Download Acoustic and Elastic Wave Fields in Geophysics, III by Alex A. Kaufman, A.L. Levshin PDF

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By Alex A. Kaufman, A.L. Levshin

This monograph is the final quantity within the sequence 'Acoustic and Elastic Wave Fields in Geophysics'. the former volumes released via Elsevier (2000, 2002) dealt normally with wave propagation in liquid media.

The 3rd quantity is devoted to propagation of airplane, round and cylindrical elastic waves in several media together with isotropic and transversely isotropic solids, liquid-solid types, and media with cylindrical inclusions (boreholes). * occurrence of actual reasoning on formal mathematical derivations * Readers do not have to have a powerful historical past in arithmetic and mathematical physics * special research of wave phenomena in a variety of forms of elastic and liquid-elastic media

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Extra resources for Acoustic and Elastic Wave Fields in Geophysics, III

Example text

In other words, mass m defines a time interval during which the center of mass of the moving bar reaches a certain value of the velocity, if Fx = const. For instance, with an increase of mass acceleration decreases and therefore this time interval increases. It is natural to raise the following question. Why does the mass TO, that is the product ISp, define inertia? To answer this question, consider in detail the influence of each factor. First, with an increase of the bar length, I, the time of the wave traveling between bar ends, T, also increases, and in accordance with eqs.

Suppose that the wave propagates along the :r-axis and reaches the cross-section S(x - dx/2). From this moment we begin to observe deformation of this bar element, dV = Sdx. With some time delay, the wave arrives at the front face of the volume, S(x+ dx/2). Force F(x, t), which accompanies the wave, has the same direction at both crosssections, but may differ in magnitude. 2 LONGITUDINAL WAVES IN A THIN BAR 17 takes place. The force at points of the section S(x + dx/2) acts on a medium located in front of the bar element.

6a. Each pulse causes a reflected pulse. Correspondingly, the resultant reflected wave has two important features, namely a. At the bar end the reflected and incident waves are of different types. b. The front of the reflected wave is caused by the front of the incident wave. Superposition of these waves is shown in Fig. 6b-g. Suppose that the extensional wave approaches the free end, Fig. 6b. Then, due to a reflection, the compressional wave appears, Fig. 6c. The thin line corresponds to this wave.

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