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Acoustics of Layered Media I: Plane and Quasi-Plane Waves by Professor Leonid M. Brekhovskikh, Dr. Oleg A. Godin (auth.)

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 constructions. those constructions should be man-made, reminiscent of ultrasonic filters, lenses, surface-wave hold up traces, or ordinary media, corresponding to the sea and the ambience, with their marked horizontal stratification. A comparable challenge is the propagation of elastic (seismic) waves within the earth's crust those issues were taken care of fairly thoroughly within the e-book by means of L. M. Brek­ hovskikh, Waves in Layered Media, the English model of the second one variation of which used to be released through educational Press in 1980. because of growth in experimental and machine know-how it has turn into attainable to research the effect of things corresponding to medium movement and density stratification upon the propagation of sound waves. a lot realization has been paid to propagation idea in near-stratified media, Le. , media with small deviations from strict stratification. fascinating effects have additionally been received within the fields of acoustics which were formerly thought of to be "completely" constructed. For those purposes, and likewise end result of the influx of researchers from the similar fields of physics and arithmetic, the circle of folks and learn teams engaged within the examine of sound propagation has relatively improved. hence, the looks of a brand new precis evaluate of the sector of acoustics of layered media has turn into hugely fascinating. for the reason that Waves in Layered Media turned relatively well known, we've attempted to preserve its confident good points and basic structure.

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Extra resources for Acoustics of Layered Media I: Plane and Quasi-Plane Waves

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16, Sects. 23,50]. 1, Sect. 27) . 16), therefore we shall confine the discussion now to cases where 1 i= - 2. If there are no other limitations on the values of I' then the choiee f = (izi + ZI)b pennits us to treat the case of nonna! incidence only. 14) with b = {f + 2)/2 Q= , I =0 , -4i(2 + I) -1 zl'Y/2 0: 1/2 m . 28) The arbitrariness of Q allows consideration of a wave of any frequency. 29) is necessary. 29), are the same equations that were derived in [Ref. 5, Chap. 3, Sect 9]. Example B. ~argq

The choice of the concrete values for the parameters can be used to make the best approximation of real profile of interest. 11) which allow exact solutions in terms of the confluent hypergeometric functions and consider three types of substitutions for fez): Example A. _argq<'! ' fez) = (Izl + Zl)b , where b f. 0 . 15) by substitution of MI,rn for WI,rn. 12]. 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.

19). Quarter-wave transmission layer. 20) For normal incidence and 1 = 0 this means that d = >'z/4. 7) yields Zin = Zj/Zl for the input impedance. 1) complete transmission takes place for Z2 = J Z I Z3 . 22) Thus, the reftection of a monochromatic wave at the boundary of two arbitrary media can be completely eliminated by placing a quarter-wave layer between them which has an impedance equal to the geometric mean of the impedances of the two media. 2]. 5 Penetration of a Wave Through a Layer We assurne that the sound velocity in the layer is greater than that in the medium from which the wave is incident.

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