Index of content:
Volume 67, Issue 1, January 1980

Mode coupling of guided elastic waves in wire with weak surface corrugation
View Description Hide DescriptionThis analytical study aims to explain the experimental result of the mode coupling of elastic waves in a long circular wire by means of the surface corrugations of the wire. It is assumed herein that the wire is made of ideally homogeneous, isotropic, linearly elasticmaterial and its free surface is subjected to weak and continuous corrugation. On the basis of the weakness of corrugation, the multiple scales are introduced to formulate the problem in a perturbation scheme. It is found, as expected, that the mode coupling does occur as the result of scattering from the corrugated surface at a certain frequency where the two modes have the same phase velocity. Coupled‐mode equations which govern the amplitude variation in the coupling are then derived systematically from the compatibility condition. The coupling coefficients depend on the modes involved, the geometrical characteristics of the surface corrugation, and the material constant of the wire. The resultant variation of amplitudes well characterizes the pulse distortion observed in the experiments.

Finite amplitude distortion of spherically diverging intense sound waves in air
View Description Hide DescriptionWaveform distortion in a free field of intense sinusoidal pressurewaves propagating in air was measured along the axis of a 122‐mm‐diam plane piston source for four fundamental frequencies, 14.7, 24.6, 35.7, and 63.6 kHz. The acoustic pressure of the fundamental and harmonic components was measured versus source amplitude at distances from 0.15 to 2.00 m from the source at amplitudes up to 160 dB r e 20 μPa. It was observed (1) that the pressure waveform reaches the stable form of an iterated shock at a smaller distance from the source for larger sourcepressure amplitudes, (2) that waveform distortion increases with frequency at a given source amplitude and a given distance, and (3) that a limiting level exists for the fundamental amplitude at a given point in a spherically diverging sound field with increasing source level. An empirical propagation relation due to Allen was further developed to include frequency dependence and air absorption. Complete shock formation was inhibited for the highest frequency sound field, presumably because of atmospheric molecular absorption.

Shape oscillation and static deformation of drops and bubbles driven by modulated radiation stresses—Theory
View Description Hide DescriptionDeformations of drops and bubbles opposed by surface tension and driven by radiation stresses at the interface are calculated using spherical harmonic expansions for the radial and tangential stresses. Superimposed acoustic waves produce stresses which oscillate at the difference frequency ω of the waves in addition to static stresses. When the effects of viscosity on the acoustic waves are omitted, the tangential radiation stress vanishes; a procedure is proposed for calculating the radial stresses from the theory for ’’Acoustic Radiation Pressure on a Compressible Sphere’’ [K. Yosioka and Y. Kawasima, Acustica 5, 167–173 (1955)]. The calculation of the response assumes incompressible second‐order flow and omits the body forces which are normally asociated with acoustic streaming. Resonance phase shifts and enhancements of the response should occur when ω is close to the natural oscillation frequency of a mode. Quadrupole resonance phase shifts and enhancements have been observed by the author [J. Acoust. Soc. Am. 67, 27–37 (1980)]. Diverse applications of the theory include the possibilities of: inference of the interfacial tension from the response; emulsification by exciting large amplitude oscillations; and deformation or splitting of bubbles by radiation stresses. The decay time of free oscillation is also calculated; a new term is found which is small but significant for drops surrounded by a liquid and supplements the theory for ’’The Oscillations of a Fluid Droplet Immersed in Another Fluid’’ [C. A. Miller and L. E. Scriven, J. Fluid Mech. 32, 417–435 (1968)].

Quadrupole resonance of drops driven by modulated acoustic radiation pressure—Experimental properties
View Description Hide DescriptionA new effect of acoustic radiation pressure was detected: the oscillating deformation of mm‐radius liquid drops (para‐xylene) acoustically levitated in a host liquid (water). A novel method is described for detecting μm amplitude deformations which utilized light scattered by the drop at the scattering angle normally associated with the rainbow. This rainbow photometry technique was used to measure the phase and relative amplitude of steady‐state, low‐frequency (?100 Hz) deformations induced by a modulated 217.5‐kHz acoustic wave. Some of the predictions in ’’Shape oscillation and static deformation of drops and bubbles driven by modulated radiation stresses—Theory’’ [J. Acoust. Soc. Am. 67, 15–26 (1980)] agreed with the measurements. Deformations driven by the radiation pressure could greatly exceed the first‐order displacement of the interface. The deformation amplitude varied as the square of the acoustic pressure, and phase had the expected dependence on the modulation frequency when data was normalized according to an experimentally determined damping parameter. The damping, however, was significantly larger than predicted for pure liquids. The interfacial tension inferred from the quadrupole resonanceproperties was 4% lower than static measurements. The apparatus was also used to levitate superheated drops and the technique may be useful for determining their interfacial tension.

Thermal effect on acoustoelasticity of isotropic elastic materials
View Description Hide DescriptionThe thermal effect on the propagation velocities in deformed isotropic thermoelastic material are investigated theoretically. First, isotropic thermoelastic materials in which the strain, the temperature or the entropy density, and the temperature gradient are adopted as the independent state variables, are defined. Then, homothermal and homentropic waves, which are purely mechanical waves, are defined. The propagation velocities of the principal longitudinal and transverse waves are determined. The transverse waves of two types have the same velocities, while the longitudinal waves of two types have different velocities, and the difference is the second order of the strain or stress.

Line integral theory of barrier attenuation in the presence of the ground
View Description Hide DescriptionA theory of diffraction is presented that is based on the line integral along the free edge of a semi‐infinite barrier. Expressions, which are not integrable analytically, are given for the cases where the source/receiver line is and is not perpendicular to the edge of the barrier. In this latter case the ’’offset’’ between source and receiver along the barrier enters into the mathematical expression in a more complicated way than hitherto supposed. When the barrier is situated on ground of finite impedance, the amplitude of the sound field is no longer expressible as a single constant that can be taken outside the integrand, but becomes a more complicated function than when the barrier is in free space and involves other parameters such as the source, receiver and barrier heights, and the impedance of the ground. These expressions are suitable for calculating (by numerical integration) the sound field behind a barrier due to the combined effects of direct, reflected, and ground waves in the practical situations where source and receiver are within a few meters of the ground and each several meters from the barrier.

Noise reduction by barriers on finite impedance ground
View Description Hide DescriptionThe sound field due to a point source behind a barrier on ground of finite impedance has been calculated from five theories that differ mainly in their theoretical approach to diffraction and the model for ground impedance. These predicted values for the sound field have been compared with results measured outdoors using plywood barriers on different combinations of hard and soft ground. Each of these theories allows for interference due to differences between several paths of propagation, determined by the geometry of the source, receiver, barrier, and ground. One of these theories that shows good agreement with measurements, has been extended to calculate the sound spectrum level behind a barrier due to an incoherent line source, and further, to calculate the overall or A‐weighted sound level for a known source spectrum. Results suggest that there is a significant effect, due to the presence of the ground, that is much greater than that due to absorptive properties of the barrier. Results also predict sound level reductions that differ from predictions using well‐known barrier theories (most noticeably a smaller insertion loss): these differences can be of the order of 10 dB(A) depending on geometry, source spectrum, and acoustical condition of the ground.

Acoustic synthesis of a flowduct area discontinuity
View Description Hide DescriptionAn experimental study of the acoustic pressurereflection coefficient at a sudden area expansion in a flowduct in regard to both magnitude and phase has been undertaken. The study was limited to low‐flow Mach numbers, frequencies supporting plane‐wave propagation, and an area transition ratio of 1:4. The magnitude of the coefficient is flow dependent and relatively insensitive to frequency while the phase is frequency dependent and relatively independent of flow. A semi‐empirical analytical model has been symthesized on the basis of available information that incorporates both frequency characteristics and flow affects through second order in the Mach number. The Karal discontinuity correction is important and appears to be a valid representation of the reactive acoustic fields at sufficiently low Mach numbers. The flow primarily influences the acoustic impedance level of both the upstream and downstream ducts and secondarily the acoustic pressure and velocity coupling parameters.

Foliage as a low‐pass filter: Experiments with model forests in an anechoic chamber.
View Description Hide DescriptionIn order to investigate the influence of foliage on sound transmission through vegetation, we have examined four model forest situations in an anechoic chamber. In general, we found that the foliage acts in the midfrequencies as a noiseamplifier, which is important for the vocalization and communication of animals. In the high frequencies the foliage of plants acts as a good noise filter. The acoustic properties of this filter are determined by the plant species, and depend mainly on the maximum size of the plant organs. A clear correlation is found between the maximum size of the plant leaves and the frequency, from which the filtering capacity of the plants starts. Also, a correlation could be detected between the total biomass of a specific plant species and the noise ’’attenuation’’ in the 1/3‐octave bands that are examined. The total noise attenuation caused by the vegetation depends on the spectrum of the noise: the sound pressure level of a noise spectrum with high levels in the high frequencies will be decreased by the plant foliage but the traffic noise spectrum will be changed only in pitch. We conclude that this filtering property of plant communities could be useful in noise abatement.

Jet noise diagnostics: Spurious sound generated by hot‐wire turbulence interaction
View Description Hide DescriptionMany attempts to measure source terms of jet noise by means of jet flow–jet noise cross correlations have been only partially successful. The major difficulty is suspected to be spurious ’’probe noise’’ generated by turbulence–sensor interaction. The present analysis predicts the effects of probe noise on measured cross correlations and cross‐spectral densities. The description relies on Ribner’s self and shear noisemodel, a development of Lighthill’s theory of jet noise. Predictions are supported by jet noise–jet flow correlations measured with a hot wire and with a nonintrusive device: a Laser Doppler Velocimeter (LDV). The hot wires are found to generate spurious but well correlated noise. This leads to major errors in jet noise diagnostics of low‐speed flows.

Propagation of sonic booms in the thermosphere
View Description Hide DescriptionA nonlinear theory for the long‐range propagation of sonic booms through the thermosphere has been developed. A realistic atmosphere is employed, and consideration is given to such factors as nonlinear stretching and decay of the wave, the effects of the caustic, the linear acousticattenuation, and the increase in Mach number due to the decreasing density at high altitudes. Detailed results are presented for the case of the Concorde SST in straight, level, and steady flight at 17.5 km and a velocity of Mach 2. We predict maximum ground level pressures of 0.3 Pa with an N‐wave ’’period’’ of about 10 s. The sound level is a minimum along the flight track with the maximum signal strength occurring about 300 km off the flight track. The strongest received signal travels initially downward and reflects off the surface of the ocean to the thermosphere. The wave turns around at an altitude of 160 km and is returned back to the ground at a horizontal distance of 320 km from the launch point. The acoustic Mach number of the wave never exceeds 0.2. Ninety percent of the wave’s energy is attenuated below 100 km with 99% attenuated by the time the wave reaches the turning point.

Theoretical and numerical Green’s function field solution in a plane multilayered medium
View Description Hide DescriptionAn explicit general form is derived for the depth‐dependent Green’s function occurring in the integral solution to the Helmholtz wave equation for range‐independent layered media. This representation permits arbitrary location of the source and receiver. In addition, a technique, the Fast Field Program (FFP), for the evaluation of the integral solution is delineated. Examples of the use of both the formulation and the FFP to the problem of modelingunderwater acoustic propagation loss versus range, where the source/receiver are in air/water, in water/bottom, and in a cross‐layer surface duct, are discussed.

Multipath interference nulls in long‐range, low‐frequency, acoustic propagation by normal modes
View Description Hide DescriptionSeveral aspects of multipath interference beats are here investigated by analyzing long‐range propagation losses computed by normal mode theory. Three typical deep water sound‐speed profiles are used at frequencies of 100 Hz and below. The phase shifts which accompany the nulls of interference beats are shown to be organized into patterns resembling certain patterns in the phase of oceantides. The average distance between nulls of a specified depth is determined by counting and is found to differ widely over the three profiles. These differences arise from the convergence zone structure, which in each of the three profiles is different and leads to different multipath combinations. Plots of interference length between adjacent modes versus mode phase velocity are shown to give a result similar to ray theory loop length and are useful in determining which multipaths are present at a given point. Certain features of the mode theory results can be identified with ray theory caustics, but at sufficiently low frequencies these features disappear. When they are not present, the propagation loss can display a series of surface interference images in depth with alternating bands of high and low loss. The distance between nulls can often be predicted from the phase velocities of the two strongest sets of arrivals.

General effects of currents and sound‐speed variations on short‐range acoustic transmission in cyclonic eddies
View Description Hide DescriptionThe effects of sound‐speed and current variations induced by a mesoscale cyclonic eddy on short‐range propagation are considered. A parametric eddymodel is used to determine acoustically relevant eddy environmental effects, so that eddy–acoustical effects can be determined for eddies of arbitrary size, strength, and position. Approximations to sound‐speed and current structures are used to investigate eddyeffects on the three‐dimensionality of rays and on ray types. The influence of current and sound‐speed variations on travel time is examined, and accurate expressions for per‐ray phase variation are obtained. Examples are presented illustrating effects of source–receiver position and orientation on per‐ray phase shifts and relative phase spreading of arrivals. Also, general results are presented which illustrate the variations of eddy–acoustical effects as functions of source–receiver range and of eddy size and strength.

Volume scattering strengths and zooplankton distributions at acoustic frequencies between 0.5 and 3 MHz
View Description Hide DescriptionMeasurements of ultra‐high‐frequency acoustic volume scattering strengths in California current waters revealed a complex structure of thin scattering layers in the upper 100 m. These scattering strength profiles are illustrated along with size distributions of zooplankton collected at the same time and depth as the acoustic measurements. Within the uncertainties in the biological measurements and the assumed physical properties of the animals collected, the principal features of the acoustic profiles can be explained by the zooplankton distributions.

A review of deep ocean sound attenuation data at very low frequencies
View Description Hide DescriptionThe behavior of the attenuation coefficient at very low frequencies (below 200 Hz) has been clouded by the unexplained scatter in experimental data. Recent experiments have indicated that some of this scatter reflects a regional dependence. An attempt is made here to review all the relevant data and to achieve some rational grouping in terms of such regional effects.

On the radiated noise due to boundary‐layer transition
View Description Hide DescriptionA theory is presented for the noise radiated by the incompressible boundary‐layer transition that occurs on an infinite, rigid flat plate. It is hypothesized that it is the intermittency of the boundary‐layer flow within the transition zone that is dominant in noise production. Using Lighthill’s analogy, it is shown that dipole, quadrupole, and octupole sources are generated. The dipole sources are attributable to the shear stress fluctuations that occur in transitional flow while the others are due to fluctuating Reynolds stresses and their images. Under the assumption that dipole sources are more efficient than quadrupoles or octupoles when the Mach number is very small, the power spectrum of the radiated noise due to the dipole contribution is derived. The spectral level rises at 6 dB/octave, peaks at a frequency corresponding to the time it takes for a turbulence burst to convect through the transition region, and then drops off again at 6 dB/octave. The radiation efficiency is analyzed and found to be quite low; it is only 20% of that for a fully developed turbulent boundary‐layer flow.

Φ and Λ computations for real and canonical oceans
View Description Hide DescriptionNumerical methods are developed for the computation of Φ, the strength parameter, and Λ, the diffraction parameter, for arbitrary vertical sound‐speed and Brunt–Väisälä frequency profiles. Normal modesolutions to the internal waveequation are obtained numerically. Conventional ray tracing using segments of constant sound‐speed gradient determines the ray paths. The ray tube method [S. Flatte e t a l., S o u n d T r a n s m i s s i o n t h r o u g h a F l u c t u a t i n g O c e a n (Cambridge U.P., Cambridge, England, 1979)] is developed and solved numerically to give the phase curvature A (x) and, in turn, used to compute Λ. Model computations examine the relationship between the parameters and source–receiver range and depth for canonical profile and profiles typical of the mid‐latitudes in the North Atlantic and Pacific Oceans. Results are compared with the approximate forms of Φ and Λ given by Flatté. We find good agreement with the approximate forms for the canonical profile, but significant differences for the real profiles.

Mode interactions in an isovelocity ocean of uniformly varying depth
View Description Hide DescriptionPierce’s treatment of normal‐mode propagation for an ocean in which physical parameters vary slowly with range is used to calculate mode interactions for isovelocity water of depth varying linearly with range. Simplifying assumptions are (a) two dimensions only, depth and range, and (b) a pressure‐release bottom interface (reasonably valid for all but the highest modes). After general procedures are established, an explicit result is derived for the interaction contribution of mode 2 to mode 1 (the lowest mode), for down‐slope propagation with several allowed modes. Changes, mainly only of signs and phases, are derived to cover up‐slope propagation as well as the contributions of mode 1 to mode 2. Each interaction yields a forward‐scattered component and a considerably weaker back‐scattered one. Each is proportional to the bottom slope. The forward component is also proportional to the ratio depth to acoustic wavelength; the back component follows the inverse ratio. When normalized to the unperturbed outgoing mode functions, the interaction contributions are essentially of equal magnitudes, as would be expected in the absence of loss mechanisms.

A theory of liquids with vapor bubbles
View Description Hide DescriptionIn this paper, which consists of three major parts, the theory of bubbly liquids developed previously by the authors is extended to the case of a liquid containing spherical vapor bubbles. In the first part, the nonlinear equations of motion are derived by a variational procedure. The equations are then linearized. In the second part, a set of constitutive relations for vapor bubbles are developed which include the temperature distributions in both the spherical bubbles and in the surrounding liquid. Nonequilibrium evaporation and condensation processes are also included. In the third part, solutions for plane harmonic wave propagation are presented for water–steam and for liquid sodium–sodium vapor mixtures. The qualitative effects of condensation and evaporation on the propagation of waves through the mixture are discussed. It is found that the wave attenuation is greatly increased and the phase velocity is substantially decreased when phase transitions are included.