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.)

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

Example text

Hence, the only pole touched is located in the shaded area fl (Fig. 6) which lies on the upper sheet between the path /1 and the real axis q. Let us introduce the function U(qs, qp) which equals 1 if qp E fl, and 0 in the opposite case. 3) is constant along the passage path. Using this fact and reasoning as in Sect. 7) 1m {qp} ;:::0. Calculating the pole residue, we obtain finally I Pr -_ exp(ikR ) RI + [ ( . 70 - [8'k~: x U(qs, qp) q;r' iN + 0 ( -1- )] -- kRI k2 Rr exp {i [kRI (qp sinO. 8) . 9) where N = -2Tf(1 + Tf cos Bo)(cos Bo + Tf)-3 ,I.

13). · Now we move on to the calculations. 27) if lui ~ 1. 6) if Re {u} > 0, where Vi must be replaced by V2(q - qd/ 2. >2 contain an additional term with the factor exp[ikR('Ij;) + u2j2] = exp[ikR('Ij;)cos(O - 8)] if lui ~ 1, Re {u} < O. The expression in the exponent has a stationary point at 'Ij; = 'lj;t. 5) we obtain the equation for 'lj;1 sin('Ij;1 - cp) = [cot 8('Ij;dcos('Ij;1 - cp) - cot 00]8'('Ij;1) . 6 Reflection from Moving Medium 35 When lui ;S 1 we have 1(8/8'IjJ) D,,(u)1 ~ 18u/8'IjJ1 ;S IkR('IjJ)ll/2.

The dependence n. V is real and Ll == 0 at real n ~ 1. If n < 1, we have the same at 00 < fJ = arcsin n.

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