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 even as care is taken that the actual usefulness in functions and the common sense of the idea will not be hidden. either relocating and desk bound media, discretely and constantly layered, together with a range-dependent surroundings, are handled for varied kinds of acoustic wave resources. distinctive appendices offer extra historical past at the mathematical methods.
This moment version displays the extraordinary 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

Example text

7)]. 5) have many analogies in the theory of pulse propagation in dispersive media [Ref. 22, Sect. 21]. The physical meaning of the displacement L1 becomes clear if we consider the following very simple case. Let the plane wave exp{ik[qx - (1- q2)1/2 z]} be incident upon the boundary z = -h where it undergoes reflection with the reflection coefficient V = l. The reflected wave will be, obviously, exp{ik[qx+ (1- q2)1/2(Z + 2h)]}. The ratio of reflected and incident waves at z = 0, V = exp[2ikh(1- q2)1/2], can be considered as the reflection coefficient at the plane z = 0 with cp(q) = 2kh(1- q2)1/2.

Below we shall call it simply "spectrum", for brevitiy. The reflected field will have an integral representation [ef. 3) where V(q) = W(q)1 exp[irp(q)] is the reflection coefficient of the plane wave with the incidence angle = arcsin q. 3). e L. M. , Acoustics of Layered Media II © Springer-Verlag Berlin Heidelberg 1999 42 h 2. r \\ \ \ \ I I I I " '" Fig. 1 Geometry of beam displacement upon reflection. The curves represent the field amplitude across the beam. 1) where Wi -+ 0 at Ixl -+ 00 and the function's In Wi variation is of the order of unity at a distance Llx ::: w; w is defined to be the width of the beam.

5) yields eo eo Ll = 2m(1 - n 2 ) tane o(sin 2 6< eo < 7f/2 .

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