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.)

Acoustics of Layered Media II provides the idea of sound propagation and mirrored image of round waves and bounded beams in layered media. it really is mathematically rigorous yet whilst care is taken that the actual usefulness in functions and the common sense of the idea usually are not hidden. either relocating and desk bound media, discretely and consistently layered, together with a range-dependent surroundings, are handled for varied forms of acoustic wave assets. distinct appendices supply additional heritage at the mathematical methods.
This moment variation displays the impressive fresh development within the box of acoustic wave propagation in inhomogeneous media.

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Extra resources for Acoustics of Layered Media II: Point Sources and Bounded Beams

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Indeed, we have V ~ 1 if 1-q 2: m- 1 and V = -1 at q = 1. 9) obtained by the method of steepest descent is invalid. 10) N --+ 0 if eo #- 7r /2 and N --+ CXJ if eo = 7r /2. This discontinuous result obviously has no physical sense. 10) the integral of the first term has the exact value exp(ikRd / R 1 . 5) and we obtain 22 1. Reflection and Refraction of Spherical Waves Pr = exp(ikRd (k R1 ~ 21fr X P = )1/2 exp (i1f-=1 + ikR1 ) /+00 -00 p(s) exp( ~lkR1Is2)ds , 2(dq/ds)J(n 2 ~ q2)q/(1 ~ q2) (rn~ + Jn2 ~ q2) -1 .

11) 30 1. 12). The factors following the Bessel function - we designate them g(q) and gl (u) - are even functions of q, u. To be sure that these factors are smooth functions at the integration contour we assume that 1m {n} -=f. 0, though this quantity may be infinitely small. The asymptotics of integrals of this type are considered in the Appendix A. 58) we find + i/kr) exp(ikr)/r i(m 2 - 1)(1 + i/kr) 2imn2(1 + i/k1r) exp(ik1r)/r -30(k-2 k- 2) + k1rm2(1 - n 2) - in 2(m 2 - 1)(1 + i/k1r) +r + 1 .

10]. That is why it is reasonable to begin with ray analysis (derivation of the laws of geometrical acoustics as well as their domain of applicability will be given in Chap. 5). The sound field intensity variation along the ray is determined by the variation of the area of the ray tube cross section. Namely, the squared sound pressure amplitude is inversely proportional to the cross section area. The coefficients of reflection from and transmission through the plane interface are the same for rays as for plane waves [Ref.

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