Showing papers on "Longitudinal wave published in 1984"

The propagation of electromagnetic waves

Abstract: This chapter describes the propagation of electromagnetic waves. For a steady monochromatic wave, frequency is a constant. This chapter also discusses the surface impedance of metals. The permittivity of metals is large compared with unity at low frequencies. The wavelength in metals is small compared with the wavelength in vacuum. As the frequency increases, the depth of penetration becomes of the same order as the mean free path of the conduction electrons. The chapter also describes the propagation of electromagnetic waves in waveguides. A waveguide is a hollow pipe of infinite length, that is, a cavity infinite in one direction. The characteristic oscillations in a resonator are stationary waves; however, those in a waveguide are stationary only in the transverse directions; waves travelling in the direction along the pipe can be propagated. The scattering of electromagnetic waves by particles is accompanied by absorption. The absorption cross-section is given by the ratio of the mean energy dissipated in a particle per unit time to the incident-energy flux density.

A unified theory for elastic wave propagation in polycrystalline materials

Abstract: We have developed a unified approach to solve for the attenuation and phase velocity variations of elastic waves in single‐phase, polycrystalline media due to scattering. Our approach is a perturbation method applicable for any material whose single‐crystal anisotropy is not large, regardless of texture, grain elongation, or multiple scattering. It accurately accounts for the anisotropy of the individual grains. It is valid for time‐harmonic waves with all ratios of grain size to wavelength. It uses an autocorrelation function to characterize the geometry of the grains, and thereby avoids coherent artifacts that occur if the grains are assumed to have symmetrical shapes and suggests new methods for characterizing distributions of grains that are irregularly shaped. We have carried out numerical calculations for materials that are untextured and equiaxed, and have cubic‐symmetry grains and an inverse exponential spatial autocorrelation function. These calculations agree with the previous calculations which are valid in the Rayleigh, stochastic, and geometric regions, and show the transitions between these regions. The complex transition between the Rayleigh and stochastic regions for longitudinal waves, and the severe limitations of the stochastic region for grains with fairly large anisotropy are of particular interest.

On the excitation of long nonlinear water waves by a moving pressure distribution

Abstract: A study is made of the wave disturbance generated by a localized steady pressure distribution travelling at a speed close to the long-water-wave phase speed on water of finite depth The linearized equations of motion are first used to obtain the large-time asymptotic behaviour of the disturbance in the far field; the linear response consists of long waves with temporally growing amplitude, so that the linear approximation eventually breaks down owing to finite-amplitude effects A nonlinear theory is developed which shows that the generated waves are actually of bounded amplitude, and are governed by a forced Korteweg-de Vries equation subject to appropriate asymptotic initial conditions A numerical study of the forced Korteweg-de Vries equation reveals that a series of solitons are generated in front of the pressure distribution

Attenuation and envelope formation of three-component seismograms of small local earthquakes in randomly inhomogeneous lithosphere

Abstract: A unified model is proposed for explaining the frequency dependence of Q−1 and the formation of velocity seismograms by a single scattering process. Adopting Birch's law and a linear correlation between P and S wave velocities, we statistically describe the inhomogeneous medium by one random fluctuation, which is spatially characterized by the exponential autocorrelation function. We calculate Q−1 for P and S waves on the basis of the Born approximation, supposing seismic waves attenuate due to scattering largely by rapidly fluctuating random structure. Resulting Qs−1 explains the observed frequency dependence well, when the mean square fractional fluctuation and the correlation distance are chosen to be 0.01 and 2 km, respectively. Nonspherical radiation due to a point shear dislocation and frequency dependent nonisotropic scattering including conversion between P and S waves complicate the seismograms. Taking those complexities into account, we synthesize the “envelopes” of three-component velocity amplitudes of P and S coda waves by summing up energy singly scattered by distributed inhomogeneities. From numerical calculations, we found that the radial component of the P coda wave is excited even in the nodal direction of the P wave radiation mostly due to SP scattering occurring near the hypocenter. The P coda waves appearing on the transverse components are a complex mixture of PP, PS, and SP scattering. The S coda waves are excited mostly due to SS scattering in all directions, and appear in all three components; their polarizations are controlled by the radiation pattern even in the later part of S coda waves.

Parametrically excited solitary waves

Abstract: A modulated cross-wave of resonant frequencyω1, carrier frequencyω =ω1 {1 + O(e)}, slowly varying complex amplitude O(e½b), longitudinal scale b/e½ and timescale 1/eω is induced in a long channel of breadth b that contains water of depth d and is subjected to a vertical oscillation of amplitude O(eb) and frequency 2ω, where 0 0.045 for d/b [gsim ] 1. The corresponding cnoidal waves (of which the solitary wave is a limiting case) are considered in an appendix.

Theory of electromagnetic waves

Abstract: Spend your few moment to read a book even only few pages. Reading book is not obligation and force for everybody. When you don't want to read, you can get punishment from the publisher. Read a book becomes a choice of your different characteristics. Many people with reading habit will always be enjoyable to read, or on the contrary. For some reasons, this theory of electromagnetic waves tends to be the representative book in this website.

Critical Level Reflection and the Resonant Growth of Nonlinear Mountain Waves

Abstract: We examine the evolution of a field of internal waves launched by stratified flow over symmetric topography in mean flows which reverse direction at some height above the surface. With the gradient Richardson number at this “critical level” in the undisturbed flow restricted to values greater than 0.25, the nonlinear interaction in the region is such that the surface strongly reflects large amplitude internal waves incident upon it. When the critical level is located near certain discrete heights above the ground the incident and reflected waves interfere constructively and the wave amplitude in the low levels is resonantly enhanced by a large factor. These results are related to our previous analyses of the process by which breaking internal waves are able to induce intense downslope windstorms.

The use of seismic shear waves and compressional waves for lithological problems of shallow sediments

Abstract: From a great variety of in situ shear wave experiments, i.e., reflection, refraction and borehole surveys in the shallow sediments of the north German plains, several specific properties have been derived. Shear waves (S) differ from compressional waves (P) in that: Correlations have been established between V s and the confining pressure and between reduced V s values and several lithological parameters like the grain size of sandy material. More lithological and hydrological information is obtained by using S- and P-wave surveys along the same profile. The best information on a sedimentological structure is obtained by the simultaneous observation of V s , V p , Q s and Q p .

Propagation and selective transmission of internal gravity waves in a sudden warming

Abstract: Longitudinally asymmetric features of gravity wave propagation in a sudden warming are examined theoretically, using observed geostrophic wind fields in the stratosphere for three days of winter 1979. It is shown that the wind patterns accompanying a sudden warming act to reduce, but not eliminate, quasi-stationary gravity wave propagation to the mesosphere. The onset of large-amplitude planetary waves leads to the formation of propagating zones and forbidden zones for gravity waves of intermediate horizontal scale (50–200 km). Lateral ray movement and horizontal refraction are secondary but observable effects for these waves. To the extent that these waves are excited isotropically in the troposphere, it is possible to evaluate the direction and magnitude of the average wavevector reaching the mesosphere as follows. Stationary waves with wavevector orthogonal to the local mean flow are selectively absorbed in the stratosphere, implying that for these waves the average wavevector transmitted to t...

Inertia–Gravity Waves in the Stratosphere

Abstract: The propagation and refraction of stationary inertia–gravity waves in the winter stratosphere is examined with ray tracing. Due to their smaller vertical group velocity these waves experience more lateral ray movement and horizontal refraction that the simple gravity waves recently discussed by Dunkerton and Butchart. Stationary waves are rotated by the transverse horizontal shear and propagate into the polar night jet. Circumstances are found in which the mean flow shear has enhanced unstable wavebreaking by compressing, the wave packet and decreasing the absolute value of wave action density required for breaking. In some other places, reflection from the caustic is more likely.

Motor device utilizing ultrasonic oscillation

Abstract: A motor device utilizing ultrasonic oscillation, which comprises an ultrasonic oscillator including an elastic body and one or more piezoelectric, electrostriction or magnetostriction elements assembled in or on the elastic body, and a movable body movable in a fixed direction. A portion of the ultrasonic oscillator and a portion of the movable body are held pressed against each other. A progressive wave, which is generated on the surface of the elastic member and constituted by a longitudinal wave and a transverse wave, is converted to a uni-directional motion of the movable body.

Formation of Singularities in Elastic Waves

Abstract: This paper deals with the radial solutions of the dynamic equations for an isotropic homogeneous hyperelastic medium. It is shown that nontrivial solutions “blow up” (cease to exist in the proper sense) after a finite time, if: (a) The equations satisfy a certain “genuine nonlinearity condition”. (b) The initial data have compact support and are “sufficiently small”.

The Generation of Mesospheric Planetary Waves by Zonally Asymmetric Gravity Wave Breaking

Abstract: A semispectral numerical model is used to study the influence of a longitudinally varying gravity wave source on the general circulation of the winter mesosphere. The gravity wave source consists of stationary (topographic) waves with a longitudinally varying amplitude distribution that is approximated by the first two terms in a zonal harmonic expansion (i.e., the zonal mean plus planetary wavenumber 1). The computed zonal mean circulation in the mesosphere is nearly the same as that computed for a zonally symmetric gravity wave source of equal amplitude. However, the asymmetric source excites a strong stationary wavenumber 1 disturbance near the level of gravity wave breaking (equal to about 71 km). This disturbance has a zonal wind maximum about 1/4-cycle upstream from the gravity wave drag maximum. It is concluded that vertically propagating gravity waves produced in the troposphere are a possible source for mesospheric planetary waves.

Short wavelength ion waves upstream of the Earth's bow shock

Abstract: The identification and explanation of short wavelength antenna interference effects observed in spacecraft plasma wave data have provided an important new method of determining limits on the wavelength, direction of propagation, and Doppler shift of short wavelength electrostatic waves. Using the ISEE-1 wideband electric field data, antenna interference effects have been identified in the ion waves upstream of the earth's bow shock. This identification implies that wavelengths of the upstream ion waves are shorter than the antenna length. The interference effects also provide new measurements of the direction of propagation of the ion waves. The new measurements show that the wave vectors of the ion waves are not parallel to the interplanetary magnetic field (IMF) as previously reported. The direction of propagation does not appear to be controlled by the IMF. In addition, analysis of the Doppler shift of the short wavelength ion waves has provided a measurement of the dispersion relation. The upper limit of the rest frame frequency was found to be on the order of the ion plasma frequency. At this frequency, the wavelength is on the order of a few times the Debye length. The results of this study now provide strong evidence that the ion waves in the upstream region are Doppler-shifted ion acoustic waves. Previously announced in STAR as N83-36328

Density distribution in looplike coronal transients: A comparison of observations and a theoretical model

Abstract: Skylab coronagraph observations of intensity changes in the five outer coronal 'loop-like' transients indicate trends toward the greatest concentration of material at the flanks of the bright loops characterizing such transients, together with the presence of a large depleted density region within the loops and the development of bright legs which contain most of the material in the transient and display minimal lateral motion as the top of the bright loop moves radially outward through the corona. Theoretical models for these phenomena predict a maximum enhancement at the top of the loop, rather than at the flanks, and legs that move laterally with a significant fraction of the propagation speed of the loop top, in contrast with observation. Agreement cannot be achieved without the use of a geometry that conflicts with that used for the model calculations.

Acoustic Microscopy of Elastic Discontinuities

Abstract: In the reflection-scanning acoustic microscope, interference fringes may be obtained from cracks and grain boundaries running at an angle to the surface. The periodicity of these fringes suggests that while sometimes they are caused by reflection of longitudinal waves within the specimen, when the feature is approximately normal to the surface, Rayleigh waves are responsible, and this confirms the dominant role played by Rayleigh waves in the contrast in acoustic microscopy. The variation of contrast with defocus may be expressed as a Fourier transform of the reflectance function of a specimen; oscillations in V(z) then arise as the transform of the change in phase around the Rayleigh angle. When Rayleigh waves strike a surface-breaking discontinuity, they may be strongly reflected even though the discontinuity is much less than a wavelength thick. This enables fine cracks and other features which would not be resolved according to conventional criteria to be revealed very clearly in acoustic micrographs.

Longitudinal surface waves for the study of dynamic properties of surfactant systems. II. Air-solution interface

Abstract: A recently developed longitudinal wave apparatus was employed to study the dynamic interfacial properties; the Gibbs elasticity, the diffusion parameter, the surface (excess) dilational viscosity, and the surface (excess) shear viscosity. The dynamic interfacial properties were calculated from the dispersion equation of the surface waves using the wave numbers and the damping coefficients of the longitudinal wave at different frequencies. The wave number and the damping coefficient were obtained by measuring, at different locations, the surface tension oscillations induced by the longitudinal wave. The system used in this study is the octanoic acid aqueous solution in a concentration range from 0.2 to 2.0 × 10 −6 mole/cm 3 . The Gibbs elasticity was observed to pass through a maximum, approximately 25 dyn/cm, at a concentration of 0.3 × 10 −6 mole/cm 3 . The diffusion parameter exhibited two apparent discontinuities. The results also indicate that the surface dilational viscosity is two orders of magnitude larger than the surface shear viscosity, corroborating with the previous findings.

High-pressure quasi-isentropic impact experiments

Abstract: A method has been developed for generating quasi-isentropic compression waves in flat plate impact experiments. Peak stresses can be in the multimegabar range, thus allowing investigations of material properties in a high-pressure, low-temperature regime which is inaccessible either quasi-statically or by conventional shock wave experiments. The key to the technique is a thin impactor with a smooth but strong gradient in shock impedance. Novel impactor fabrication and testing methods have been developed to attain the excellent uniformity and relatively close control of the shock impedance profile which are needed. In using the method, it is normally desirable to obtain time-resolved measurements of either pressure or particle velocity at two distances from the impact surface. The stress-volume loading path followed by the specimen can then be obtained from a centered-wave analysis, provided certain assumptions are valid. The data and results of several experiments are presented.

Rayleigh waves in a poroelastic half‐space

Abstract: The propagation of Rayleigh waves in a poroelastic half‐space is investigated for pervious and impervious surfaces. It is seen that the solutions presented by Jones for ‘‘Rayleigh waves in a porous elastic saturated solid’’ [J. Acoust. Soc. Am. 33, 959–962 (1961)] are incorrect. A plot of phase velocity versus Poisson’s ratio is presented.

Magnetostatic waves and spin waves in layered ferrite structures

Abstract: Collective magnetic excitations are supported by multiple ferrite layers. The character of magnetostatic waves is calculated for such systems and is illustrated for three different layers variously spaced (accurate control of the delay characteristics is shown to be possible) as well as for very many similar layers equally spaced. For volume waves on many layers, collective spin-wave-like modes of long wavelength form a continuum that evolves smoothly into narrow bands characteristic of the layers at short wavelength. For surface waves, an excitation similar to the surface wave on a continuous medium appears when the spacing is less than the layer thickness, but a dense continuum of other excitations (not analogous to those of a uniform medium) always persists even for small spacings. This unexpected spectrum is related to a novel system of modes localized on the gaps.

Shear waves by an explosive point-source: the earth surface as a generator of converted P-S waves

Abstract: The most common source of seismic energy is an explosion at some depth in a borehole. The radiated waves are reflected not only at the subsurface layers but also at the free surface. The earth's surface acts as a generator of both P- and S-waves. If the source depth is much less than the dominant wavelength the reflected waves resemble closely the waves generated by a single force. Theoretical seismograms were computed with different methods to look for the relevance of the surface-reflected waves. The numerical experiments show reflected shear waves even for small shotpoint—receiver distances. Due to their polarization these waves can be detected most easily on in-line horizontal geophones. The existence of these waves was examined during a conventional survey in Northern Germany. Conventional data analysis shows a large variability in the νp/νs ratio. The method used here produced a shear-wave section with a rather good signal-to-noise ratio down to 4 s S-wave reflection time.

Reconstruction of inclusions in solids using ultrasonic Born inversion

Abstract: Voids and inclusions in elastic solids are characterized experimentally using scattered ultrasonic waves The flaws are reconstructed using a one‐dimensional elastic wave inverse scattering algorithm based on the Born–Neuman expansion This method emphasizes the role of low and intermediate frequency longitudinal waves The utility of the inverse Born approximation is tested for several new circumstances First the algorithm is tested for pitch‐catch (bistatic) geometries Secondly the effects of resonant excitation of the scatterer on flaw characterization are measured for several spherical flaws The third and major result shows that the one‐dimensional algorithm can be used to determine the size, shape and orientation of nearly ellipsoidal flaws when access angle is limited The effects of varying access aperture on the reconstruction are reported Another common experimental limitation in flaw characterization arises from interferences of the flaw signal with nearby surfaces We briefly report that th