Effective wave speed

Some data for the case of solid inclusions in a solid medium are shown in Figure 5. The figure shows a general lack of agreement between measured (36) and calculated (39) effective wave speeds in the dipole resonance region for 15 percent lead in epoxy. The curve was derived from... 

Melting, a major physical event, has small, subtle effects on shock-compression wave profiles. The relatively small volume changes and limited mixed-phase regions result in modest, localized changes in loading wave speed. Consequently, shock-induced melting and freezing remains an area with little data and virtually no information on the influence of solid properties and defects on its kinetics. 

Because of the subtle effects on the loading wave profile, many of the melting studies have utilized physical property measurements such as resistivity or optical opacity. Perhaps more direct are the release-wave speed... 

Lu, Vyn, Sandus and Slagg (Ref 17) conducted ignition delay time and initiation studies on solid fuel powder-air mixts in an attempt to determine the feasibility of solid-air detonations. The materials investigated included Al, Mg, Mg-Al alloy, C and PETN. Ignition delay time was used as a method of screening the candidate fuels for further work in initiation studies which determined detonation wave speed, detonation pressure, detonation limits, initiation requirements, and the effect of particle size and confinement. The testing showed the importance of large surface area per unit mass, since the most... 

The effect increased with penetration of the wave front into the electric field. Addition of a magnetic field decreased the total current across the slug, by about 40% when the j x B force was in the direction of wave propagation, but by about 25% when the force was against this direction. There was no effect on the wave speed unless the j x B force was against the flow, in which case the wave speed was lowered by up to 10% on account of an increase of turbulence in the boundary layer. The changes in wave structure observed were attributed to the "Hall Effect ... 

It is clear that sound, meaning pressure waves, travels at finite speed. Thus some of the hyperbolic—wavelike-characteristics associated with pressure are in accord with everyday experience. As a fluid becomes more incompressible (e.g., water relative to air), the sound speed increases. In a truly incompressible fluid, pressure travels at infinite speed. When the wave speed is infinite, the pressure effects become parabolic or elliptic, rather than hyperbolic. The pressure terms in the Navier-Stokes equations do not change in the transition from hyperbolic to elliptic. Instead, the equation of state changes. That is, the relationship between pressure and density change and the time derivative is lost from the continuity equation. Therefore the situation does not permit a simple characterization by inspection of first and second derivatives. 

Figure 3. Effects of Mass Loading on the Wave Speed in Sylgard 18A. Solid Curves Theory Equation 3,...

Chapman-Jouguet speed. For example, detonation velocities decrease approximately linearly with the reciprocal of the tube diameter at fixed initial conditions standard experimental practice is to plot the detonation velocity as a function of the reciprocal of the tube diameter and to extrapolate to zero to obtain the true experimental wave speed (for example, [57]). Also, detonation velocities have been observed to decrease approximately linearly with the reciprocal of the initial pressure in a tube of fixed diameter. The first satisfactory explanation of these effects was presented by Fay [58], who accounted for the influence of the boundary layer behind the shock front in a Chapman-Jouguet wave with the ZND structure. 

For cubic symmetry materials, three independent elastic properties that are orientation dependent are required to describe the mechanical behavior of the material. This anisotropy effect increases significantly the number of the nonzero elements in the FE stiffness matrix leading to alteration in the calculated stress components and the wave speed. In order to test these anisotropy effects, we plot the wave profiles of three different orientations and compare it with the isotropic behavior with a loading axis in the [001] directions as shown in Fig 8. We observed that under the same loading condition, the peak stress of [111] and [Oil] orientations are slightly higher than those of the [001] which is lower that that of isotropic material. Furthermore, wave speed varies moderately with orientation with the fastest moving wave in the [ 111 ] followed by [011 ], isotropic medium and [001 ] respectively. 

Summary of the calculations is listed in table 2. This table displays the shock wave parameters calculated in the code and the corresponding theoretical values. The values of the axial stress (O33) obtained from our calculations are in a very good agreement with the corresponding theoretical values given by equation 16. However, the speeds of the longitudinal elastic wave are underestimated when compared to their theoretical values. This is attributed to the effect of FE mesh size. In fact when a fine mesh is used, the velocity approaches the theoretical wave speed value as shown in Fig. 19. 

Consider a small-amplitude sinusoidal plane wave of length A and amplitude a propagating along an air-water interface in the positive x direction with wave speed c, as sketched in Fig. 10.4.1. The water is taken to be incompressible with viscosity and other dissipative effects neglected so that the wave amplitude at the interface remains unchanged. The vertical displacement of the disturbed surface, f, may be written... 

Here n = cq/cq is the ratio of the wave speeds in the two media. They also provide more general expressions for the case of sound beams (rather than plane waves) that are approximated by a one-term Fourier-Bessel series, having both a radial and an axial wave number. The radiation pressure difference (32) at the interface is said to explain the acoustic fountain effect where the directed sound beam creates a liquid jet. 

Rossby radius of deformation Length scale that is equal to c/l/l, where c is the wave speed in the absence of rotation effects and / is the Coriolis parameter caused by Earth s rotation. 

Plantier KB, Pantoya ML, Gash AE (2005) Combustion wave speeds of nanocomposite Al/Fe203 The effects of Fe203 particle synthesis techniques. Combustion and Flame 140 299. 

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