Interaction Of Sound Waves Research Articles

Quantum wave turbulence.

The nonlinear quantum kinetic equation for the interaction of sound waves is solved via analytic and numerical techniques. In the classical regime energy cascades to higher frequency (\ensuremath{\omega}) according to the steady-state power law ${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}3/2}$. In the quantum limit, the system prefers a reverse cascade of energy which follows the power law ${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}6}$. Above a critical flux, a new type of spectrum appears which is neither self-similar nor close to equilibrium. This state of nonlinear quantum wave turbulence represents a flow of energy directly from the classical source to the quantum degrees of freedom.

Interaction of soft modes and sound waves in glasses.

The soft potential model (an extension of the tunneling model to include soft localized vibrations) is shown to describe the anomalous features of the specific heat, the sound absorption and the thermal conductivity of glasses over the entire low temperature range.

Resonant interaction of sound wave with internal solitons in the coastal zone

Naturally occurring internal solitary wave trains (solitons) have often been observed in the coastal zone, but no reported measurements of such solitary waves include low-frequency long-range sound propagation data. In this paper, the possibility that internal waves are responsible for the anomalous frequency response of shallow-water sound propagation observed in the summer is investigated. The observed transmission loss is strongly time dependent, anisotropic and sometimes exhibits an abnormally large attenuation over some frequency range. The parabolic equation (PE) model is used to numerically simulate the effect of internal wave packets on low-frequency sound propagation in shallow water when there is a strong thermocline. It is found that acoustic transmission loss is sensitive to the signal frequency and is a ‘‘resonancelike’’ function of the soliton wavelength and packet length. The strong interaction between acoustic waves and internal waves, together with the known characteristics of internal waves in the coastal zone, provides a plausible explanation for the observed anomalous sound propagation in the summer. By decomposing the acoustic field obtained from the PE code into normal modes, it is shown that the abnormally large transmission attenuation is caused by ‘‘acoustic mode-coupling’’ loss due to the interaction with the internal waves. It is also shown that the ‘‘resonancelike’’ behavior of transmission loss predicted by the PE analysis is consistent with mode coupling theory. As an inverse problem, low-frequency acoustic measurements could be a potential tool for remote-sensing of internal wave activity in the coastal zone.

Interaction of second sound acoustic waves with a counterflow-induced turbulent field

The evolution of the flow and temperature fields produced by rectangular heat pulses on the background of a steady velocity and vortex line density (VLD) field is considered. This flow is described by a simplified linearised theoretical model exhibiting the dynamics of the VLD evolution. The Gorter-Mellink coefficient A is obtained from experiments on the decay of weak temperature pulses with distance from the heater. A comparison of experimental and theoretical temperature-time slopes yields a correction factor to the growth and decay coefficients of Vinen's VLD evolution equation.

Resonant interaction of a sound wave with a cylindrical vortex

The interaction of a plane sound wave with a compressible fluid rotating about an axis in the form of a Rankine vortex is considered for the case of small Mach numbers. It is shown that when the frequency of the sound wave is close to that of the rotating core of the vortex, resonance is generated in the vortex core. Resonance is also possible when the frequency of the sound wave is a multiple of the frequency of the rotating core. The amplitude of the scattered wave is reexamined and it is shown that in some limiting cases the details of some published material are inaccurate.

Effects of a fluid boundary layer on the interaction of sound waves with a plate

The influence of a flow boundary layer on sound radiation from, and sound transmission through, a plate is discussed. The angular dependence of the transmission loss has been calculated. Difficulties encountered in the numerical analysis for the determination of the angler‐averaged value of the transmission loss in a diffuse field are discussed. An asymptotic closed‐form expression obtained for the averaged transmission loss shows that, at high frequencies, the transmission coefficient for a damped plate is proportional to ω−3. The conditions under which the flow increases or decreases the transmission loss or the radiated sound intensity are investigated. [Work supported by NSF and ONR.]

The electroacoustic equations for a colloidal suspension

The term ‘electroacoustic’ is used in connection with phenomena that involve the interaction of sound waves and electric fields, such as the voltage difference generated across a transducer by the passage of a sound wave. This paper is concerned with electroacoustic effects in suspensions of electrically charged colloidal particles. The existing methods for calculating electroacoustic effects in suspensions are limited either to the dilute case, or to one particular effect, namely the open-circuit voltage generated between two parallel wire probes by a locally plane sound wave, propagating perpendicular to the wires. In this paper we present a procedure for calculating any electroacoustic effects in suspensions of arbitrary concentration. The only restriction on the method is that the particles must be small compared with the sound wavelength. The procedure involves the solution of a set of differential equations – referred to here as the ‘electroacoustic equations’ – for the macroscopic pressure, velocity and electrical potential in the suspension. The derivation of these equations and the associated boundary conditions form the major part of this paper. General features of the solution are also discussed, and an application is given involving a novel electroacoustic measurement.

Interaction of sound waves. Part IV: Scattering of sound by sound

A theory for the nonlinear interaction between two sound beams produced by real sources in a lossless fluid was presented in a previous work [Naze Tjo/tta and Tjo/tta, J. Acoust. Soc. Am. 83, 487–495 (1988)]. A general solution of the governing equation in the quasilinear approximation, valid at any range, crossing angle, and frequency ratio, was obtained for prescribed boundary conditions. An asymptotic formula for the sum and difference frequency sound pressure was obtained at large distance from the sources. It relates the amplitude and directivity of the sound field in the farfield to the on-source conditions. In the present work, the theory is further developed, and numerical results are presented for uniform piston and Gaussian sources. The influence of source geometry (separation, and intersection angles from 0° to 90°) and frequency on the beam pattern of the nonlinearly generated sound is studied. The results obtained are related to earlier works on scattering of sound by sound, which are discussed. Necessary conditions are also given to determine when scattering of sound by sound can be observed. In the special case of thin Gaussian beams intersecting at a small angle, the results are compared with that obtained by Darvennes and Hamilton [submitted to J. Acoust. Soc. Am.] using the paraxial approximation. Also discussed are some properties of the automatic global adaptive quadrature routine used to compute the two-dimensional integral in the asymptotic formula.

A Sound Intensity Probe Using the Nonlinear Behaviors of Sound Wave

A sound intensity probe using the nonlinear behaviors of the sound wave is presented. The principle of the probe is theoretically discussed with regard to the variation and angular dependence of the phase velocity caused by the non-collinear interaction of sound waves. Two parametric receiving arrays whose probing waves propagate in opposite directions are applied to the sound intensity probe. The basic characteristics of the probe are observed, and the results support that the probe is applicable for the sound intensity measurements.

Interaction of sound waves. Part III: Two real beams

This article is a theoretical study of the nonlinear interaction between two sound beams in a lossless fluid, intersecting each other at arbitrary angles. The governing equation for the sum and difference frequency components is solved in the quasilinear approximation for prescribed conditions on the sources of the two beams. A solution that is uniformly valid in space is obtained in the form of a Fourier integral. Asymptotic evaluations at large distance from the sources lead to simple formulas that relate the amplitude and phase of the generated sound to the on-source conditions. Diffraction effects are fully accounted for, and shown to be important even at large distances. Relevance to earlier literature on the scattering of sound by sound is discussed.

Resonance interaction of sound waves with a stratified seabed

A novel approach to analyze the reflection and transmission of sound waves from a penetrable and layered fleet interface between two media is described. This approach generalizes the first‐order prediction of the resonance scattering theory (RST), which was developed earlier for stacks of arbitrarily many elastic plates separating dissimilar fluid media [Jackins and Gaunaurd, J. Acoust. Soc. Am. 80, 1762–1776 (1986)]. The generalization consists of two portions. The first one makes the lower fluid medium become an elastic half‐space, which makes the model useful to predict reflections from a stratified ocean bottom. This portion was briefly analyzed earlier [J. Acoust. Soc. Am. Suppl. 1 80, S116 (1986)]. The second portion, now married to the first, consists in a second‐order approximation for the parameters involved in the description of the bottom reflection/transmission coefficients, which retains second‐order terms containing second derivatives of the pertinent parameters. This is an application to fl...

Interaction of sound waves. Part I: Basic equations and plane waves

The nonlinear interaction of sound waves in a lossless fluid is considered theoretically. The basic equations are valid to square-order terms in the acoustic variables. The structure and origin of various terms, and their effect on the solution, are discussed. Emphasis is given to the effects of nonlinear on-source conditions, illustrated with plane wave models.

Interaction of sound waves. Part II: Plane wave and real beam

The nonlinear interaction in a lossless fluid between an infinite plane sound wave and a sound beam generated by a real source is considered theoretically in the quasilinear approximation. The importance of a proper choice of acoustic variables and their correct on‐source values are analyzed. The governing equation for the sum and difference frequency components is solved for prescribed boundary conditions. A solution uniformly valid in space is obtained in the form of a double Fourier integral. In the farfield, the integration can be performed and a simple formula is obtained. This relates the amplitude and directivity at the observation point to the on‐source amplitude and phase of the beam. Relevance to earlier literature on parametric acoustic receiving arrays is also discussed.

Sound wave interaction with Josephson junction and transformation of the contact coherent binding energy into ultrasonic waves

The problem of ultrasonic wave propagation in narrow Josephson junctions at nonzero temperature has been investigated. Using the derived solution of the nonstationary Fokker-Planck equation, the total current flowing through the narrow Josephson junction is calculated, and the coefficient of the ultrasonic wave passage through the Josephson junction is determined. The singularity of this coefficient is studied in the ultrasound amplification mode associated with the transformation of coherent binding energy of the contact into ultrasonic waves, and the possibility of experimental measurement of the lifetime of the Josephson junction in the metastable state under the conditions of maximum ultrasound amplification by the contact is discussed.

Resonantly Interacting, Weakly Nonlinear Hyperbolic Waves. II. Several Space Variables

A uniformly valid asymptotic theory of resonantly interacting high‐frequency waves for nonlinear hyperbolic systems in several space dimensions is developed. When applied to the equations of two‐dimensional compressible fluid flow, this theory both predicts the geometric location of the new sound waves produced from the resonant interaction of sound waves and vorticity waves as well as yielding a simplified system which governs the evolution of the amplitudes. In this important special case, this system is two Burgers equations coupled by a linear integral operator with known kernel given by the vortex strength of the shear wave. Several inherently multidimensional assumptions for the phases are needed in this theory, and theoretical examples are given which delineate these assumptions. Furthermore, explicit necessary and sufficient conditions for the validity of the earlier noninteracting wave theory of Hunter and Keller are derived; these explicit conditions indicate that generally waves resonate and interact in several dimensions.

Sound absorption in a shock wave

It was shown in [1–4] that the reflection of a sound wave or its transmission through a shock front should be accompanied by attenuation or intensification of the wave is regarded as a discontinuity. In accordance with current representations [5, 6], a shock wave includes a viscous shock and a lengthy relaxation zone. Equilibrium is established with respect to translational and rotational degrees of freedom in the viscous shock and with respect to internal degrees of freedom in the relaxation zone. The result of the interaction of the shock and sound waves is determined by the relationship between the length of the sound wave and the width of the shock wave.

On the interaction of second sound shock waves and vorticity in superfluid helium

Two second sound shock waves were propagated successively into initially quiescent superfluid helium. With long separation times the waveforms are identical, but with shorter times the flow behind the second shock decays anomalously, revealing the presence of fluid disturbances produced near the heater by the first pulse. In order to study the vortical nature of these disturbances, second sound shocks were produced in rotating superfluid helium. Propagation of shocks both along and normal to the axis of rotation was studied, the former case proving to be similar to the experiment with successive shocks.

Ultrasound absorption in liquid metals

The excess longitudinal ultrasonic absorption over and above the classical value has been attributed to the solid-like mechanisms of the interaction of sound waves with the conduction electrons and the thermal phonons in liquid metals, both exhibiting a quadratic dependence on the sound frequency.

Parametric acoustic conversion in ocean sediments

The interaction of acoustic waves from a parametric acoustic array at a water‐sediment interface has been studied theoretically. This investigation was motivated by the observation of better penetration of acoustical energy into sediments using a parametric acoustic array rather than a conventional source [T. G. Muir, C. W. Horton, Sr., and L. A. Thompson, J. Sound Vib. 64, 539 (1979)]. In order to treat the nonlinear interaction of sound waves in a sediment, the inhomogeneous elastic wave equation for a solid was solved. One effect of the nonlinear terms in this equation is the coupling of compressional and shear waves. The separation of the coupling effect is shown. The primary waves from a parametric source are expected to excite Stoneley waves along the water‐sediment interface. The Stoneley waves are assumed to serve as a source for parametric acoustic conversion in the sediment. The analytic solutions of the inhomogeneous wave equation are spherical waves modified by an angular dependence in the amp...

Parametric acoustic conversion in ocean sediments

The interaction of acoustic waves from a parametric acoustic array at a water‐sediment interface has been studied theoretically. This investigation was motivated by the observation of better penetration of acoustical energy into sediments using a parametric acoustic array rather than a conventional source [T. G. Muir, C. W. Horton, Sr., and L. A. Thompson, J. Sound Vib. 64, 539 (1979)]. In order to treat the nonlinear interaction of sound waves in a sediment, the inhomogeneous elastic wave equation for a solid was solved. One effect of the nonlinear terms in this equation is the coupling of compressional and shear waves. The separation of the coupling effect is shown. The primary waves from a parametric source are expected to excite Stoneley waves along the water‐sediment interface. The Stoneley waves are assumed to serve as a source for parametric acoustic conversion in the sediment. The analytic solutions of the inhomogeneous wave equation are spherical waves modified by an angular dependence in the amplitude. [Work supported by ONR.]