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

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

Acoustics of Layered Media II offers 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 good judgment of the speculation should not hidden. either relocating and desk bound media, discretely and always layered, together with a range-dependent setting, are taken care of for numerous forms of acoustic wave resources. unique appendices supply extra historical past at the mathematical methods.
This moment variation displays the amazing fresh growth within the box of acoustic wave propagation in inhomogeneous media.

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

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Consider the ray leaving the source S at an angle (}o and arriving at the observation point P 1(r, z) (Fig. 4). The ray leaving the source at the angle (}o + d(}o arrives at the point P2 (r + dr, z), where dr = d(}o o ' The cross section of the ray tube in the plane of the figure is IMP11 = IP1P21cos(} = lor/o(}olcos(}d(}o and that in three-dimensional space is ds = rlor/o(}ol cos Od(}o d

6 Reflection from a Moving Medium o 33 J v 2 Fig. 1. 7 Comparison of the reflected field asymptotics with the exact calculation in the case of m = 1, 7r/2 - 8 = 7r/250, 7r/2 - eo = 311"/1000 for several values of v = (kRI) 1/2 (7r /2 - 8). 911) However, these asymptotics give values for IPrl that are too high (even higher than the ray approximation) at very small Iv I. 75]. Let the lower medium (z < 0) move relative to the upper one (where the point source is located) with the velocity Vo = (vo, 0, 0).

If this ratio remains bounded when m, n --+ 1 (for example, in the case when the difference in the parameters of the media is due to a temperature difference) the term (m - 1) / (m + 1) can be neglected. 4). 1), multiplied by (m1)/(m + 1), for a boundary with impedance Z = 2Qc(1 - m 2)/m(l- n 2)1/2. Let us consider two extreme cases. We have Iwl « 1 if 7f /2 - eo « IkR I I- I / 2 . 9) gives in the limit w --+ 0 the field which does not depend on eo. If 1m-II is sufficiently small simultaneously, IPrl ;::::; ik(n 2 -1)/4, and IPrl does not also depend on R I .

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