Propagation of longitudinal waves

Malvern, L.E., Propagation of Longitudinal Waves of Plastic Deformation In a Bar of Material Exhibiting a Strain-rate Effect, J. App. Mech., Vol. l8, pp. 203-8. 

The temperatures Tq and T were determined with great exactness by means of a bolometer in the interior of the vessel. (c) The determination of k from the velocity of sound. In the propagation of longitudinal waves (sound waves) in a gas, compressions and dilatations of the gas follow one another very rapidly. These compressions and dilatations may be regarded as taking place adiabatically, as the rate at which they follow... 

The ultrasound wave is longitudinal in nature (i.e., the direction of propagation is the same as the direction of oscillation). Longitudinal sound waves cause compression and expansion of the medium at a distance of half the wavelength, leading to pressure variations in the medium. The resistance of the medium to the propagation of sound waves is dependent on the... 

The propagation of longitudinal acoustic waves in choked nozzles has been analyzed on the basis of the one-dimensional, time-dependent forms of equations (4-45) and (4-46) by introducing linearizations of the previously indicated type (for example, p = p(l + p )] for the stream wise velocity v as well—that is, v — v(l + i )—and by allowing the mean quantities p, p, and V to vary with the streamwise distance z through the nozzle, in a manner presumed known from a quasi-one-dimensional, steady-flow nozzle analysis [20]. The perturbation equations... 

There are two distinct types of ultrasonic waves the most commonly used in fats characterization are longitudinal waves (Fig. lA) where deformations occur in the direction of propagation of the wave. It is also possible to generate shear waves with deformations normal to the direction of propagation (Fig. IB). Shear waves do not travel macroscopic distances in fluids so it is often impossible to make good measurements in foods. Throughout this work I will exclusively focus on longitudinal waves. 

To perform measurements of longitudinal wave propagation and damping characteristics, a device designed by Lemaire Langevin (1992) can be used. While the longitudinal wave is... 

The influence of micellisation on the propagation of capillary waves has been discovered only for solutions of the nonionic surfactant - DePO. The determined values of Z2 are comparable with the results for solutions of DePB but they decrease monotonously with concentration. Therefore, the obtained results evidence that relations (5.284) and (5.285) describe the concentration dependence of the dynamic surface elasticity well. Hence, the method of transverse capillary waves can be used for studies of micellisation kinetics of surfactants with relatively low surface activity. For surfactants with higher surface activity where the formation and disintegration of micelles proceed slower the method of longitudinal surface waves can be used [102, 103]. The characteristics of longitudinal waves are more sensitive to the dynamic surface elasticity, and this allows one to study the micellisation kinetics under the condition... 

Aside from the frequency and sound intensity, the key point in the design of sound-assisted dryers is the mode of energy propagation. Sound energy can be propagated as longitudinal waves (also called compression waves) or transverse waves for which vibration of the particle in the material occurs... 

Pulsatile flow in an elastic vessel is very complex, since the tube is able to undergo local deformations in both longitudinal and circumferential directions. The unsteady component of the pulsatile flow is assumed to be induced by propagation of small waves in a pressurized elastic tube. The mathematical approach is based on the classical model for the fluid-structure interaction problem, which describes the dynamic equilibrium between the fluid and the tube thin wall (Womersley, 1955b Atabek and Lew, 1966). The dynamic equilibrium is expressed by the hydrodynamic equations (Navier-Stokes) for the incompressible fluid flow and the equations of motion for the wall of an elastic tube, which are coupled together by the boundary conditions at the fluid-wall interface. The motion of the liquid is described in a fixed laboratory coordinate system (f , 6, f), and the dynamic... 

Surface Acoustic Waves. All of the discussion so far has dealt with the propagation of acoustic waves in bulk pol5uners. In addition to longitudinal and shear waves, however, a surface or Rayleigh wave, called a surface acoustic wave, can also be propagated. 

FIGURE 1.102 Generation of a longitudinal sound wave by the rapid movement of a piston in the end of a tube, showing the propagation of the wave pulse at the speed of sound down the length of the tube. 

---