Waves ultrasonic - propagation, equation

After the leakage has been created, the flat expansion pressure waves are propagated in two converse sides. These waves have sonic speed and after clashing to the upstream and downstream boundaries, return to the form of compression or expansion wave depending on the edge type (Fig. 1). In the leak location, depending whether the ratio of pressure to ambient pressure is more or less than the CPR quantity, the equation of which is showed in equation (1), the flow will be sonic and ultrasonic or subsonic respectively. 

Here E is the appropriate elastic modulus (which depends on the physical state of the material and the type of wave propagating) and p is the density. By combining equations 3 and 4 the physical properties of a material (E and p) can be related to its ultrasonic properties (c and a). 

Let us begin our discussion with a description of a plane ultrasonic wave in terms of the displacement of a particle, from its equilibrium position as a function of the distance that wave has traveled. Let us assume that the wave propagates along the x coordinate. We can then write the general wave equation as... 

Ultrasonic Nebulizers. Ultrasound can be used to break up a liquid mass into smaller particles. In the ultrasonic nebulizer, an ultrasonic generator drives a piezoelectric crystal at a frequency between 200 kHz and 10 MHz. The surface of the liquid sample will breakdown into an aerosol when the longitudinal wave propagates from the surface of the crystal toward the liquid-air interface. The wavelength of the surface wave is given by the following equation ... 

An important improvement of reconstructions can be obtained by selecting a more appropriate model and abandon the straight pathway approximation . A more sophisticated model gives a description of the propagation of ultrasonic waves in a medium based upon the wave equation ... 

Elastic Coefficients The elastic stiffness coefficients Cy can be calculated from the measured velocity of propagation of bulk acoustic ultrasonic waves, according to the Papadakis method (quartz transducer with center frequency of 20MHz) (Papadakis, 1967), on differently oriented bar-shaped samples using the equations given by Truell et al. (1969) and corrected for the piezoelectric contributions (Ljamov, 1983 Ikeda, 1990). The samples were oriented in axial directions XYZ, and 45° rotated against the X- and Y-axes, respectively. In order to obtain optimized values for the elastic materials parameters, the elastic stiffness coefficients Cy were used to calculate and critically compare the results of surface acoustic wave (SAW) measurements. 

In Equation 2.10 B is a constant and the A/s represent the relaxation amplitudes that are proportional to the square of the isentropic volume change 0/° given by Equation 2.9 and that contains both 07 and AH°. Indeed, the propagation of ultrasonic waves in fluids gives rise to harmonic changes of p and T. The investigated equilibria are shifted periodically by these two perturbations, thus the ultrasonic relaxation amplitude dependence on... 

Table 1 shows relations between the elastic constants of materials of a hexagonal symmetry and the velocity,direction of propagation and plane of polarisation of the ultrasonic waves. The relations between the material constants (Young"s modulus, stiffness modulus and Poisson number) and the elastic constants, derived from the equations quoted in Table 1 are as follows ... 

The same method of surface ultrasonic waves can also be used for determining that thickness of the surface layer in which the prt rties differ from the properties within the bulk (IS). The values obtained for polymers of various chemical nature are within 200 and 700 /u, depending on the thidcness of the surface layers of the polymers in heterogeneous filled systems (14). It follows from the theoretically obtained equations that the thidcness of the layer derived from the data on the propagation of surface ultrasonic waves, depends both on the mechanical properties of the bulk and surface layer and on the frequency. The difference in the modulus of elasticity of the bulk and surface layer are associated with the surface tension forces. The frequency-dependence of the thickness is determined by the types of molecular motions involved in the process in accordance with the mechanical models indicated above. 

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