Acoustics of Layered Media II: Point Sources and Bounded - download pdf or read online

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

ISBN-10: 3642084893

ISBN-13: 9783642084898

ISBN-10: 3662038897

ISBN-13: 9783662038895

Acoustics of Layered Media II provides the speculation of sound propagation and mirrored image of round waves and bounded beams in layered media. it's mathematically rigorous yet even as care is taken that the actual usefulness in functions and the common sense of the idea should not hidden. either relocating and desk bound media, discretely and continually layered, together with a range-dependent surroundings, are taken care of for numerous forms of acoustic wave resources. targeted appendices offer additional heritage at the mathematical methods.
This moment variation displays the awesome fresh growth within the box of acoustic wave propagation in inhomogeneous media.

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2) equals zero at q = 0, the first term of the asymptotics for ifJ I is of the order of (kR(7/J))-3/2 if cos(cp - 7/J) = 0 and of the order of (kR( 1/;)) -2 if cos( cp - 7/J) < O. Hence, those values of 1/; which correspond to qo <::; 0 make a negligible contribution to Pl. 1) can also be estimated by the method of steepest descent. Stationary points for the expression in the exponent can be found from sin 2( 7/J - cp) = O. 6 Reflection from a Moving Medium 35 these points, only one, 't/J = 'P, lies on the integration contour and satisfies the condition qo > O.

The sound field behavior in the vicinity of the boundary of existence of the lateral wave as well as the uniform asymptotics for P2 valid at any Bo and 'P are described by the parabolic cylinder functions, as was the case in media at rest. Now we move on to the calculations. 27) if lui» 1. 6) if Re{u} > 0, where V l must be replaced by V2 (qql)l/2. 1) the main contribution to the integral is due to the integration in the vicinity of the stationary point 'lj; = 'P. The asymptotics for P2 contain an additional term with the factor exp[ikR('lj;)+u 2/2] = exp[ikR( 'lj;) cos(B-8)] if lui» 1, Re {u} < o.

43]. 44]. Corrections to the ray theory become important only when the distance from the source as well as the receiver to the boundary are smaller than the wavelength. 84]. 45,46]. 47,48,85, 86,91], the boundary with porous media was considered as an impedance boundary. 49]. 46,47,49]. , when the densities, sound velocities and absorptions in both media are similar (m ;:::; 1, n ;:::; 1). 8) can be near them. This problem is of considerable theoretical and practical interest. 50,51]. The same situation occurs at boundaries between different water masses in the ocean and air masses in the atmosphere.

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Acoustics of Layered Media II: Point Sources and Bounded Beams by Professor Leonid M. Brekhovskikh, Dr. Oleg A. Godin (auth.)

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