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.)

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

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The curves represent the field amplitude across the beam. 1) Pi(x, z) is of the order of where rJii unity at a distance Llx ~ w; w is defined to be the width of the beam. The last will be assumed to be large as compared to the wavelength. (q) has a maximum in the vicinity of q = qo == sin (Jo and is close to zero at Iq - qol ;:;: (kw)-l, where (Jo is, by definition, the incidence angle of the beam. P;(x, h) = 0 beyond. (q) = A[7rka(q - qo)]-I sin ka(q - qo) . (qo) is small when Iq - qol ~ (ka)-l, that is, the beam has high directivity if kw ~ 1.

10) the integral from the first term has the exact value exp(ikRl)/RI. 5) and we obtain Pc = exp(ikRl) (k Rl 2;;:- )1/2 exp (i7r. 4" + lkRI ) P = 2(dq/ds)V(n 2 - q2)q/0 - q2) 1+ 00 -00 2 pes) exp( -l kR lls )ds , (m~ + Vn2 _ q2) -1. 2)]. 3). 11) for the lateral wave PI which tends to zero when m -+ 00. Therefore, the lateral wave in the case under the consideration (m ~ 1) can, as a rule, be neglected. It was shown in Sect. 2 that other branch points are not important to us. 8) can be close to the stationary point s = 0 if m ~ 1.

The distance 6zo is much greater than the wavelength if 1171 ~ 1. 5 Weak Boundaries 25 wave of this kind is discussed also in [Ref. 1, Sect. 4]. The wave ps decreases 0 and is analogous to the leaky wave exponentially in r-direction if Re {Z} considered in [Ref. 1, Sect. 4], but at the boundary it loses, and does not gain its 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). 5(1 + sgn x), that is, the Heaviside function.

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