By Philip M. Morse, K. Uno Ingard (auth.), S. Flügge (eds.)

ISBN-10: 3642459560

ISBN-13: 9783642459566

ISBN-10: 3642459587

ISBN-13: 9783642459580

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**Extra info for Akustik I / Acoustics I**

**Sample text**

And k, are in the x, z plane. (~coscjl )eikXSin~-iwt. 2) = (~~ )p(f'B). We should note that Eq. 1) is not valid for * identically tn, unless {J is identically zero. At grazing incidence the reflected wave is exactly equal and opposite in sign to the incident wave, so the two cancel. The difficulty is [68J that a truly plane wave cannot travel tangential to an infinite plane surface which yields, however slightly, to the acoustic pressure. For a truly plane wave tangential to the surface would have acoustic velocities exactly parallel to the surface, and if the surface yields to the pressure there would have to be a component of velocity normal to the surface. *

UNO INGARD: Linear Acoustic Theory. Sect. 14. sider the motion as having started at t = 0 and continuing to the present t = t. The integration over to thus goes from 0 to t+, which is just enough larger than t so that we do not stop the integration in the middle of a Dirac delta function. The generalized boundary surface thus includes the surface t = O. The integral equation is t+ lJI(r, t) = f dto f f f G(r, tl ro, to) q(ro, to) dv o+ o t+ + f dto f f [lJI(r~) o~o G (r, tl r~, to) - G o~o lJI] ds o + (13·6) o +C'2 fff[(~~ )olJlo(ro) - Go (~~)o] dvo where the subscripts 0 in the last integral indicate that these quantities are to be taken for to=O (initial conditions).

The behavior of simple acoustic systems. Having derived the basic equations of linear acoustics and indicated their range of validity, the remainder of this article will be devoted to examples of the solution of those equations, for a variety of conditions of interest. The present Chapter B will be devoted to the analysis of sound waves in a single region, not coupled to any other region. In view of the discussion preceding Eq. 1), this is equivalent to assuming that the normal acoustic impedance of the boundary surrounding the region is a point function of position on the boundary, independent of the configuration of the enclosed wave, at every point on the boundary.

### Akustik I / Acoustics I by Philip M. Morse, K. Uno Ingard (auth.), S. Flügge (eds.)

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