Showing papers on "Group velocity published in 1970"
TL;DR: In this article, an approach to compute the near and farfield transient radiation resulting from a specified velocity motion of a piston or array of pistons in a rigid infinite baffle is presented.
Abstract: An approach is presented to compute the near‐ and farfield transient radiation resulting from a specified velocity motion of a piston or array of pistons in a rigid infinite baffle. The approach, which is based on a Green's function development, utilizes a transformation of coordinates to simplify the evaluation of the resultant surface integrals. A simple expression is developed for an impulse response function, which is the time‐dependent velocity potential at a spatial point resulting from an impulse velocity of a piston of any shape. The time‐dependent velocity potential and pressure for any piston velocity motion may then be computed by a convolution of the piston velocity with the appropriate impulse response. The response of an array may be computed using superposition. Several examples illustrating the usefulness of the approach are presented. The farfield time‐dependent radiation from a rectangular piston is discussed for both continuous and pulsed velocity conditions. For a pulsed velocity of time duration T it is shown that the pressure at several of the field points can consist of two separate pulses of the same duration, when T is less than the travel time across the piston.
580 citations
TL;DR: In this article, the propagation of a Gaussian light pulse through a medium having a positive or negative absorption line is examined, and analytical approximations are obtained for the case where the spectral width of the pulse is much smaller than that of the line.
Abstract: The propagation of a Gaussian light pulse through a medium having a positive or negative absorption line is examined. Analytical approximations are obtained for the case where the spectral width of the pulse is much smaller than that of the line. It is shown that the pulse remains substantially Gaussian and unchanged in width for many exponential absorption depths, and that the locus of instants of maximum amplitude follows the classical expression for the group velocity, even if this is greater than the velocity of light, or negative. Numerical calculations have been used to examine what happens beyond the limit of usefulness of the analytical approximations.
427 citations
TL;DR: In this paper, phase velocity and Q of long-period waves have been determined for 13 great-circle paths for Rayleigh waves and 12 great circle paths for Love waves by band-pass filtering technique.
194 citations
TL;DR: A rapid decrease in shear velocity in the suboceanic mantle is used to infer the thickness of the lithosphere and it is proposed that new and highly precise group velocity data constrain the solutions and imply a thickness near 70 km.
Abstract: A rapid decrease in shear velocity in the suboceanic mantle is used to infer the thickness of the lithosphere. It is proposed that new and highly precise group velocity data constrain the solutions and imply a thickness near 70 km.
149 citations
01 Mar 1970
TL;DR: In this paper, the wavenumber and the group velocity of the magnetostatic surface wave guided by a ferrite slab magnetized parallel to its face were investigated and an aspect of experimental observation of the group delay times of the magnetic wave supported by a metal plate placed against one of the faces was explained.
Abstract: The wavenumber and the group velocity of the magnetostatic surface wave guided by a ferrite slab magnetized parallel to its face are investigated. One aspect of experimental observation of the group delay times of the magnetostatic surface waves supported by a ferrite slab without and with a metal plate placed against one of the faces is explained.
122 citations
TL;DR: The centrovelocity as mentioned in this paper is a new velocity which was introduced for the description of the transport of electromagnetic radiation since it does not have any of the short comings of the standard definitions of the group velocity or the velocity of energy transport.
Abstract: The definitions, the physical significances, the interrelationships, and the observability of seven velocities of light are discussed. One of the seven, the centrovelocity, is a new velocity which is introduced here. It is suggested that this velocity can be used for the description of the transport of electromagnetic radiation since it does not have any of the short comings of the standard definitions of the group velocity or the velocity of energy transport.
87 citations
TL;DR: In this article, it was shown that a necessary condition for causality violation is that the infinite-frequency limit of the phase velocity shall exceed the speed of light, which is the condition for all Lorentz-invariant wave equations.
Abstract: The classical analysis of Brillouin and Sommerfeld has shown that the appearance, in some frequency range, of group velocities in excess of the speed of light does not imply causality violation. The group velocity is not always identical with the velocity of signal propagation. We show that a necessary condition for causality violation is that the infinite- frequency limit of the phase velocity shall exceed the speed of light. Application of the theorem leads to the conclusions ( a ) that all Lorentz-invariant wave equations (and in particular the Feinberg ‘tachyon’) are causal, and ( b ) that the quasi-acoustic branch of the Bludman-Ruderman model is causal.
53 citations
TL;DR: In this paper, the pulse velocity in a Ne absorption cell placed inside a self-locked He-Ne (6328 A) laser has been found to exceed c, the free space velocity of light, by about 3 parts in 104.
Abstract: The pulse velocity in a Ne absorption cell placed inside a self‐locked He–Ne (6328 A) laser has been found to exceed c, the free‐space velocity of light, by about 3 parts in 104. Conversely, the pulse velocity in a He–Ne gain cell was less than c by about the same fraction. These results are consistent with the classical group velocity dω/dk, where the frequencies are confined to the central region of the resonant line.
41 citations
TL;DR: In this paper, the authors used the Sacramento Peak Doppler-Zeeman Analyzer to study the velocity and magnetic fields in 60″ × 300″ areas on the solar disk.
Abstract: We used the Sacramento Peak Doppler-Zeeman Analyzer to study the velocity and magnetic fields in 60″ × 300″ areas on the solar disk. We map the steady component of the line-of-sight velocity and longitudinal magnetic fields and compare them with the coarse Ca+ network. The collective phase behavior of the 5-min oscillations is studied in detail. We find large scale phase coherence, including waves with typical horizontal phase velocities of 100 km/sec which can be followed up to 50 000 km. The important oscillatory features are interpreted in terms of the properties of modified sound waves. We find no apparent relationship between the steady and oscillatory fields.
41 citations
TL;DR: The theory of internal equatorial planetary-scale waves as developed by Matsuno and by Lindzen is extended to include the effects of shear in the basic state by means of a numerical study as discussed by the authors, which finds that both the equatorial Kelvin wave and the Yanai wave are absorbed shortly before reaching critical levels where their frequencies are Doppler shifted to zero.
Abstract: The theory of internal equatorial Planetary-scale waves as developed by Matsuno and by Lindzen is extended to include the effects of shear in the basic state. By means of a numerical study we find that both the equatorial Kelvin wave (the gravest symmetric westerly mode) and the Yanai wave (the gravest anti- symmetric easterly wave), the two most commonly observed internal equatorial waves, are absorbed shortly before reaching critical levels where their frequencies are Doppler shifted to zero. Away from such levels, these waves retain their identity within shear zones. However, they become more closely confined to the equator as their Doppler-shifted frequencies are reduced. It is found, moreover, for a given frequency and vertical wavelength, that the vertical group velocity of the Yanai wave is smaller than that of the Kelvin wave. In addition, as the Doppler-shifted frequency ωˆ is reduced, the vertical group velocity of the Yanai wave diminishes as ωˆ3 while the vertical group velocity of Ke...
39 citations
TL;DR: In this article, the velocity distribution function for particles in the beam was determined and the effect of condensation and subsequent evaporation of water on particle motion was discussed, and a theoretical model describing the beam deceleration was presented.
TL;DR: In this paper, the authors used the full adiabatic theory to describe wave propagation in a warm magnetoplasma for frequencies around the plasma frequency and the upper hybrid resonance frequency.
Abstract: The full adiabatic theory is used to describe wave propagation in a warm magnetoplasma for frequencies around the plasma frequency and the upper hybrid resonance frequency. By comparison with the microscopic theory for directions perpendicular and parallel to the static magnetic field, we can well define the range of validity of the full adiabatic theory, which can then be used for computation of the group velocity. The variation of this group velocity as a function of frequency for several directions of propagation is shown for models corresponding to the ionosphere and the far magnetosphere. Three factors deserve attention: (1) the upper hybrid resonance and its neighborhood can be rigorously studied for far magnetospheric conditions by using the full adiabatic theory; (2) the computed modes present a mixed electrostatic-electromagnetic character; (3) The minima in group velocities for pseudoresonance frequencies progressively fill up as the temperature increases.
TL;DR: In this paper, an explanation for a phenomenon observed e.g. in a wall jet in a small region near the maximum velocity is given, where the turbulence shear stress is expressed as the sum of two terms, proportional to the first and second derivative of the mean velocity, respectively.
Abstract: An explanation is given for a phenomenon observed e.g. in a wall jet in a small region near the maximum velocity. The turbulence shear stress is expressed as the sum of two terms, proportional to the first and the second derivative of the mean velocity, respectively. Use is made of the nonsymmetric flow pattern around the maximum velocity, and of the nonuniform distribution of the intensity of the lateral turbulence velocity component. The coefficient of the second derivative of the mean velocity is shown to contain the first derivative of this turbulence velocity component. Since the second derivative of the mean velocity is negative around its maximum, a positive turbulence intensity gradient as observed in the region concerned in the wall jet, results in a negative contribution to the shear stress. Hence, in this region the shear stress can have a sign opposite to the positive — though very small — gradient of the mean velocity. Consequences with respect to the mechanical energy balance of the mean flow and of the turbulence are discussed.
TL;DR: In this article, the beam steering angles were observed up to ∼50° for a wave number approximating 830 cm−1, for a 10° rotation of the bias field from the collinear situation.
Abstract: High quality epitaxial YIG films grown on gadolinium gallium garnet have certain geometrical advantages over flux‐grown material for refined investigation of basic magnetic wave propagation phenomena. Better uniformity of internal field under magnetic bias and convenience for placement of spatially periodic current‐carrying couplers on the free YIG surface, ensures enhanced field uniformity by confining the region of propagation. Surface magnetostatic waves are dispersive and exhibit wave vector anisotropy so that, in general, the phase and group velocity vectors are noncollinear, with the beam steering angle variable by the magnetic bias field. Scanning magnetic probe experiments were conducted at 3 GHz on 10‐μm thick films wherein beam steering angles were observed up to ∼50° for a wave number approximating 830 cm−1, for a 10° rotation of the bias field from the collinear situation. Use of the theoretical model applicable to thin film media, which neglects exchange effects, led to good agreement with th...
TL;DR: In this article, the dispersive property of a lossless, isotropic, and homogeneous plasma is used to enhance the resolution of transmitted pulses at the receiver, and an expression is obtained for the carrier phase variation of a rectangular envelope pulse so that the pulse collapses on itself at the receiving node.
Abstract: The compression of frequency-modulated RF pulses is discussed when the dispersive property of a lossless, isotropic, and homogeneous plasma is used to enhance the resolution of transmitted pulses at the receiver. Using the basic concept of group velocity, an expression is obtained for the carrier phase variation of a rectangular envelope pulse so that the pulse collapses on itself at the receiver. Unlike the chirp radar pulse, the frequency variation is not linear and the optimum detection of transmitted pulses depends on both the plasma frequency and the distance between the transmitter and the receiver. The method of convolution was used to obtain numerical results, which indicate that the formulation given results in compression for short propagation distances.
TL;DR: The dispersion relationship for surface magnetostatic modes propagating in a ferrite slab with a conducting plate at a small distance parallel to the surface of the slab has been derived in this paper.
Abstract: The dispersion relationships for surface magnetostatic modes propagating in a ferrite slab with a conducting plate at a small distance parallel to the surface of the slab have been derived. It is shown that the group velocity of the surface magneto-static mode in this configuration can be both positive and negative, depending on the wavelength of the mode and the distance of the conducting plate from the ferrite surface.
TL;DR: The phase and group velocities of electrostatic ion waves in a uniform magnetic field have been studied experimentally, both as a function of propagation angle (θ) with respect to the field, and as the function of wave frequency.
Abstract: The phase and group velocities of electrostatic ion waves in a uniform magnetic field have been studied experimentally, both as a function of propagation angle (θ) with respect to the field, and as a function of wave frequency. For ω ≫ ωci, the ion cyclotron frequency, the phase velocity is found to be identical to the ion acoustic velocity (KTe/M)1/2. For ω ≳ ωci, the electrostatic ion cyclotron mode has been observed. The slow mode (ω < ωci cos θ) has been observed to have a constant phase velocity (KTe/M)1/2 cos θ, in apparent contradiction to theory. The frequency gap (ohgr;ci cos θ < ω < ωci), where waves theoretically do not propagate, has been demonstrated.
TL;DR: In this article, it was shown that the plane-wave picture of a leaky mode proposed by Burg, Ewing, Press and Stulkin (1951) yields the accepted period equation for leaky modes in a water layer a half-space.
Abstract: It is shown that the plane-wave picture of a leaky mode proposed by Burg, Ewing, Press and Stulkin (1951) yields the accepted period equation for leaky modes in a water layer a half-space. The resultant mode is formed by an inhomogeneous wave with real frequency and complex wave number and phase velocity. Another form of mode considered is that formed by a homogeneous wave in the guide with real phase velocity and complex frequency and wave number. The phase-velocity dispersion curve for this case is appropriate for determining shear-wave coupling to PL waves. The procedures of the article could be readily extended to the more complicated case of a solid layer over a half-space. It is also demonstrated that the derivative of the real part of angular frequency with respect to the real part of the wave number is a good approximation to the group velocity for leaky modes with low losses.
TL;DR: In this article, the authors compare two presently used schemes for estimating vertical air velocity in convective clouds, namely, the positive bound of the Doppler velocity spectrum and the air velocity obtained by the use of a procedure proposed by R. R. Rogers in 1964.
Abstract: Observations of a thunderstorm by means of a vertically pointing pulsed-Doppler radar were used to compare two presently used schemes for estimating vertical air velocity in convective clouds. It was found that the air velocity given by the positive bound of the Doppler velocity spectrum and the air velocity obtained by the use of a procedure proposed by R. R. Rogers in 1964 were well correlated. In regions where raindrops would be expected, the standard deviation of the difference of the two velocity estimates was 1.2 m sec−1. Part of the differences can be attributed to uncertainties in the size distribution of the scatterers and to difficulties in establishing the correct upper bound of the Doppler spectrum. This analysis concludes, in the rain-filled region of this cloud, that the effects of turbulence on the Doppler spectrum were small. The observations show that the vertical velocity and radar reflectivity fields in some convective clouds are much more variable than they are usually assumed...
TL;DR: In this article, it is shown that lines parallel to the imaginary axis can be mapped from the wave-number plane into the frequency plane to locate the frequencies at which the group velocity vanishes.
Abstract: The colliding-pole criterion for determining instability types from dispersion relations calls for a process of conformal mapping from the frequency plane into the wave-number plane. It is shown that this process can be inverted by mapping lines, parallel to the imaginary axis, from the wave-number plane into the frequency plane. Lines mapping into a cusp locate the frequencies at which the group velocity vanishes. These frequencies determine the instability character of the system.
TL;DR: In this article, a study of the spatial and final velocity distributions for gaseous particles reflected from a solid surface is reported, showing that the spatial distribution dependence upon initial velocity causes velocity-selected and thermal beams to give similar spatial scattering.
Abstract: A study of the spatial and final velocity distributions for gaseous particles reflected from a solid surface is reported. The three‐dimensional classical model previously used by the authors is employed to study the scattering distributions as functions of the incident particle velocity, the velocity distribution in the incident beam, and surface temperature. The broadness of the spatial scattering distributions is predicted to decrease with increasing incident velocity. The spatial distribution peak position is specular for large incident velocity, shifts toward the surface for intermediate velocity, and approaches the surface normal for small incident velocity. The model indicates that the spatial distribution dependence upon initial velocity causes velocity‐selected and thermal beams to give similar spatial scattering. For hot surfaces the spatial scattering is indicated to be a rather insensitive function of surface temperature. The velocity distributions of reflected particles are predicted to be non...
TL;DR: In this paper, the phase velocity and direction of an unknown plane-wave signal propagating across a two-dimensional array in a dispersive waveguide are estimated by smoothing over frequency and transforming.
Abstract: A relatively simple method is discussed for estimating the phase velocity and direction of an unknown plane‐wave signal, propagating across two‐dimensional array in a dispersive waveguide. The finite Fourier transform is applied to the output signal of each sensor, and the phases of the smoothed frequency components calculated. The phases of the components are linearly regressed on sensor positions to produce estimates of the wave slowness components. Neither the phase nor group velocity dispersion curves need to be known, except for upper and lower estimates of the range. By smoothing over frequency and transforming, estimates are obtained of the direction and phase velocity of the signal. The precision of estimates depends on the signal‐to‐noise ratio, the square root of the number of sensors, and the number of wavelengths that fall in the array. Each frequency is treated separately, so that the direction and phase velocity are obtained as a function of frequency. Since the individual frequency components of the signal are separated, the signals observed on a large array can be combined, even though the dispersion is appreciable over the array. For good signal‐to‐noise power ratios, the dispersion curves are a direct result from the analysis.
TL;DR: In this paper, the authors extended Dyson's theory to the case of a superconductor, taking into account the penetration depth of electromagnetic fields, the change in phase of the surface impedance, and change in group velocity and relaxation time of the quasiparticles compared to the normal case.
Abstract: In order to determine whether electron spin resonance in type-I superconductors is experimentally possible, we have extended Dyson's theory to the case of a superconductor, taking into account the penetration depth of electromagnetic fields, the change in phase of the surface impedance, and the change in group velocity and relaxation time of the quasiparticles compared to the normal case. We have calculated line shapes and magnitudes of power absorbed and rf field transmitted for various frequencies and temperatures for thin-film superconductors. From our calculation, we determine the optimum temperatures and frequencies, and conclude that even for these conditions, the experiment would be difficult.
TL;DR: In this article, the phase velocity of a wave at the edge of a thick plate under initial stress is derived, and the frequency equation for the phase velocities of the wave in a thin and an infinite-thick plate is derived.
Abstract: The frequency equation giving the phase velocity of a wave at the edge of a thick plate under initial stress is obtained. Some particular cases are discussed to derive (a) the velocity of edge waves in a thin plate and (b) the velocity of Rayleigh waves in a plate of infinite thickness under initial stress.
TL;DR: In this paper, the phase velocity curves of the Π and Σ modes on the (+ −) sheet combine to form two families of almost continuous curves, called Π pseudo modes, which are formed by the plateaus of the dispersion curves; they have a high group velocity, low attenuation, and a low excitation; they depend solely on the P velocities.
Abstract: In a multiple elastic wave guide, the phase velocity curves of the Π and Σ modes on the (+ −) sheet combine to form two families of almost continuous curves. The curves of the first family, called Π pseudo modes, are formed by the plateaus of the dispersion curves; they have a high group velocity, a low attenuation, and a low excitation; they depend solely on the P velocities. The curves of the second family, called Σ pseudo modes, are formed by the slopes of the dispersion curves and have the opposite characteristics. The Π pseudo modes make up the oscillatory part of the seismogram between P and S. The study is based on a simplified CIT 11 GB model, which consists of 6 layers, is 653 km thick, and contains a 54-km low-velocity P channel. The frequency range studied is from 0 to 0.146 Hz. The influence of the P channel is very restricted. At wavelengths smaller than ⅓ of its thickness, the layer below the channel (α = 8.19 km/sec) supports what is essentially a head wave.
TL;DR: In this paper, two methods for the calculation of the fields in a microstrip transmission line are presented, and the dependence of phase velocity on frequency is considered; some fundamental effects are discussed and demonstrated numerically and experimentally by an example.
Abstract: Two methods for the calculation of the fields in a microstrip transmission line are presented. Longitudinal field components and the dependence of phase velocity on frequency are considered. Some fundamental effects are discussed and are demonstrated numerically and experimentally by an example.
TL;DR: In this article, the rigorous impulse response function is given for propagation in lossless waveguide, and it is shown that its instantaneous frequency is that which has reached the output at that time by propagating at the group velocity.
Abstract: For propagation in lossless waveguide, the rigorous impulse response function is given. It is shown that its instantaneous frequency is that which has reached the output at that time by propagating at the group velocity. For a square envelope pulse with a carrier frequency /spl omega/ above the cutoff frequency /spl omega//sub c/, the propagation of the envelope and of the phase are essentially described by the group and phase velocity, respectively. In addition, however, the bulk of the pulse is preceded by the so-called Sommerfeld precursors having an increasing amplitude and a frequency which decreases from a high value to /spl omega/. Similarly the bulk of the pulse k followed by the Sommerfeld postcursors in which both amplitude and frequency decrease, the latter from /spl omega/ to /spl omega//sub c/. The analytic results are illustrated by computed examples of waveguide transients.
TL;DR: In this article, a microwave interferometer is described which is capable of giving a continuous monitor of the velocity of a marginal planar detonation wave propagating in a narrow rectangular channel of transverse dimensions 3×¼ inch and 6 metres long.
Abstract: A prerequisite to a study of a detonation wave structure is the establishment of an equilibrium frontal configuration, which is repeatable at equi-spaced distances along the detonation tube, together with a constant average wave velocity. A microwave interferometer is described which is capable of giving a continuous monitor of the velocity of a marginal planar detonation wave propagating in a narrow rectangular channel of transverse dimensions 3×¼ inch and 6 metres long. One important conclusion of this work is that some marginally propagating waves may appear to acquire a sensibly constant velocity, near the C-J value, over a distance of 1-2 m before a rapid decay in velocity occurs. This observation emphasizes the need for continuous velocity measurement in all waves near the limit.