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 constructions might be man-made, similar to ultrasonic filters, lenses, surface-wave hold up strains, or typical media, comparable to the sea and the ambience, with their marked horizontal stratification. A comparable challenge is the propagation of elastic (seismic) waves within the earth's crust those themes were handled relatively thoroughly within the ebook by way of L. M. Brek­ hovskikh, Waves in Layered Media, the English model of the second one version of which was once released through educational Press in 1980. because of development in experimental and laptop expertise it has turn into attainable to investigate the effect of things equivalent to medium movement and density stratification upon the propagation of sound waves. a lot recognition has been paid to propagation idea in near-stratified media, Le. , media with small deviations from strict stratification. attention-grabbing effects have additionally been got within the fields of acoustics which have been formerly thought of to be "completely" built. For those purposes, and likewise a result of influx of researchers from the comparable fields of physics and arithmetic, the circle of folks and study teams engaged within the learn of sound propagation has fairly improved. consequently, the looks of a brand new precis overview of the sphere of acoustics of layered media has turn into hugely fascinating. seeing that Waves in Layered Media turned relatively well known, we have now attempted to preserve its optimistic beneficial properties and basic structure.

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When the parameters of the media are the same (ei = e2, Ci = C2) these angles can be found explicitly. 19) is now equivalent to the system of equations a + b =M , (a 2 - b2 )[(ab)2 + 2ab - M 2] =0 == (V2 - vl)lcl. 20) the solutions of which can be found elementarily. The only resonance angle possible when 2 $ M $ 23/2. 21) . Two more resonance angles appear when M . l is arbitrary. For gases, this means 1'1 =1'2· Wave amplification by reflection does not contradict the energy conservation law: the reflected wave takes some amount of energy from the flow.

5) cos (}j M I . 4 and 11), respectively. 6), respectively. ) are still valid. It is important to note, however, that the above expressions now have a new and deeper meaning. 12), on the angle between the vectors and vo. Hence the maximum transparency of the half-wave layer occurs when + e CP2 = k3(1 + M3 sin ~)-1 sin ~ ·d2 ·cot(}2 = Irr , I = 1,2, ... 13) The angle of maximum penetration now depends on the angle between the flow direction and the x-axis. 3 Reßection at a Single Interface Consider more closely the reflection of aplane monochromatic wave from aplane interface between moving homogeneous media.

Let us consider some particular cases. C We see that c, c}, e, and [>1 enter into these expressions only as products [>C and e1C}, called the wave or characteristic impedances. 19) If n :1= 1, (J -+ 7r/2 (grazing incidence) Eqs. 16, 17), yield V - t -1, W -+ O. If (J satisfies the equation m cos (J = (n 2 - sin2 (J)lfl, the refteetion eoeffieient becomes zero. This is the case of a eompletely transparent interface. 20) The complete transpareney angle is real if (m2 - n 2 )/(n 2 - 1) > O. This oceurs when 1 < n < m or when 1 > n > m.

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