Traveling wave

The sonic tool measures the time taken for a sound wave to pass through the formation. Sound waves travel in high density (i.e. low porosity) formation faster than in low density (high porosity) formation. The porosity can be determined by measuring the transit time for the sound wave to travel between a transmitter and receiver, provided the rock matrix and fluid are known. 

By means of the pair SI/El a longitudinal wave travels parallel to the object surface. 

A laser beam is capable of putting so much energy into a substance in a very short space of time that the substance rapidly expands and volatilizes. The resulting explosive shock wave travels through the sample, subjecting it to high temperatures and pressures for short times. This process is also known as ablation. 

We consider, for ease of manipulation, the wave travelling in the x direction and assume that f (x, t) can be factorized into a time-dependent part 0 t) and a time-independent part iA(x), giving... 

A. The simplest solution to this equation is the uniform plane wave traveling in an arbitrary direction denoted by the vector k ... 

Ultrasonic Spectroscopy. Information on size distribution maybe obtained from the attenuation of sound waves traveling through a particle dispersion. Two distinct approaches are being used to extract particle size data from the attenuation spectmm an empirical approach based on the Bouguer-Lambert-Beerlaw (63) and a more fundamental or first-principle approach (64—66). The first-principle approach implies that no caHbration is required, but certain physical constants of both phases, ie, speed of sound, density, thermal coefficient of expansion, heat capacity, thermal conductivity. 

Interference of Waves. The coherent scattering property of x-rays is used in x-ray diffraction appHcations. Two waves traveling in the same direction with identical wavelengths, X, and equal ampHtudes (the intensity of a wave is equal to the square of its ampHtude) can interfere with each other so that the resultant wave can have anywhere from zero ampHtude to two times the ampHtude of one of the initial waves. This principle is illustrated in Figure 1. The resultant ampHtude is a function of the phase difference between the two initial waves. 

Noise Control Sound is a fluctuation of air pressure that can be detected by the human ear. Sound travels through any fluid (e.g., the air) as a compression/expansion wave. This wave travels radially outward in all directions from the sound source. The pressure wave induces an oscillating motion in the transmitting medium that is superimposed on any other net motion it may have. These waves are reflec ted, refracted, scattered, and absorbed as they encounter solid objects. Sound is transmitted through sohds in a complex array of types of elastic waves. Sound is charac terized by its amplitude, frequency, phase, and direction of propagation. 

A detonation shock wave is an abrupt gas dynamic discontinuity across which properties such as gas pressure, density, temperature, and local flow velocities change discontinnonsly. Shockwaves are always characterized by the observation that the wave travels with a velocity that is faster than the local speed of sound in the undisturbed mixtnre ahead of the wave front. The ratio of the wave velocity to the speed of sound is called the Mach number. 

Scaled peak overpressure and positive impulse as a function of scaled distance are given in Figures 6.17 and 6.18. The scaling method is explained in Section 3.4. Figures 6.17 and 6.18 show that the shock wave along the axis of the vessel is initially approximately 30% weaker than the wave normal to its axis. Since strong shock waves travel faster than weak ones, it is logical that the shape of the shock wave approaches spherical in the far field. Shurshalov (Chushkin and Shurshalov... 

TNT explosions have a very high shock pressure close to the blast source. Because a shock wave is a non-isentropic process, energy is dissipated as the wave travels from the source, thus causing rapid decay of overpressures present at close range. 

The peak shock pressure directly after the burst, p, is much lower than the initial gas pressure in the vessel / . As the shock wave travels away from the vessel, the peak shock pressure decreases. The nondimensional peak-shock overpressure directly after the burst is defined as (pjpo) 1. It is given by the following expression (see Section 6.3.1.1) ... 

In Steps 2 and 3, the vessel s nondimensional radius and the blast wave s nondimen-sional peak pressure at that radius were calculated. As a blast wave travels outward, its pressure decreases rapidly. The relationship between the peak pressure and the distance R depends upon initial conditions. Accordingly, Figure 6.21 contains several curves. Locate the correct curve by plotting (R, P ) in the figure, as illustrated in Figure 6.28. 

Shock waves travel at supersonic velocities and exhibit a near discontinuity in pressure, density, and tempera-... 

Type 2 - fI = fi t) is characterized by a saw-tooth-like pattern of peaks of various amplitudes, with the peaks appearing at almost regular intervals transition waves travel outward from a central focus to the boundary, with widely differing radii type-2 behavior typically appears for 3 < i/ < 8. 

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