By Professor Leonid M. Brekhovskikh, Dr. Oleg A. Godin (auth.)
This monograph is dedicated to the systematic presentation of the idea of sound wave propagation in layered buildings. those buildings should be man-made, resembling ultrasonic filters, lenses, surface-wave hold up strains, or average media, corresponding to the sea and the ambience, with their marked horizontal stratification. A similar challenge is the propagation of elastic (seismic) waves within the earth's crust those themes were handled quite thoroughly within the e-book by means of L. M. Brek hovskikh, Waves in Layered Media, the English model of the second one variation of which was once released through educational Press in 1980. because of development in experimental and machine know-how it has turn into attainable to research the impact of things resembling medium movement and density stratification upon the propagation of sound waves. a lot consciousness has been paid to propagation concept in near-stratified media, Le. , media with small deviations from strict stratification. attention-grabbing effects have additionally been bought within the fields of acoustics which were formerly thought of to be "completely" built. For those purposes, and in addition due to the influx of researchers from the comparable fields of physics and arithmetic, the circle of people and study teams engaged within the examine of sound propagation has quite multiplied. for this reason, the looks of a brand new precis evaluate of the sector of acoustics of layered media has turn into hugely fascinating. considering that Waves in Layered Media grew to become fairly renowned, we have now attempted to preserve its confident beneficial properties and normal structure.
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Extra resources for Acoustics of Layered Media I: Plane and Quasi-Plane Waves
4) c(z) The quantity W is the transmission coefficient and is independent of z. 3) is found the reflection coefficient is determined by [cf. 3) is a one-dimensional Helmholtz equation and seems to be simple, its solution in quadratures, however, is possible only in exceptional cases. The general method for finding such solutions consists of reducing this equation to some basic soluble one by the substitution of dependent or independent variables. (For methods of reduction of ordinary second-order differential equations see, for exampIe, [Ref.
It can be shown that the same result can be obtained, if we proceed to the limit q --+ 0 in the case q =/:- O. 19) Consider the behavior of the wave in the lower half-space at z --+ - 00. 9, 10, 17) and retaining only the main terms in the expansion in apower series of Iztlzl. 20,21) that with the error O( Iz 1-1), p ~ const· exp x) in the lower half-space at large Iz land does not depend on z. Note that the parameter Q2 is absent in the main terms of the above asymptotic expansions. 16) is sm all compared to k~.
2 only by the phase factor exp (iep). The appearance of the latter is caused by displacement of the reference point of the phase of the refracted wave frorn z = d to z = o. 3 Another Approach to the Reflection and Transmission Coefficients Calculation There is another derivation of the expression for the reflection coefficient that is of interest. 4) as a superposition of: (a) the wave reflected frorn the front surface of the Iayer 28 (boundary between media 3 and 2, the first number is taken for the medium from which the wave is indicent); (b) the wave penetrating the front surface of the layer, passing through the layer, reflecting from its back surface (boundary between the media 2 and 1), passing through the layer again and finally leaving it through its upper boundary between the media 2 and 3; (c) the wave penetrating the layer, undergoing two reflections at the back surface and one at the upper surface, passing twice through the layer back and forth, and then again leaving the layer, etc.