Read e-book online Acoustics of Layered Media I: Plane and Quasi-Plane Waves PDF

By Professor Leonid M. Brekhovskikh, Dr. Oleg A. Godin (auth.)

ISBN-10: 3540647244

ISBN-13: 9783540647249

ISBN-10: 3642523692

ISBN-13: 9783642523694

This monograph is dedicated to the systematic presentation of the speculation of sound­ wave propagation in layered constructions. those buildings will be man-made, akin to ultrasonic filters, lenses, surface-wave hold up traces, or usual media, corresponding 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 subject matters were taken care of quite thoroughly within the publication via L. M. Brek­ hovskikh, Waves in Layered Media, the English model of the second one variation of which used to be released by means of educational Press in 1980. because of development in experimental and desktop know-how it has develop into attainable to research the impression of things reminiscent of medium movement and density stratification upon the propagation of sound waves. a lot recognition has been paid to propagation concept in near-stratified media, Le. , media with small deviations from strict stratification. attention-grabbing effects have additionally been received within the fields of acoustics which have been formerly thought of to be "completely" constructed. For those purposes, and in addition end result of the influx of researchers from the similar fields of physics and arithmetic, the circle of people and learn teams engaged within the examine of sound propagation has quite increased. accordingly, the looks of a brand new precis evaluation of the sphere of acoustics of layered media has develop into hugely fascinating. because Waves in Layered Media turned really well known, we've got attempted to preserve its optimistic good points and normal structure.

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9). 11) with proper choice of the function TJ(z). 8). 11) does not depend on the incident angle of the wave. Hence, in this method oblique incidence with arbitrary can be treated only if an arbitrary additive constant is present in the right-hand side. For nondispersive media one also has k '" w. 11). Thus, we see that not every choice for the functions TJ(z) and g(TJ) is suitable. For brevity, those functions k(z) (wave number "profiles") which allow exact solutions to the problem of the reftection of aplane wave are called "solvable profiles".

0 . 15) by substitution of MI,rn for WI,rn. 12]. We shall assume that Zl > O. Formally our solutions are also true if Zl < 0, but in this case k2 becomes infinite at finite z, which is impossible in acoustics. 16) , where k~, 0:10 and 0:2 are arbitrary constants. 17b) Here k2 is the wave number at Z = -00 and ZI is the vertical scale of inhomogeneities in the lower medium. We see that reflection of a wave with any ~ can be treated due to the arbitrariness of q. The frequency may also be arbitrary depending on the choice of 1 and m.

Furthermore it is continuous across the interfaces between layers. 7). 24) we obtain . 4a) = -IWeo op/o( , or in ordinary coordinates Z = . -IWe ß2 P oploz . 3) is valid for waves of any physical nature provided that the corresponding wave equation is written as a one dimensional Helmholtz equation which does not contain the derivatives of the media parameters in the coefficients. The impedance of a harmonie wave for moving media has a clear physical meaning. W2ß2 oz Hence, impedance is the ratio of the sound pressure to the vertical particle displacement, times a constant factor.

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Acoustics of Layered Media I: Plane and Quasi-Plane Waves by Professor Leonid M. Brekhovskikh, Dr. Oleg A. Godin (auth.)

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