Damped Wave Trains Research Articles

Numerical simulation of acoustic wave propagation via a liquid with gas bubbles

Wave propagation through a liquid with gas bubbles is numerically investigated, in 1D and 2D cases. The mathematical model is constructed in one-velocity, two-temperature approximation. The liquid is described by the empiric Tait equation. The bubble oscillations are described by Rayleigh-Plesset-type equation. The heat exchange between bubbles and the liquid is taking into account. Comparison of analytical solutions to results of numerical simulation has shown, that the developed model adequately describes dynamics of the wave propagation in a gas-liquid mixture. In the 2D case different regimes of wave propagation through a liquid containing gas bubbles are found. The leading wave with damped wave train is formed in a gas-liquid mixture out of bell-shaped impulse. The pressure splash can appear behind, on and before initial solitary wave in a liquid with a bubble channel and exist for a long time. The heat exchange effect on wave propagation is investigated. It is shown that properties of the wave propagation and it structure depend on the gas volume content, wavelength and on the bubble area width.

Coherent X-rays at MAMI

Coherent radiation in the range from soft X-rays up to hard X-rays, produced by the low-emittance electron beam of MAMI, can be used for various applications. Novel types of interferometers have been developed for the measurement of the complex index of refraction of thin self-supporting foils. For the vacuum ultraviolet and soft X-ray region the interferometer consists of two collinear undulators, and a grating spectrometer. A foil placed between the undulators causes a phase shift and an attenuation of the oscillation amplitude. The complex index of refraction has been measured at the L 2,3-absorption edges of nickel. A novel method is described for the measurement of the X-ray magnetic circular birefringence. For the hard X-ray region the interferometer consists of two foils at which the 855 MeV electron beam produces transition radiation. Distinct interference oscillations have been observed as a function of both, the photon emission angle and the distance between the foils. The refractive index decrement δ(ω) of a 2 µm thick nickel sample foil has been measured at X-ray energies around the K absorption edge at 8333 eV and at 9930 eV with an accuracy of better than 1.5 %. The line width of parametric X radiation (PXR) was measured in backward geometry with a Si single-crystal monochromator. Upper limits of the line width of 42meV, 50meV, and 44meV, have been determined for the (333), (444) and (555) reflections at photon energies of 5932 eV, 7909 eV, and 9887 eV, respectively. Small angle scattering of the electrons in the crystal leads to a stochastic frequency modulation of the exponentially damped wave train which results in the line broadening. To elucidate the quest if the production of PXR is a kinematical or a dynamical process the radiation from silicon single-crystal targets, emitted close to the electron direction, has been studied. The observed interference structures and the narrow-band radiation in forward direction shows that PXR is produced in a dynamical process.

Upper Limits on Gravitational-Wave Emission in Association with the 27 Dec 2004 Giant Flare of SGR1806-20

At the time when the giant flare of SGR1806-20 occurred, the AURIGA "bar" gravitational-wave (GW) detector was on the air with a noise performance close to stationary Gaussian. This allows us to set relevant upper limits, at a number of frequencies in the vicinities of 900 Hz, on the amplitude of the damped GW wave trains, which, according to current models, could have been emitted, due to the excitation of normal modes of the star associated with the peak in x-ray luminosity.

The thickness of resistive‐dispersive shocks

The purpose of this paper is to examine the thickness of slow, intermediate, and fast shocks described by the resistive‐dispersive plasma model, which contains two scale lengths: the resistive length λr and the ion inertial length λi. It is found that for the case where λr ≪ λi, i.e., for small resistivity, slowly damped wave trains dominate the structure yielding an effective shock thickness much greater than the ion inertial length. When λr ≫ λi, i.e., for large resistivity, the shock structure has a thickness of the order of the resistive length so that it is again much larger than λi. Thus a minimum thickness is predicted by the resistive‐dispersive model and occurs for intermediate resistivity: it is found to be a few λi for the slow shocks in distant magnetotail as well as for subcritical bow shocks and about 20λi for intermediate shocks with typical magnetopause parameters. It is shown that the shock thickness also depends critically on the upstream plasma beta, β1 = 2μop1/B1², small β1 values leading to smaller thickness. The effect of regular Newtonian viscosity on the shock thickness is also examined briefly.

On the stability of rotational discontinuities

The stability of symmetric rotational discontinuities in which the magnetic field rotates by 180° is investigated by means of a one‐dimensional self‐consistent hybrid code. Rotational discontinuities with an angle Θ > 45° between the discontinuity normal direction and the upstream magnetic field are found to be relatively stable. The discontinuity normal is in the x direction and the initial magnetic field has a finite y component only in the transition region. In the case of the ion (lefthanded) sense of rotation of the tangential magnetic field, the transition region does not broaden with time. In the case of the electron (right‐handed) sense of rotation, a damped wavetrain builds up in the By component downstream of the rotational discontinuity and the discontinuity broadens with time. Rotational discontinuities with smaller angles, Θ, are unstable. Examples for a rotational discontinuity with Θ = 30° and the electron sense of rotation as well as a rotational discontinuity with Θ = 15° and the ion sense of rotation show that these discontinuities disintegrate into waves. These waves travel approximately with Alfvén velocity in the upstream direction and are therefore phase standing in the simulation system. The magnetic hodograms of these disintegrated discontinuities are S‐shaped. The upstream portion of the hodogram is always right‐handed; the downstream portion is always left‐handed.

Structure of slow magnetosonic shocks in low beta plasmas

Slow magnetosonic shocks are an efficient way in which magnetic energy in a collisionless plasma is converted into particle flow and thermal energy. Previous analytic and simulation studies of slow shocks have suggested that their structure consists of a damped wavetrain beginning at the shock transition and extending into the downstream region. Spacecraft observations in the solar wind and the Earth's magnetotail have found structures that resemble slow shocks except that most of them do not possess a trailing wavetrain. To resolve the conflict between theory and observations of slow shocks, we have performed new simulations which correct some of the previous results and show that depending on the sonic Mach number and the ratio of electron to ion temperature, slow shocks may or may not possess a wavetrain.

Flow in the high latitude ionosphere: measurements at 15s resolution made using the EISCAT ‘Polar’ experiment

We present a first overview of flows in the high latitude ionosphere observed at 15 s resolution using the U.K.-Polar EISCAT experiment. Data are described from experiments conducted on two days, 27 October 1984 and 29 August 1985, which together span the local times between about 0200 and 2130MLT and cover five different regions of ionospheric flow. With increasing local time, these are: the dawn auroral zone flow cell, the dayside region of low background flows equatorward of the flow cells, the dusk auroral zone flow cell, the boundary region between the dusk auroral zone and the polar cap, and the evening polar cap. Flows in both the equatorward and poleward portions of the auroral zone cells appear to be relatively smooth, while in the central region of high speed flow considerable variations are generally present. These have the form of irregular fluctuations on a wide range of time scales in the early morning dawn cell, and impulsive wave-like variations with periods of a few minutes in the afternoon dusk cell. In the dayside region between the flow cells, the ionosphere is often essentially stagnant for long intervals, but low amplitude ULF waves with a period of about 5 min can also occur and persist for many cycles. These conditions are punctuated at one to two hour intervals by sudden ‘flow burst’ events with impulsively generated damped wave trains. Initial burst flows are generally directed poleward and can peak at line-of-sight speeds in excess of 1 km s −1 after perhaps 45 s. Flows in the polar cap are reasonably smooth on time scales of a few minutes and show no evidence for the presence of ULF waves. Under most, but not all, of the above conditions, the beam-swinging algorithm used to determine background vector flows should produce meaningful results. Comparison of these flow data with simultaneous plasma and magnetic field measurements in the solar wind, made by the AMPTE IRM and UKS spacecraft, emphasizes the strong control exerted on high latitude flows by the north-south component of the IMF.

Comparison of stimuli used in sound field audiometric testing

The problems associated with performing pure-tone threshold measurements in reverberant or diffuse sound fields are illustrated with the use of three-dimensional representations of the sound field within a typical test booth. A microphone mounted on a motorized trolley is used to perform these measurements. A comprehensive comparison is then made of the efficiency with which FM tones, AM tones, damped wave trains, and narrow bands of noise provide a uniform sound field. The conclusion is reached that the bandwidth of the stimulus is the major factor determining the uniformity of the field. A decision about the most appropriate stimulus for sound field work must thus be based on factors other than field uniformity. When the constraints of obtaining suitable spectral distributions, and being able to relate thresholds obtained with complex stimuli to those obtained with pure tones are also considered, FM tones and suitably generated narrow bands of noise appear to be the most suitable stimuli. The selection of suitable parameters is discussed and an Appendix discusses the spectrum and bandwidth of FM signals with different modulation waveforms. The relative accuracy of testing in the direct and reverberant regions in a nonanechoic environment is also discussed.

Problematik einer frequenzspezifischen Schwellenmessung mit den Hirnstammpotentialen unter Verwendung des otometrischen Signals (DWT)

This study aimes at investigating if the damped wavetrain stimulus (Victoreen) may be used in the evaluation of frequency specific thresholds using brainstem potentials. Stimulus frequencies were 1, 4, and 8 kHz. Starting with a control group (10 persons) latency curves for the brainstem potentials were established. The test group included patients with various forms of sensorineural hearing loss in the audiogram. Threshold measurements at the three stimulus frequencies were done with these patients using the potential IV (Jewet V). The latency curves of the normal hearing control group reveal a frequency-specific information being present in the brainstem potentials. This can be derived from latency shifts at different stimulus frequencies. However, investigating patients with a steep slope or a notch in the pure-tone audiogram introduces some difficulties in the ERA-threshold evaluation.

Pi 2 micropulsations as indicators of substorm onsets and intensifications.

Pi2 micropulsations are impulsive wave trains which accompany the onset of magnetospheric substorm disturbances. At middle and low latitudes Pi2's are observed as relatively monochromatic damped wave trains, while at auroral observatories onsets of substorms are marked by impulsive increases in noise across the Pi1 and Pi2 bands. Because they are often clearly apparent on normal low latitude magnetograms their presence or absence has been used as an indicator of the presence or absence of substorm activity. In this paper we shall demonstrate the relationship between Pi2 bursts and substorm onsets and Intensifications. We shall show that the degree of spatial localization of the Pi2 disturbance often makes it unidentifiable at middle and lower latitudes using conventional recording techniques. Thus while the presence of a Pi2 pulsation may be taken as an indication of substorm occurrence, its absence at a particular station may be due to the location of the station relative to the substorm region and may not necessarily imply the absence of substorm activity. Sonograms from an east-west array of observatories in the auroral oval will be employed to demonstrate the use of Pi signals at auroral zone latitudes to define the times of substorm onsets and intensifications. It is recommended that the present subjective means of identifying Pi2's be replaced by more objective criteria, based upon careful analysis of Pi2 signals.

Relative Loudness and Wavetrain Signals

Relative loudness determinations are reported for three adults using damped wavetrain signals delivered by means of circumaural earphones. Measurements were made by observing the amount of sound-pressure change required to produce subjective loudness changes of 0.5 to 1 and 2 to 1 at various sound-pressure levels from about 0.002 μbar to about 100 μbar. Using signals having a decrement of 0.90 loudness was found to vary in direct proportion to sound pressure at 1100 Hz. An empirical expression is given which describes the variation of loudness sensation with sound pressure at other frequencies. This expression enables the calculation of equal loudness data which agree with experimentally measured values to within about ±1 dB over the usual frequency and sound-pressure range of the nondeficient ear.

Equal Loudness Pressures and the Normal Ear

Measurements are presented to show equal-loudness sound-pressure values for a number of ears. Observations are given as average values for a number of ears that are useful in defining how a “perfect average” ear would be expected to perform. Equal-loudness sound-pressure observations are also given for several individual ears showing how supposedly “normal” ears deviate from a “perfect average” normal ear. Measurements were made by means of damped wavetrain signals having a decrement of 0.90. Signals were applied to the ear by means of a Sointrex HA10 circumaural earphone, which was calibrated on a flat-plate coupler. A number of conclusions are suggested which relate this type of measurement to the behavior of the average normal ear as a standard of general comparison without attempting to define specific numerical values.

Acoustical Wavetrain Signals and Equal Loudness Pressures

Equal loudness measurements were made for 12 young adult ears over a frequency range of 250–6000 Hz. A damped wavetrain signal having a decrement of 0.90 was used and this was delivered by a pair of circumaural earphones. A well-defined but empirical relationship is shown to exist between relative loudness and sound pressure and the mathematical expression is given. Observational accuracy attainable was, when averaged, usually consistent with the calculated values to within about 12 dB over a pressure range of about 0.0001–100 μbars. With this method of measurement comfortable loudness pressure for the normal ear was found to be independent of frequency over the normal frequency range. Damped wavetrains with circumaural earphones appeared to give about four times greater accuracy than pure tones and supraaural earphones for identical measurements.

Multiple Pseudowaves Produced by a Single Voltage Pulse

A multiple pseudowave—or a series of fast ion bursts—is generated when a short negative voltage pulse is placed on a transparent grid immersed in a plasma. The phenomenon resembles, but is not, a damped wave train. Using a single-particle model, it is shown that multiple pseudowaves can be explained in terms of ions trapped and oscillating in the ion sheath formed around the grid by the negative voltage pulse. A pulsed grid used in this manner constitutes a simple diagnostic technique for measuring plasma density.

RAPID PERIODIC FLUCTUATIONS OF THE GEOMAGNETIC FIELD. I

Part I of this paper contains the presentation of a new analysis of observational material, mainly from Eskdalemuir, and describes some unexpected properties of geomagnetic fluctuations. The chief of these are (a) that there is a change of type at sunset from a continuous flux of disturbance to a comparative quiet punctuated by short damped wave trains, and (b) that the daytime fluctuations have a spectrum with definite fine structure. Part II is a discussion of the probable origin of geomagnetic pulsations. By comparing the characteristics found in Part I with those reported by previous observers it is concluded that the effects have a common cause, and very general arguments are then put forward to show that their origin is terrestrial. A survey of possible physical models points, after elimination, to a magneto-hydrodynamical resonance in one or more of the ionospheric layers.

Spherical Wave Radiation in Solid Media

Divergent compressional waves in solids differ from similar waves in fluids, even though the particle displacement be parallel to the direction of propagation in both media. Perhaps the simplest example is the wave propagating from a radially oscillating spherical cavity in an infinite solid medium. When a sinusoidally varying pressure is generated in such a cavity, the normalized acoustic radiation impedance is a function of σ, the Poisson's ratio of the medium, as well as of the ratio of cavity radius to wavelength. As σ increases from zero to one-third, the radiation reactance varies in magnitude, but remains a negative or stiffness reactance at all frequencies. When σ becomes greater than one-third, a resonance frequency of zero radiation reactance appears, above which the reactance is positive or inertial. Then as σ approaches its limiting value of one-half, the resonance frequency decreases to zero and the familiar accession to inertia of fluid medium acoustics is obtained. When an impulsive pressure is generated in the cavity, as by an explosion, the form of the radiated pulse is a damped wave train which does not closely reproduce the original pressure pulse.

Thyratron operated wave generator

A simple and new type of radio wave generator using the thyratron relaxation oscillator exciting a high frequency oscillatory circuit is described. The generator can produce damped wave trains of any radio frequency at a rate corresponding to any audio frequency and it can be operated on battery or mains supply.

On the scattering of X- and γ- rays by rings of electrons.—The effect of damping of the incident radiation

1. The object of the present investigation is to examine whether damping of the incident radiation can account for the abnormally small scattering of hard γ -rays by aluminium, iron and lead, which was observed by Ishino and was left unexplained in a previous investigation, based on the hypothesis that scattering is a phenomenon of the diffraction by electron rings in the atom of undamped simple harmonic wave-trains of high frequency. It may be stated at once that the result of the enquiry is negative: it is true that damping of an amount small enough to be consistent with the generation of moderately sharp lines in the X- and γ -ray spectrum diminishes the scattering of long waves, but it increases that of short waves, and in each case the change is far too small to explain Ishino’s result. On the other hand, very large damping probably diminishes the scattering of all waves, but it is practically certain that it does not diminish it below the amount required by the Simple Pulse theory, whilst Ishino’s values are only of the order of one-quarter of that amount. This result was to be expected, since an infinitely damped wave-train may be regarded as equivalent to a pulse.

On the vibrations in the field round a theoretical Hertzian oscillator

(1) The object of this paper is to investigate the types of wave motion in the neighbourhood of a theoretical Hertzian oscillator. By a theoretical Hertzian oscillator the writers understand a Maxwellian “double point” of initial maximum moment ± E l . But as the actual oscillator has been shewn by Bjerknes and others to give a damped wave train, we take the maximum moment to run down with the time, and to oscillate between the limits ± E le -p 1 t .