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

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

ISBN-10: 3642084893

ISBN-13: 9783642084898

Acoustics of Layered Media II provides the speculation of sound propagation and mirrored image of round waves and bounded beams in layered media. it really is mathematically rigorous yet while care is taken that the actual usefulness in functions and the common sense of the speculation will not be hidden. either relocating and desk bound media, discretely and continually layered, together with a range-dependent atmosphere, are handled for varied forms of acoustic wave assets. distinct appendices supply additional historical past at the mathematical methods.
This moment version displays the amazing contemporary development within the box of acoustic wave propagation in inhomogeneous media.

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Additional info for Acoustics of Layered Media II: Point Sources and Bounded Beams

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5) . J!. = (-7fi/2)H6 1\u). 3) can be neglected. 7) . 1). 7). We introduce the substitution (u 2 + t 2 ) 1/2 - U = 8 2 . 8) U . In the case we are interested in (7f /2 - eo « 1) 86 = 2kR1 sin 2 (i _ e~) « u = kR1 sin eo. 5). 7) is elementary. We have finally: _exp(ikR 1 ) {m-l imkR1(n 2 -1)[ r= W2( f I)]} R + ( )2 l+v 7fwe er w+ , 1 m+l m+l Prw 37fi) VInI:D . (7f = exp ( 4 2kR1 sm "4 - 2eo) . 6), in terms of Fresnel integrals with real arguments. 3) is in powers of kRI(n2 -1). 17,18). 9). 9) depend on the quantity (m - 1) / (n - 1).

3) the integration path must lie in the region It I < 1. To obey this condition we choose the path going around the point q = 1 in quadrant IV along the halfcircle of the radius which is large enough, and then again return to the path T (Fig. 2). Since the integrand has no singularities on the upper sheet, such deformation of the integration path is permissible. In the integrals obtained, the integration path can be transformed into the real axis without any influence on the value of the integral.

J!. = (-7fi/2)H6 1\u). 3) can be neglected. 7) . 1). 7). We introduce the substitution (u 2 + t 2 ) 1/2 - U = 8 2 . 8) U . In the case we are interested in (7f /2 - eo « 1) 86 = 2kR1 sin 2 (i _ e~) « u = kR1 sin eo. 5). 7) is elementary. We have finally: _exp(ikR 1 ) {m-l imkR1(n 2 -1)[ r= W2( f I)]} R + ( )2 l+v 7fwe er w+ , 1 m+l m+l Prw 37fi) VInI:D . (7f = exp ( 4 2kR1 sm "4 - 2eo) . 6), in terms of Fresnel integrals with real arguments. 3) is in powers of kRI(n2 -1). 17,18). 9). 9) depend on the quantity (m - 1) / (n - 1).

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