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 idea 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 purposes and the good judgment of the idea will not be hidden. either relocating and desk bound media, discretely and regularly layered, together with a range-dependent surroundings, are taken care of for varied varieties of acoustic wave resources. distinct appendices offer extra historical past at the mathematical methods.
This moment version displays the impressive contemporary growth within the box of acoustic wave propagation in inhomogeneous media.

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

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I z :S O. Using the definition of impedance [Ref. 1, Eq. 7)] Z = -iwQP(opjoz)-l , we rewrite this condition as 0 ;::: I z = -lpl2Re {Z} j2w or Re {Z} ;::: O. The reflection will be total if Re {Z} = o. (The same conclusions can be obtained by analysis of Eq. 2--4) (where V must be replaced by v) in approximate form. 5) for the path 11 does not depend on the nature of the boundary. Since the Hankel function branch point q = 0 is of no importance for us and v(q) has only two branch points q = ±1, the Riemann surface will be two-sheeted.

Then lu(cp)1 » 1. 10), Il,bl - cpl « 1. Hence IBo - o(cp)1 ;::::0 IB(l,bd - O(l,bl) + [B'(l,bd - o'(l,bd](cp -l,bdl « 1. This contradiction shows that the two cases considered above, IBo -o(cp)1 « 1 and lu(cp)1 » 1, IU(l,bdl » 1, cover the entire problem. Three last inequalitites can be satisfied simultaneously. 16) 38 1. p)]. 14) give the same results. The results obtained above can be written as a single formula for the component P2 of the reflected field: where the functions B 1,2 and U2 are yet to be determined.

The distance oZo is much 26 1. Reflection and Refraction of Spherical Waves greater than the wavelength if hi « 1. A surface wave of this kind is discussed also in [Ref. 1, Sect. 4]. The wave Ps decreases exponentially in r-direction if Re { Z} f= 0 and is analogous to the leaky wave considered in [Ref. 1, Sect. 4], but at the boundary it loses rather than gains energy. In contrast to the geometric acoustical component, it is observed in the bounded region of space which is determined by the function U(qp, qs).

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