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.)

Acoustics of Layered Media II offers the speculation of sound propagation and mirrored image of round waves and bounded beams in layered media. it's mathematically rigorous yet while care is taken that the actual usefulness in purposes and the good judgment of the speculation usually are not hidden. either relocating and desk bound media, discretely and consistently layered, together with a range-dependent setting, are taken care of for varied kinds of acoustic wave resources. exact appendices offer additional history at the mathematical methods.
This moment version displays the striking contemporary development within the box of acoustic wave propagation in inhomogeneous media.

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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. 3 the condition qp E fl can be written in analytical form: 24 1. Reflection and Refraction of Spherical Waves Im{q} itan0 0 ", , ", , o \sin0 0 Fig. 6 Integration contour deformation in the case of sound reflection at an impedance boundary in a non absorbing medium. is the region of location of those reflection coefficient poles which give rise to surface or leaky waves.

9]). Indeed if eo is not too close to (j "'" 7r 12, the branch point q = 1 is far enough from the stationary point and the problem is very simple. 9) obtained by the passage method tends to the exact solution Pr = (m - l)(m + 1)-1 Rl1 exp(ikRd. 1) 1=0 t == (n 2 - 1)/(q2 - 1) , Bo = (m - 1)/(m + 1) , B1 = m(m + 1)-2 . = Subsequent coefficients can be found by using the recursion relation (m 2 - I)Bl(m) = mB1(1) - Bl(m) . 5 exp (iv~) qdq . 1) equals 1. 3) the integration path must lie in the region It I < 1.

This displacement is caused by the reflection coefficient's 44 2. Reflection of Bounded Wave Beams phase dependence on q. This dependence changes the interference of primary plane waves in the reflected beam from that in the incident one. The dependence l{J( q) leads apparently to the effective displacement of the reflective boundary in the z-direction, with this displacement dependent on the incident angle. We shall see below that there exist also other physical interpretations of a beam displacement in some cases.

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