Showing papers on "Longitudinal wave published in 1971"

Single crystal elastic constants and calculated aggregate properties

Abstract: : Data on the elastic properties of single crystals have been collected from the literature published through mid-1964. The elastic properties of isotropic aggregates (Young's modulus, Poisson's ratio, shear modulus, bulk modulus, compressibility, velocity of shear waves, and the velocity of compressional waves) are calculated according to the schemes of Voigt and Reuss. The tables include about 1100 determinations. (Author)

Nonlinear waves in the pitaevskii--gross equation.

Abstract: Nonlinear waves, solitary and periodic, are studied exactly in the Pitaevskii-Gross equation for the wave function of the condensate of a superfluid. We also study the relationship between these two waves and Bogoliubov's phonon, and the energies associated with these waves. The creation energy of a solitary wave with amplitudeA is proportional toA3/2. Solitary waves show interesting behavior on their collision due to their localized character. The effect of collision on solitary waves can be described by the phase shift. We give a formula of the phase shift on a collision of two solitary waves. We further discuss the decay of an arbitrary initial disturbance into solitary waves.

Weak turbulence of capillary waves

Abstract: In recent years the theory of weak turbulence, i.e. the stochastic theory of nonlinear waves [I, 9], has been intensively developed. In the theory of weak turbulence nonlinearity of waves is assumed to be small; this enables us, using the hypothesis of the random nature of the phases of individual waves, to obtain the kinetic equation for the mean squares of the wave aplitudes.

Thermoelastic waves in solids with thermal relaxation

Abstract: Maxwell's modified heat conduction equation is used to study plane harmonic waves in unbounded media as well as Rayleigh's surface waves propagating along a half-space consisting of linearly elastic materials that conduct heat. Explicit expressions are obtained for various parameters that characterize these waves. Relevant results of previous investigations are deduced as special cases.

Quantization of Evanescent Electromagnetic Waves

Abstract: The problem of the quantization of evanescent waves, which appear in the angular spectrum representation of the electromagnetic field in a half-space, is discussed. Although evanescent waves are associated with material sources, scatterers, etc., we are able to treat the electromagnetic field, including the evanescent waves, effectively as a free field, by making use of the idea of the refractive index of a passive, macroscopically continuous medium. We consider a space which is filled with a homogeneous dielectric to the left of the plane $z=0$, and is empty to the right of the plane. Triplets of incident, reflected, and transmitted waves at the interface form the fundamental orthogonal modes of the space. By expanding the field in terms of these triplet modes, we show that the field Hamiltonian reduces to the sum of independent harmonic-oscillator Hamiltonians. The quantization is therefore straightforward. We introduce the creation and annihilation operators for the triplet wave modes, and encounter Fock states, coherent states, etc., for a field having evanescent wave components. The field commutator at two space-time points in the right half-space is shown to have an explicit contribution from evanescent waves, characterized by an exponential decay to the right and a propagation parallel to the interface. We also examine the problem of atomic excitation by quantized evanescent waves, and show that the results are of the form given by semiclassical treatments.

On the generation of long waves

Abstract: For relatively long waves generated by a piston-type wave maker, the classical linear wave-maker theory is extended to second order accuracy. Within the limits of validity of the theory, this agrees well with experimental results for the motion generated by a sinusoidally moving wave maker, and shows that secondary waves are associated with the existence of a second harmonic free wave. By giving the wave maker a motion that consists of a first and a second harmonic, it is shown that this free second harmonic wave may be eliminated, so that the generated wave is virtually of permanent form.

Plane Waves in Linear Viscoelastic Media

Abstract: Summary A class of plane inhomogeneous waves which propagate in linear viscoelastic media is considered. A theoretical description of the physical properties and energy associated with these waves is given. Attention is restricted to harmonic P- and SV-waves.

Density fluctuations driven by Alfvén waves

Abstract: The equations for a linearly polarized Alfven wave, propagating parallel to the direction of the average magnetic field in a perfectly conducting fluid, are solved to second order in the wave quanities for cases where the fluid obeys single adiabatic or double adiabatic equations of state. To this order, we find no change in the wave magnetic field or transverse wave velocity, but longitudinal wave velocity and density fluctuations appear, driven by gradients in the wave magnetic-field pressure. This is in contrast to the common belief that even large-amplitude Alfven waves remain purely transverse. The density fluctuations can become quite large when the Alfven speed is close to the ion sound speed in the fluid; this condition may at times exist in the solar wind at 1 AU. We suggest that part of the density fluctuations observed in the solar wind by satellites and interplanetary scintillation may be associated with large-amplitude Alfven waves. Heating of the solar wind might result if the ion sound waves, which are driven by the Alfven waves, are appreciably damped.

Group rays of internal gravity waves in a wind‐stratified atmosphere

Abstract: The propagation of internal gravity waves in a model atmosphere with stratified neutral winds is studied. The waves are subjected to a ray-tracing analysis and, as a result, are grouped into three types: (1) those that penetrate the F region of the ionosphere, (2) those that are reflected, and (3) those that nearly reach the critical-layer condition and are absorbed. Examples of the three types of ray paths are shown. The traveling waves observed in the ionosphere are excited by the propagating acoustic-gravity waves launched at lower levels in the atmosphere. The characteristics of the waves, such as period and velocity, are dependent on atmospheric conditions, as well as on the nature of the source. Extensive computations show that neutral winds provide a directional filter effect as depicted in several contour plots. From Faraday rotation data taken during the summer of 1968, the characteristics of 13 traveling waves that were observed fit into the calculated contours reasonably well.

Conversion of Electrostatic Plasma Waves into Electromagnetic Waves: Numerical Calculation of the Dispersion Relation for All Wavelengths

Abstract: The dispersion curves have been computed for a wide range of wavelengths from electromagnetic waves to electrostatic waves in a magnetoactive warm plasma with a Maxwellian velocity distribution function. The computation was carried out mainly for the perpendicular propagation mode. The upper hybrid resonance is the connection point of the electrostatic waves and the electromagnetic waves. The electrostatic waves not associated with the upper hybrid resonance are subjected to electron cyclotron damping when the wavelength becomes long. Oblique propagation is allowed for the electrostatic waves in a frequency range from the plasma frequency to the upper hybrid resonance frequency in the long-wavelength region where Landau damping can be neglected and where the electrostatic mode smoothly connects to the electromagnetic X-mode. In a slightly inhomogeneous plasma, the Bernstein-mode electrostatic wave can escape by being converted into the O-mode electromagnetic wave; two reflections take place during this escape process.

Elastic moduli and anisotropy of dunite to 10 kilobars

Abstract: Longitudinal and transverse wave velocities are reported for several directions at pressures to 10 kb in two samples of dunite from the Twin Sisters peaks, Washington. For both dunites, elastic-wave propagation is controlled to a large extent by olivine fabric. Dunite A, which has a strong concentration of olivine a crystallographic axes and girdles of b and c axes, is uniaxial in elastic properties. The longitudinal wave velocity at 10 kb for propagation parallel to the olivine a axes maximum is 8.76 km/sec. For propagation normal to the a axes maximum, longitudinal wave velocities are low (Vp=7.98 km/sec at 10 kb) and two transverse waves (Vs=4.41 and 4.69 km/sec at 10 kb) are clearly transmitted through the rock. Dunite B, with strong concentrations of all three olivine crystallographic axes, is similar in elastic properties to orthorhombic crystals with a high longitudinal wave velocity (9.15 km/sec at 10 kb) along the olivine a axes maximum and a low longitudinal wave velocity (7.83 km/sec at 10 kb) along the olivine b axes concentration. Elastic stiffnesses and compliances were computed from the velocities, and the physical properties of isotropic aggregates of the two dunites were calculated using the Voigt and Reuss averaging techniques. Primarily because of the presence of accessory minerals in the dunites, the Voigt and Reuss velocities are lower than values computed from olivine single-crystal data. The high pressure gradient (∂Vp/∂P=17.0 km sec−1 mb−1) observed for the longitudinal velocity of dunite B at 8 kb is interpreted as being due to the effect of grain boundary cracks.

Transmission and Reflection of Plane Waves at an Elastic-Viscoelastic Interface

Abstract: Summary The reflected and transmitted waves due to an elastic plane sinusoidal P or SV wave impinging on the plane interface between an elastic and a linearly viscoelastic medium are found analytically for any type of viscoelastic behaviour. The properties of these waves depend both on the frequency of the incident wave and the angle of incidence of the impinging wave. Some general properties of the transmitted waves are that both the dilatational and equivoluminal waves in the viscoelastic media have refraction angles less than 90°, the displacement trajectories of material points in the viscoelastic media are ellipses, and the waves attenuate with increasing distance from the interface.

Run-up distributions of waves breaking on slopes

Abstract: Run-up of irregular waves which break on a slope is calculated by assuming that on the average the run-up of each wave with a given height and period equals the run-up of a periodic wave train of the same height and period. General expressions are derived for the distributions of the run-up and the wave steepness as functionals of an arbitrary joint distribution of the wave height and the square of the period. Explicit results are obtained for the case when these variates are jointly Rayleigh distributed with arbitrary degree of correlation. Some of the assumptions are verified by a comparison of the analytical results with previous experimental data.

Wave Propagation in Nematic Liquid Crystals

Abstract: Basic laws of motion of micropolar continuum are presented, and the adequacy of applying micropolar theory to liquid crystals is indicated. A set of constitutive equations is derived for nematic liquid crystals. Wave propagation problems are solved, and it is shown that the theoretical analysis is in good agreement with the experimental data, which indicates the isotropy of the phase velocity of the longitudinal wave and the anisotropy of the damping coefficient. The coupling, although small, is shown to exist between longitudinal and rotational waves.

Ion Acoustic Waves in a Multi‐Ion Plasma

Abstract: An exact treatment of the multispecies ion acoustic dispersion relation is given for an argon/helium plasma. Phase velocity and damping are obtained as a function of ion‐electron temperature ratio and relative densities of the two species. There are two important modes in the plasma, with quite different phase velocities, which are referred to as principal heavy ion mode and principal light ion mode. Which of these is dominant depends on the relative densities of the two components, but, in general, the light ion mode becomes important for surprisingly small light ion contamination. Approximate analytic expressions are derived from damping rates and phase velocities and their domains of validity are investigated. Relevance of the results for the investigation of collisionless shocks is discussed.

Structure of the Electromagnetic Field in a Spatially Dispersive Medium

Abstract: The exact mode expansion is derived for the electromagnetic field in a spatially dispersive model dielectric occupying the volume 0<∼z<∼d. The dispersion relations for the transverse as well as the longitudinal waves are deduced and the nature of the modes is briefly discussed.

Reflection and Refraction Coefficients at a Fluid‐Solid Interface

Abstract: For an infinite plane elastic wave which strikes the plane interface separating two semiinfinite isotropic media, the calculation of the complex reflection coefficient, R*, for varying angles of incidence, θ, is not difficult. In the past, calculations have been made for a number of lossless media and, consequently, an important facet of the R*−θ curve for real materials has been overlooked. The total reflection, |R*|=1, which occurs at the longitudinal‐ and shear‐wave critical angles is well known, but the appearance of a minimum (sometimes a zero) in R* is not and its existence defines a third critical angle, sometimes inappropriately called the Rayleigh‐wave angle, at which a wave with large surface components is generated. During experiments with beams of acoustic waves, there is an apparent lateral displacement of the reflected beam at the third critical angle which manifests itself markedly only when there is a near‐zero in |R*|. Notwithstanding the calculations of Schoch [Ergeb. Exakt. Naturw. 23, 127–234 (1950)] and the experimental measurements of others apparently to the contrary, it is strongly suggested that no actual lateral displacement occurs and that re‐radiation from the region outside that ensonified by the incident beam gives rise to the apparent lateral displacement. Some outcomes of the investigation are discussed and of these the more important are: (1) Rayleigh and other interface and surface waves in real media are degenerate; (2) no interface wave can exist independently at the junction of two nonideal media; (3) Huyghens's principle in its elementary secondary‐wavelet form does not apply to lossy media; (4) the usefulness of the sensitivity of R* to minute changes in elastic parameters at the Rayleigh angle as a measuring tool has a wide application; (5) elliptical polarization of both shear and longitudinal waves can occur, owing to boundary influences in lossy refracting media. The real part of the propagation vector lies in the plane of the ellipse.

Theory and performance of acoustical dispersive surface wave delay lines

Abstract: A summary is given of properties of Love and Rayleigh waves in stratified isotropic media. The study of propagation of such waves in anisotropic and piezoelectric media, carried out in view of obtaining "pure" modes, shows that two modes can be "pure" and only one of them at a time can be piezoelectrically stiffened. The Rayleigh wave is stiffened if the sagittal plane is a plane of symmetry whereas the Love wave is stiffened if the perpendicular to the sagittal plane is a binary axis. The problems in devising dispersive delay lines using these waves are discussed and the pairs of materials which seem to be the most interesting ones are given together with the different excitation methods and expected performance of these delay lines relating to large bandwidths and high compression ratios. The results of experiments carried out with Love and Rayleigh waves excited by ceramic transducers directly bonded onto the layer show that the total untuned insertion losses can be less than 20 dB with a 2.5-MHz bandwidth and less than 50 dB with a 100-MHz bandwidth. Also described is the performance of a delay line whose time delay variation is nearly 8 µs with a 30-MHz bandwidth, the central frequency being 32.5 MHz.

Surface Waves on Two‐Dimensional Corrugated Structures

Abstract: The characteristic equation is derived for the propagation of surface waves guided by a planar two-dimensional corrugated structure. This equation is solved numerically to obtain the propagation wave number as a function of the direction of propagation on the surface. The data obtained illustrate the anisotropic nature of the wave propagation. In addition, an isolated surface wave is found to exist with its propagation wave number in a ‘forbidden’ region of wave number space. The relevance of this wave to a transmission null in a phased array antenna is discussed.

Solitary and cnoidal planetary waves

Abstract: A class of long planetary waves in a zonal channel analogous to the solitary and cnoidal waves of surface and internal gravity wave theory is discussed. On a mid-latitude β-plane, such waves exist as the result of divergence, non-uniform zonal velocity fields or bottom topography. In all cases studied the wave profile along the channel was found to satisfy the Korteweg-de Vries equation.

Propagation of Harmonic Waves in a Composite Elastic Cylinder

Abstract: In this paper, the propagation of harmonic waves with an arbitrary number of circumferential nodes in an infinitely long two‐layered composite circular elastic rod is investigated. The composite rod is made of a circular solid rod encased by a circular shell having different material properties. The frequency equation derived on the basis of the three‐dimensional linear isotropic elastic theory is presented. The reduction of this equation to the frequency equations for some special problems, such as longitudinal wave propagations, torsional wave propagations, flexural wave propagations, axial‐shear vibrations, and plane‐strain vibrations is discussed. Simplified equations for phase velocities of longitudinal and torsional waves at very long wavelength are obtained. Numerical results, in terms of frequency and real wavenumber, are given for a composite rod made of a soft core with a stiff casing.

Laboratory investigation of air turbulence above simple water waves

Abstract: The structure of turbulent-shear flows above propagating waves is investigated experimentally in a wind and wave facility at the University of Florida. Wave-induced perturbations and their importance in transferring momentum to waves is a central question in this study. The turbulent air velocities were measured in the horizontal and vertical directions by using a two channel hot-film anemometer system. Turbulence measurements were obtained both in the presence and absence of mechanical waves with wave height =8.9 cm and wave speed =2.23 m/sec. Power spectra of air turbulence indicate the presence of significant wave-induced peaks in both the horizontal and vertical velocities at the frequency of mechanical wave. The peaks disappear in the absence of mechanical waves. Calculations of momentum transfer to waves based on the wave-induced Reynolds stress and on the measured growth rate of waves indicate that the interaction of surface waves with the turbulent flow above them produces significant momentum transfer in addition to the wave-induced stress.

Leaky wave couplers for guided elastic wave and guided optical wave devices

Abstract: Couplers are disclosed for use with guided elastic waves and guided optical waves. The coupling is effected by means of a coupling region having a different phase velocity characteristic than that of the waveguide. The presence of the coupling region causes the waves traveling in the waveguide to become highly leaky. These leaky waves then encounter a second waveguide or transducer and are coupled into it. Utilizing the electro-acoustic effect in the acoustic wave devices and the electro-optic effect in the optical wave devices, the phase velocity characteristic of the coupling region is controllable, permitting switchable couplers.

Holographic study of propagating transverse waves in plates

Abstract: The technique of double-exposure holographic interferometry was used to record the propagation of transverse waves in a plate. The waves were initiated by striking the plate in the center with a ballistic pendulum; this technique produced axisymmetric response of the plate. Several pulsed-laser interferograms were obtained, each of which showed the bending wave at a different time after the initiation of impact. From the interferograms, plots of the transverse displacement vs. distance from the center of impact were obtained. The experimental data compared favorably with analytical results for the problem.