Read e-book online Acoustics of Layered Media II: Point Sources and Bounded PDF

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

ISBN-10: 3662027763

ISBN-13: 9783662027769

ISBN-10: 366202778X

ISBN-13: 9783662027783

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

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3) at the plane z = h is located at the point x = O. This choice of coordinates (x, z) we will use everywhere below. 14). 4) +ikh[(1 _l)1/2 - (1 - qt)1/2]} . Note that we have a large parameter k2 w 2 in the exponential. Hence, the integral from Vi (q) can be calculated by the steepest descent (SD) method (Sect. 1). In the integral from Vi(q) the branch point q = n may be close to the stationary point q = qo. Integrals of this type are considered in Sect. 3. Pr(x, 0) = V(~o) (~y/2 [Vi (qo) + V2(qo)(2a)-1/4 exp (~ _ x exp [- : : (x - XO)2] [1 + 0 (k~ )] .

23,24]. That is why this effect is usually called the Goos-Hanchen effect. 8] the reader can find a rather complete bibliography of literature which appeared before the early 1970s as well as a description of applications of this effect in different branches of science. 25,26]. If the sound wave in a liquid is incident upon the interface of solid and liquid homogeneous halfspaces, the reflection coefficient is [Ref. 1, Eq. 8) where ~ = k sin 0 = k/ sin 0/ = kt sin 0(0 a = k cos 0, al = k/ cos 0" ,81 = kt COS Ot, -kt COS 20t /2 sin 0(0 k, k/, kt are the wave numbers for the sound wave in the liquid, and longitudinal and shear waves in the solid, respectively; 0, 0/, Ot are the incidence angle and refraction angles for the corresponding waves.

We have IZI ~ ec and Z = -ilZI if n < 1. At such impedances Z, the values of the reflection coefficients v and V are similar at any incidence angle. The same approximation for the reflection coefficient V(q) holds if n ~ 1 (low sound velocity in the lower halfspace as is the case, for example, for some porous media or for silt ocean bottoms saturated by gaseous bubbles), since cos ()I = (1- n- 2 sin2 ()1/2 :::::: 1 at any (). The approximation of a boundary as one described by the angle-independent impedance is of practical use in architectural acoustics, in atmospheric acoustics (reflection from the surface of the earth) and so on.

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


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