By F.P. Mechel, M. L. Munjal, Michael Vorländer, Peter Költzsch, Martin Ochmann, A. Cummings, W. Maysenhölder, Walter Arnold

This choice of formulation has been written through utilized scientists and commercial engineers for layout pros and scholars who paintings in engineering acoustics. it's subdivided into crucial fields of utilized acoustics, every one facing a well-defined kind of challenge. It presents effortless and speedy entry to profound and finished details. as well as formulation, worthy rules and computational strategies are given.

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Magnitude of the reflection factor |r| of wall with grooves for normal incidence. Full line: periodic surface; dashed: homogeneous 48 B General Linear Fluid Acoustics Magnitude of the reflection factor |r| of wall with grooves for oblique incidence, as a periodic surface for a list of ˜ values (dashes become shorter for increasing list place). 5; T/t = 1; R = 1 The examples shown below use the parameters F = f · t/c0 = t/Š0 ; R = ¡ · t/Z0 with the ﬂow resistivity ¡ of the porous material (glass fibres) in the grooves; a/T; T/t.

Cos (m(œ − œq )) (n + m) ! m ·Pm n (cos ˜q ) · Pn (cos ˜ ) · ⎧ ⎨jn (k0r) · h(2) n (k0 rq ) ; r < rq , ⎩ ; r > rq , jn (k0rq ) · h(2) n (k0 r) (40) 18 B General Linear Fluid Acoustics m where jm (z) , h(2) m (z) are spherical Bessel and Hankel functions and Pn (x) are associated Legendre functions. If the source distance rq goes to infinity, one gets for the plane wave incident from the spherical directions œq , ˜ q (in the spherical angles œ, ˜ ) e−j k0 ·r = ∞ n=0 (−j)n (2n + 1)·jn (k0 r) (n − m) !

I, Ch. 12 (1989) An object with a periodic surface is a special case of an object with an inhomogeneous surface (other inhomogeneous surfaces which are amenable to analysis are those in which either the scale of the inhomogeneities and their distances is small compared to Š0 , then the average admittance is relevant, or the inhomogeneities are at large distances from each other, then scatter matrices can be set up). The method to be applied with periodic structures will be displayed in this and the next sections with some typical examples.