application of boundary integral methods to the problem of acoustic radiation suffers from nonexistence or nonuniqueness problems at the characteristic frequencies of the associated interior Dirichlet problem. To overcome this difficulty, an iterative overdetermination scheme is developed. First, the surface integral Helmholtz equation is discretized, and at noncharacteristic frequencies, the resulting system of linear algebraic equations can be solved directly, yielding the values of the acoustic pressure at the boundary nodal points. At characteristic frequencies, the system matrix becomes ill‐conditioned and the direct solution is not possible. An approximate surface impedance function is then assumed to serve as a basis for the computation of approximate farfield pressures. These are then utilized to form an overdetermined system, which is solved with the least‐squares procedure. This solution can be used to compute the next‐order approximation, and the process is continued. The method is applied to the cylindrical transducer problem and proves to yield good results at characteristic frequencies. It is also used to solve a structural radiation problem, for which no characteristic frequencies are found. Nonexistence of such frequencies for problems of this type is conjectured, although no general proof is given.

Diffraction effects in surface acoustic wave harmonic generation
View Description Hide DescriptionFourier analysis method has been applied to model the diffraction integral of the second harmonic field nonlinearly generated by a surface acoustic wave beam. Cross‐section profiles of the second harmonic field have been calculated at different longitudinal positions along an acoustic beam propagating on a yz‐LINbO_{3} crystal. Theoretical curves are reported together with experimental results relative to the case of a fundamental wave emitted by a 24‐wavelengths‐wide transducer at the frequency of 35 MHz. A theoretical determination of the energy loss produced by diffractioneffects in second harmonic generation is performed by evaluating the acoustic energy of the second harmonic wave over cross sections of the acoustic beam and by normalizing these quantities to the ones relative to plane wave propagation. Diffraction loss in isotropic and anisotropic materials has been calculated as a function of the longitudinal position along the beam axis for different directivities of the source. A generalized diffraction loss curve is reported, which takes different beam directivities and different anisotropy parameters into account for the case of isotropic media and of anisotropic media with parabolic velocity surfaces.

Reflection of impulses as a method of determining acoustic impedance
View Description Hide DescriptionAn impulse technique has been developed which allows investigation of the reflection of acoustic transients at different angles from an impedance boundary. From measurements of the direct and reflected impulses, the complex surface impedance has been calculated from the ratio of the corresponding Fourier components. The surfaces were modeled as a locally reacting boundary between homogeneous media; this representation was found to be adequate for grassland and a carpet layer but unsatisfactory for a thick fiberglass layer. There was no need to include a ground wave term when reconstituting pulse shapes at different angles over grass or carpet for the range of frequencies and angles investigated in this paper.

Optimal frequencies for meteorological sodar
View Description Hide DescriptionThe expression for the signal‐to‐noise ratio at the input of a sodar receiver when sounding the boundary layer of the atmosphere has been obtained and investigations of the frequency dependence of this ratio have been made. It is shown that at an acoustic sounding of the atmosphere there are optimal frequencies, corresponding to a maximum of the signal‐to‐noise ratio, and equations for calculating these frequencies were obtained. Investigations of optimal frequencies of sounding have shown that their values are determined by the geometry of sounding,spectrum of the ambient background noise, and meteorological conditions at the place of sodar operation. The use of carrier frequencies being nonoptimal for the given conditions results in loss in the signal‐to‐noise ratio and to ineffective use of potential possibilities of sodars.

Spatial coherence of multipath underwater acoustic transmission: An experiment at two frequencies concurrently
View Description Hide DescriptionMeasurements were made of the fluctuations in amplitude and spatial coherence of acoustic wavefronts transmitted through the deep ocean at two frequencies concurrently, 114 and 400 Hz. The signals were generated by a ship‐suspended souce at 1000‐ft depth and received over two ranges, 130 and 145 nmi, on a string of five bottomed receivers laid horizontally on a deep‐water slope at about 5000‐ft depth. The receiver spacing varied from 500–2500 ft. Amplitude fluctuations were found to differ significantly at receiver separations of 500 ft and appeared unrelated at separations of 2000 ft or more. For multipath transmission, unlike single‐path transmission, the relative phase fluctuations between given receiver pairs were not proportional to frequency, and phase coherence at a given receiver separation was generally less than for single‐path transmission. Coherence at 145 nmi was almost as good as for single path, presumably because ray‐tracing predicts a dominant path and because the phase measurements were averaged over 10 s, and thereby discriminated against frequency modulationeffects by the sea surface. Thus frequency resolution and time resolution of the experiment are as important to the results as range, frequency, and receiver separation. Poorer coherence at 130 nmi is tentatively attributed to lack of a dominant arrival at 114 Hz, and near‐surface refractions at both frequencies.

Low‐frequency sound propagation in the South Fiji Basin
View Description Hide DescriptionIn March 1976, a joint experiment of the Naval Underwater Systems Center, New London, and the New Zealand Defence Scientific Establishment was carried out to investigate the characteristics of low‐frequency (10–400 Hz) underwater sound propagation in the South Fiji Basin north of New Zealand using explosive sound sources. The source depth was 18 m and as a result propagation nearly everywhere within the basin was dominated by bottom‐reflected modes. There were 5‐dB level enhancements associated with the bathymetric features forming the southern, western, and eastern boundaries of the basin and 15–20‐dB enhancements associated with the slope up to the Fiji Plateau to the north. The propagation loss across the abyssal plains is predicted well, while the level enhancements associated with all the features bounding the basin and the typically 15‐dB shadowing losses associated with the ridges east and west of the basin can be approximately predicted with a model (ASTRAL) which allows for horizontal changes in the environment. However, it appears that more sophisticated models may be required to accurately predict the enhancement and shadowing.

Acoustic propagation in a shallow sound channel in the Northeast Pacific Ocean
View Description Hide DescriptionAn experiment was carried out off the west coast of Canada to investigate the effects of a shallow sound channel on propagation for the frequency range from 20–4000 Hz. Using small explosive charges deployed in the shallow channel, the propagation loss was measured at receivers located in both the shallow and deep sound channels. The shallow channel behaved like an acoustic waveguide with an optimum duct propagation frequency of 800 Hz. At the optimum frequency, the propagation loss closely approached that due to cylindrical spreading, while at frequencies lesser or greater than the optimum the loss increased by up to 20–30 dB. The sound channel propagation was strongly dependent on changes in the environment with range, therefore the parabolic equation was used to model the experimental results. The parabolic equationmodel correctly predicts the range and frequency‐dependent trends observed in the measured data.

Arctic Ocean background noise caused by ridging of sea ice
View Description Hide DescriptionA new method is presented to explain how noise is generated under pack ice by ridging of the pack ice. The energy dissipated during the ridging process is assumed to be the proper measure of the noise source level. Noise source levels generated by ridging are simulated. Noise intensity at a specific site is calculated by summing signals from all these sources after accounting for propagation losses. Calculations are made to compare this simulated noise with observations for an experiment conducted during the winter of 1975–76 in the Beaufort Sea. During a 120‐day period, 46% of the intensity of the noise signal is explained using this process, and over several 20‐day periods, in excess of 64% is explained. In addition to explaining a significant amount of energy and ambient noise, the model is attractive on physical grounds and properly explains lack of noise when winds are high but ice is strong enough to resist ridging.

Horizontal spatial coherence of ocean reverberation
View Description Hide DescriptionReverberation from the oceansurface, bottom, and volume is discussed in the context of the point scatterer model, with uniform spatial distributions. It is shown that, for sufficiently narrow beamwidths or bandwidths, the covariance factors into a product of spatial and temporal covariances. The spatial covariance is shown to vanish for separations larger than the horizontal width of the transmitting array. This prediction is found to be in reasonable agreement with the experimental results of Wilson and Frazer and with our own sea surface reverberation data reported here.

Profile of laser‐produced acoustic pulse in a liquid
View Description Hide DescriptionRecently, Lai and Young [J. Acoust. Soc. Am. 7 2, 2000 (1982)] and Heritier [Opt. Commun. 4 4, 267 (1983)] have independently calculated the profile of a thermo‐elastically generated opto‐acoustic pulse due to the passage of an excitation laser pulse of certain spatial and temporal intensity distributions in a weakly absorbing medium. We have found that their results are essentially equivalent for Gaussian intensity distribution of the excitation laser. We report the first experimental verification of such theoretical opto‐acoustic profiles excited by laser pulses of various pulse widths τ_{FWHM} (8 ns and 1.3 μs) focused to different beam waists w _{0}. Our observation of the profile is performed with a probe beam deflection technique instead of using conventional acoustic transducers which have limited rise times and nonflat frequency response. Our results are in reasonable agreement with theory, and clearly indicate that sharp opto‐acoustic pulses can be generated by laser pulses of short τ_{FWHM} and small w _{0}.

The vibrational response of the rectangular parallelepiped with completely stress‐free boundaries
View Description Hide DescriptionPresented here are exact normal modesolutions for the free and forced vibration of the rectangular parallelepiped (block) with completely stress‐free boundaries. Such solutions are meaningful in the field of quantitative nondestructive evaluation where the object is to deduce flaw growth mechanisms from perceived transducer outputs. In order to do this, it is necessary to know the frequency response of the specimen, the transducer, and the specimen–transducer interface, since each of these elements distorts the flaw growth signal. This presentation quantitatively describes the specimen response for the stress‐free rectangular parallelepiped with both impulsive and step function inputs, two common forcing functions used to modelacoustic emission source mechanisms.

The effect of numbers of noise events on people’s reactions to noise: An analysis of existing survey data
View Description Hide DescriptionThe effect of the number of noise events on noise annoyance has been examined in an analysis of data from large‐scale social surveys. The relative impact of noise level and number on human reactions is measured by the decibel equivalent number effect (k) expressed as the number of decibels which have an effect equivalent to that of a tenfold increase in number of events. Values of k differ between surveys but none is significantly greater ( p>0.05) than the value of k=10 which is implicit in L _{eq} or L _{dn}. The mean of the existing data provide a best estimate of k=5. Although there are some surveys in which annoyance decreases as numbers of events increase above about 150 a day, the available evidence is not strong enough to reject the conventional assumption that reactions are related to the logarithm of the number of events. The conventional assumption that the effects of number and peak noise level are additive cannot be rejected with these data. Differences between the surveys’ estimates of the effect of number of events remained large even when equivalent questionnaire items and definitions of noise events could be used. The most likely explanations for inconsistent estimates are (1) errors in specifying the values of noise parameters, (2) the effects of unmeasured acoustical and area characteristics which are correlated with noise level or number, and (3) large sampling errors which are due to community differences in response to noise. Multipoint annoyance scales give more reliable estimates than do dichotomous ‘‘very annoyed’’ measures. It is concluded that significant improvements in the knowledge about the effects of numbers of noise events will only occur if surveys include large numbers of study areas, a requirement which can only be met if economical noise measurement techniques are developed which have known levels of precision.

Effects of traffic noise on quality of sleep: Assessment by EEG, subjective report, or performance the next day
View Description Hide DescriptionTwelve people living in areas of high traffic noise were studied to assess its effect on their sleep. During 3 weeks, their sleep was monitored physiologically in the natural setting of their own bedrooms. Their performance and subjective report of sleep were recorded each day. For the middle week, the bedroom windows were double glazed to reduce the prevailing level of traffic noise at the bedside (L _{eq} 46.6 dB(A) over the whole night) by an average of 5.8 dB(A). Most physiological measures were unaffected by the noise reduction, but stage 4 sleep and low‐frequency, high‐amplitude delta waves in the EEG, both thought to be signs of deep sleep, were increased. Also unprepared simple reaction time, a test sensitive to drowsiness, was improved the next day, whereas a more stimulating short term memory test was not. Subjects also reported sleeping better. These improvements with double glazing were all modest in degree, but as they occurred in three independent and predicted measures of sleep quality, the view is supported that the prevailing level of traffic noise does indeed impair sleep.