By Professor Leonid M. Brekhovskikh, Dr. Oleg A. Godin (auth.)
This monograph is dedicated to the systematic presentation of the speculation of sound wave propagation in layered buildings. those constructions might be man-made, comparable to ultrasonic filters, lenses, surface-wave hold up traces, or normal media, corresponding to the sea and the ambience, with their marked horizontal stratification. A similar challenge is the propagation of elastic (seismic) waves within the earth's crust those subject matters were handled relatively thoroughly within the ebook by way of L. M. Brek hovskikh, Waves in Layered Media, the English model of the second one version of which was once released by means of educational Press in 1980. because of growth in experimental and desktop expertise it has turn into attainable to research the impact of things comparable to medium movement and density stratification upon the propagation of sound waves. a lot recognition has been paid to propagation thought in near-stratified media, Le. , media with small deviations from strict stratification. attention-grabbing effects have additionally been acquired within the fields of acoustics which were formerly thought of to be "completely" constructed. For those purposes, and likewise a result of influx of researchers from the comparable fields of physics and arithmetic, the circle of people and study teams engaged within the examine of sound propagation has fairly increased. consequently, the looks of a brand new precis assessment of the sector of acoustics of layered media has turn into hugely fascinating. due to the fact that Waves in Layered Media turned really well known, we now have attempted to maintain its optimistic positive factors and basic structure.
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Extra info for Acoustics of Layered Media I: Plane and Quasi-Plane Waves
We shall assume that Zl > O. Formally our solutions are also true if Zl < 0, but in this case k2 becomes infinite at finite z, which is impossible in acoustics. 16) , where k~, 0:10 and 0:2 are arbitrary constants. 17b) Here k2 is the wave number at Z = -00 and ZI is the vertical scale of inhomogeneities in the lower medium. We see that reflection of a wave with any ~ can be treated due to the arbitrariness of q. The frequency may also be arbitrary depending on the choice of 1 and m. Hence, the profile is specified by four parameters.
N), BI and An+l. (The amplitude B n+l of the incident wave in the upper half-space is assumed to be known). The conditions of continuity of the pressure and the normal component of partide velocity at the boundaries between media yield linear equations for determining the unknown Aj, Bj: Aj exp(i 16 and 17) that ordinary reflection (with IVI < 1) occurs when ci 1 -:--() > sm 1 V2 - VI CI + C2 0 >. 23) Obviously, IVI < 1 at any positive incidence angle if VI + cl> v2 + c2. 23). 20) if the parameters of the media are identical. It appears that there exist two such angles: ()l = 0 and . 24) for any M:/: O. 6 and 7 illustrate the results obtained above. The former shows IVI as a function of incidence angle in the case of moving media with identical parameters and M =± 3. 7 in the plane ()J, M.
16 and 17) that ordinary reflection (with IVI < 1) occurs when ci 1 -:--() > sm 1 V2 - VI CI + C2 0 >. 23) Obviously, IVI < 1 at any positive incidence angle if VI + cl> v2 + c2. 23). 20) if the parameters of the media are identical. It appears that there exist two such angles: ()l = 0 and . 24) for any M:/: O. 6 and 7 illustrate the results obtained above. The former shows IVI as a function of incidence angle in the case of moving media with identical parameters and M =± 3. 7 in the plane ()J, M.