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Volume 77, Issue 6, June 1985

Audiovisual materials and microcomputer software for teaching vibration and sound
View Description Hide DescriptionCurrently available films, filmloops, slides, overhead transparencies, and microcomputer software are listed for those who teach courses involving vibration and sound. The topics covered and addresses of the suppliers are given.

A high‐angle one‐way wave equation for seismic wave propagation along rough and sloping interfaces
View Description Hide DescriptionA model of acoustic propagation in solid media has been derived. It is a one‐way wave equation based on a high‐order approximation, called a Padé approximation, to the square‐root function. The physical properties of the environment are modeled as stratified, thin, homogenous layers. The model can be applied to obtain an approximate solution in range‐dependent environments by allowing the properties of the layers to vary in range. Furthermore, the effects of rough or sloping reflecting interfaces can be approximated using an equivalent reflector, consisting of two thin layers whose properties vary in range.

Scattering by a partially illuminated, doubly periodic, doubly infinite surface
View Description Hide DescriptionUsing the plane‐wave decomposition of the incident field and the T‐matrix method, scattering by a partially illuminated, doubly periodic, doubly infinite surface is investigated. The general expressions thus derived are simplified for the case when the illuminated area is large. Numerical examples illustrating the applicability of the procedure are also given.

The inverse source problem for an oblique force on an elastic plate
View Description Hide DescriptionA time‐dependent concentrated force applied obliquely on the surface of a plate generates elastic waves in the plate. The determination of the location, orientation, and time history of the force from the transient wave records is referred to as the inverse source problem of elastic waves. This paper presents an iterative method of deconvolution which determines the orientation and time‐dependent amplitude of the force from the transient response of the plate surface at a minimum of two locations, the source location being given. Numerical results are presented for forces with various orientations and time histories, and for synthetic data both with and without noise.

Radiation from a point source and scattering theory in a fluid‐saturated porous solid
View Description Hide DescriptionThe time harmonic Green function for a point load in an unbounded fluid‐saturated porous solid is derived in the context of Biot’s theory. The solution contains the two compressional waves and one transverse wave that are predicted by the theory and have been observed in experiments. At low frequency, the slow compressional wave is diffusive and only the fast compressional and transverse waves radiate energy. At high frequency, the slow wave radiates, but with a decay radius which is on the order of cm in rocks. The general problem of scattering by an obstacle is considered. The point load solution may be used to obtain scattered fields in terms of the fields on the obstacle. Explicit expressions are presented for the scattering amplitudes of the three waves. Simple reciprocity relations between the scattering amplitudes for plane‐wave incidence are also given. These hold under the interchange of incident and observation directions and are completely general results. Finally, the point source solution is Fourier transformed to get the solution for a load which is a delta function in time as well as space. We obtain a closed form expression when there is no damping. The three waves radiate from the source as distinct delta function pulses. With damping present, asymptotic approximations show the slow wave to be purely diffusive. The fast and transverse waves propagate as pulses. The pulses are Gaussian‐shaped, which broaden with increasing time or radial distance.

Solution of the fundamental problem of transient acoustic propagation in a borehole with the hybrid method
View Description Hide DescriptionThe fundamental acoustic logging problem of a pulsed point source surrounded by both vertical and horizontal boundaries is solved with the hybrid method. The hybrid method yields the complete synthetic waveform including the head wave and the normal mode arrivals. The essence of the hybrid method consists in converting the head wave branch‐cut contribution into discrete modes which, together with the normal modes, form a complete basis for the solution in each region. Boundary conditions at the horizontal bed boundary then couple the modes between different regions and enable the solution to be expressed in terms of reflection and transmission matrices of modes. Numerical results are illustrated as a function of the formation parameters. Transmission coefficients of head waves are calculated. The advantages of the hybrid method are also discussed.

On the acoustic power radiated by line forces on elastic beams
View Description Hide DescriptionThe importance of the spatial extent of applied forces in the topic of structural radiation is studied through formulation of the sound power radiated by a line force acting on an infinite elastic beam. The expression for sound power is integrated numerically and the results examined as a function of k L, the acoustic length of the force, and the wavenumber ratio. Below coincidence the power was found to be generally proportional to (k L)^{−} ^{2}. Near and at coincidence, sufficiently large force scales have a significant effect on the power produced. In particular, when the length of the force is an integral multiple of the critical wavelength, the coincidence peak is completely suppressed. Above coincidence, minima in the second power occur when the force length is a multiple of the wavelength of the free bending wave. These minimal values of power are shown to be nearly equal to the power radiated far below coincidence. These results are discussed in terms of the coupled structural/acoustic wavenumber response function and the wavenumber spectrum of the applied force. In addition the relative effects of light fluid loading on the radiation at coincidence are presented.

Acoustic impedance of small, circular orifices in thin plates
View Description Hide DescriptionMeasurements of acoustic impedance have been made on a series of small, circular orifices (0.1–0.3 mm radius) in thin plates (0.038 and 0.38 mm thickness). Both real and imaginary components, over the frequency range 0.6–3 kHz, were obtained using an impedance tube technique. The zero frequency limit of resistance was measured with a flow resistance device. Only small amplitude acoustic signals were considered. For the range of orifice radii and frequencies selected the boundary layer thickness is comparable to the radius, and the usual high‐frequency expressions for orifice impedance do not apply. Within the limits of experimental error (approximately 12% for resistance and 6% for reactance) the measured values are in reasonable agreement with Thurston’s general but approximate theory [G. B. Thurston, J. Acoust. Soc. Am. 2 4, 653–656 (1952)]. The measurements support the simple idea that b o t h real and imaginary components of orifice impedance can be calculated assuming an effective total end correction 16a/3π, where a is the orifice radius.

Observations of sound propagation during a southern Alberta chinook
View Description Hide DescriptionAn experimental investigation of the propagation of sound in the presence of an elevated temperature inversion has been conducted on a farm site in southern Alberta. The refractive focusing of sound in the inversion layer was observed to cause shadow zones and regions of sound enhancement in which sound levels were up to 20 dB lower and 20 dB higher, respectively, than during normal afternoon conditions. Fluctuations of 35 dB in the sound intensities at microphones 1730 and 2180 m from the source have been witnessed as the location of the focusing region changed. Ray tracinganalysis for meteorolgical data acquired predicts excess attenuations of sound consistent with those recorded. The use of a monostatic acoustic sounder proved useful in correlating anomalous sound levels with the appearance of temperature inversions.

Generalized Burgers equation for plane waves
View Description Hide DescriptionBurgers’ equation, an equation for plane waves of finite amplitude in thermoviscous fluids, is generalized by replacing the thermoviscous term A u _{ t’t’} (A is the thermoviscous coefficient, uparticle velocity, and t’ retarded time) with an operator L(u). This operator represents the effect of attenuation and dispersion, even if known only empirically. Specific forms of L(u) are given for thermoviscous fluids, relaxing fluids, and fluids for which viscous and thermal boundary layers are important. A method for specifying L(u) when the attenuation and dispersion properties are known only empirically is described. A perturbation solution of the generalized Burgers equation is carried out to third order. An example is discussed for the case α_{2}=2α_{1}, where α_{1} and α_{2} are the small‐signal attenuation coefficients at the fundamental and second‐harmonic frequencies, respectively. The growth/decay curve of the second harmonic component is given both with and without the inclusion of dispersion. Dispersion causes a small reduction of the component. The extension of the generalized Burgers equation to cover nonplanar one‐dimensional waves is given.

Nonlinear sound waves from a uniformly moving point source
View Description Hide DescriptionNonlinear sound waves from a uniformly moving source with dimensions smaller than the wavelength of the emitted sound are investigated. They are described by spherical Burgers’ equations with parameters depending on the sourcevelocityV and the direction angle θ from the source to the point of observation. It is seen that for certain V and θ values, both for V less than and greater than the sound velocity in the medium, shock waves occur, which do not occur in nonlinear waves from a fixed sound source.

Bubble interaction effects on waves in bubbly liquids
View Description Hide DescriptionWe derive effective equations for wave propagation in bubbly liquids which include bubbles interactions effect. We homogenize both the linear and the nonlinear versions of the microscopic equations by two methods. The interaction between the pressure fields is found to increase the speed of sound relative to the Foldy approximation.

A shallow water experiment to determine the source spectrum level of wind‐generated noise
View Description Hide DescriptionAn experiment was conducted in a shallow water region of the Mediterranean Sea to study wind‐generated noise. In addition to measuring the noise field, propagation‐loss data were collected and used in a detailed modeling of the environment. The environmental information was then used as input to a noise model based on wave theory that computes the noise field in the water column for a given (unknown) source strength. By comparing model predictions with data, the influence of the environment on recorded noise levels could be removed and a measure of the noise source spectrum levels obtained as a function of wind speed. It was found that noise levels correlate better with wind speed than with wave height. In addition it was found that the nearfield contribution dominates the noise level, with the result of producing virtually constant noise intensity over depth from moderate to high wind speeds and frequencies above 200 Hz.

An assessment of second‐order perturbation theory for scattering of sound by hard, statistically rough surfaces
View Description Hide DescriptionPerturbation theory and boss models for rough surfacescattering are compared for the case of a surface bossed with oblate hemispheroids (height a≤radius b). In particular, the surface consists of identical, hard, hemispheroidal bosses sparsely and independently distributed on a hard plane by means of a uniform probability law. To apply perturbation theory we compute the surface correlation function, operate on that function, and compute an effective boundary admittance. Finally, we compare that admittance with (farfield) near‐exact results for hemispherical bosses and for oblate hemispheroidal bosses. Calculations of the magnitude of the reflection coefficient ‖R‖ are presented showing that for low frequencies, i.e., k b=0.1, the discrepancy is approximately 70% for a=b but less than 10% for a/b=0.1. In general, the error decreases as grazing angle increases and decreases as a→0. Thus, at low frequencies perturbation theory is shown to give excellent results for ‖R‖ when a/b≪1, despite the discontinuous and infinite slope in the surface where the bosses meet the base plane. We also examine the effects of increasing frequency for hemispherically bossed surfaces, and in particular, we see errors as large as 3 dB for sparse, hemispherical bosses with a=b=5 m and frequencies less than 60 Hz. We conclude that perturbation theory is excellent in the case of oblate hemispheroids, shows significant percentage errors for hemispheres and should not be used for prolate hemispheroids.

Resonance response of submerged, acoustically excited thick and thin shells
View Description Hide DescriptionWe study the elastodynamic spectral response of thick and thin shells in water when they undergo resonancescattering caused by the incidence of sound waves that impinge upon them at selected aspects. All the shells considered are elastic, air‐filled, and of cylindrical and prolate spheroidal shapes. Their thickness is intentionally varied three orders of magnitude from very thick (i.e., h≡1−b/a=90%) to very thin (i.e., h=0.1%), so that the effects of shell stiffness on their scattering behavior can be quantitatively analyzed and understood. The quantities a and b are the outer and inner shell radii, respectively. Material composition effects are studied by comparing various metals such as steel and aluminum. The shell motions are described by the exact equations of elastodynamics in all cases, so that comparisons may be drawn concerning the regions of applicability of pertinent shell theories. For the spheroidal shells no exact solution is possible, thus, we have presented results based on an extended T‐matrix method that still makes use of the exact 3‐D equations of elastodynamics to describe the shell vibrations.
For a wide range of shell thicknesses and compositions, we have computed the positions of the poles of the scattering amplitudes, in the complex frequency plane x _{1}. Here, x _{1} is k _{1} a, where k _{1}=ω/c _{1}, ω is the angular frequency of the incident wave,c _{1} is the sound speed in the outer medium, and a is the shell’s outer radius. These poles group themselves in certain families and give rise to surface waves that circumnavigate the shell, either in the water side (Franz or SEM‐type poles or waves) or inside the shell metal (Rayleigh/whispering gallery waves for solid bodies, or Lamb momentless and flexural waves for shells). This latter set of waves is the least attenuated and the most dominant. We have shown how the pole families affect the spectral shape of the form function, and that of it’s partial waves, with their interacting modal backgrounds and resonances. As the shells become thinner, only one‐pole family is shown to remain within the displayed boundary of the complex x _{1} plane. This single‐pole family becomes responsible for the generation of the first‐order set of symmetric/antisymmetric Lamb waves in the shell. All these concepts are illustrated with many examples which show the crucial importance of the pole‐position diagrams to understand the spectral behavior of the form function, and the way it reveals information about the shell and the types of waves it supports on its surfaces. A transition from the rigid to the soft background is observed as the shells become very thin, and it is used to properly isolate the resonances of very thin shells. Extensions of these spectral results to the time domain are forthcoming.

Sound transmission loss: Comparison of conventional techniques with sound intensity techniques
View Description Hide DescriptionSound transmission losses for a single layer wall are measured in a reverberation room facility using conventional methods (ASTM E90) and the more recently introduced sound intensity method. The specimen is placed in five positions in the tunnel between the two reverberation rooms and measurements are made for four different absorptive conditions in the smaller room. Significant differences between the two measurement techniques are found at low frequencies and at high frequencies. Low‐frequency differences are attributed partly to the increase in sound energy close to the surfaces of the receiving room (the Waterhouse effect) and the lack of any consideration of this in standard test methods. Inclusion of the Waterhouse term in the conventional transmission loss formula improves the agreement between the conventional and the sound intensity measurement technique at low frequencies. High‐frequency differences are not explained.

Introduction of mass conservation law to improve the tomographic estimation of flow‐velocity distribution from differential time‐of‐flight data
View Description Hide DescriptionThe mass conservation law is combined as one of the utilizable physical constraints with differential time‐of‐flight data to improve the tomographic estimation of flow‐velocity distribution by means of inverse operation of the matrix. The formulation and computer simulation are described.

Asymptotic analysis of a viscous cochlear model
View Description Hide DescriptionA model of cochlear macromechanics, involving a viscous cochlear fluid, is analyzed asymptotically for slowly varying membranes. The results exhibit the effect of viscosity on the amplitude, wavelength, and damping rate, and confirm the conclusion that viscosity is not important. However the method can be used on other models, such as those of cochlear micromechanics, where viscosity is more important.

Cochlear nucleus, inferior colliculus, and medial geniculate responses during the behavioral detection of threshold‐level auditory stimuli in the rabbit
View Description Hide DescriptionRabbits were conditioned to respond behaviorally to auditory stimuli by pairing a white‐noise conditioned stimulus (CS) with a corneal airpuff unconditioned stimulus (US). The conditioned response (CR) was movement of the nictitating membrane (NM). After the subjects were responding at better than the 90% correct level, the intensity of the auditory stimulus was reduced to behavioral threshold using a staircase procedure. Simultaneous measurements of neural unit activity and behavioral NM responses were then made in rabbits performing at behavioral threshold. After the experiment was completed neural unit responses during behavioral detection trials were compared to neural responses made during nondetection trials. Neural unit responses to a constant intensity, white‐noise stimulus at behavioral threshold were well defined and essentially identical on behavioral detection and nondetection trials in the ventral cochlear nucleus, the ventrolateral division of the central nucleus of the inferior colliculus, and the ventral division of the medial geniculate body. This suggests that an auditory stimulus can be neuronally ‘‘detected’’ without being behaviorally detected, and that the neural ‘‘decision’’ to respond behaviorally is not made in these nuclei. Responses recorded from the dorsomedial division of the central nucleus of the inferior colliculus, the pericentral nucleus of the inferior colliculus, and less commonly in the medial division of the medial geniculate body were also clearly present and nearly identical during the onset of the auditory stimulus, but were sometimes consistently different for detection and nondetection conditions during the latter part of the auditory stimulus. These brain regions appear to receive both auditory and nonauditory inputs, and show responses which are more highly correlated with detection behavior.

A power‐law transformation predicting masking by sounds with complex spectra
View Description Hide DescriptionIn a previous paper [R. Lutfi, J. Acoust. Soc. Am. 7 3, 262–267 (1983)], the following rule was proposed for predicting masking by pairs of simultaneous maskers; X _{ a b } =[X ^{ P } _{ a }+X ^{ P } _{ b }]^{1/P }, where in units of power, X _{ a } and X _{ b } are the individual masking effects of the maskers, X _{ a b } is the combined effect, and 0.20≤p≤0.33. In this paper, the rule is used to predict the results of studies in the literature that have measured masking by sounds with various other complex spectra. In most of these studies, the individual maskers comprising the complex have nominally nonoverlapping power spectra. A single value of p=0.33 yields predictions in good agreement with the data of these studies. For a study in which the component maskers overlap more appreciably, a larger value of p=0.50 produces equally accurate predictions. The rule also predicts some general features of the results of studies in which the individual effects of the maskers in the complex are not known but can be estimated. It is suggested that the general applicability of the rule reflects a conjoint analysis by the auditory system of two or more waveform statistics.