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Plane Wall with Wide Grooves

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→ See also Mechel, Vol. I, Ch. 12 (1989)

In contrast to the previous → Sect.  B.19 the grooves are no longer narrow; higher modes may exist in them.

The ground of the grooves is supposed to be terminated with an admittance G\({}_{{s}}\) (e.g. produced by a porous layer there).

Where possible, the relations are taken from the previous → Sect.  B.19 .

The grooves are numbered \(\nu\)= 0,\(\pm\)1,\(\pm\)2,… and a co-ordinate z\({}_{{\nu}}\)= z–\(\nu\) \(\cdot\)T is used in the \(\nu\)th groove with –a/2 \(\leq\)z\({}_{{\nu}}\) \(\leq\) +a/2. The field in the groove is formulated as

$$p_{k}(x,z_{\nu})=e^{{-j\,{\beta}_{0}\cdot\nu T}}\sum\limits _{{m\geq 0}}{\left[{B_{m}\cdot e^{{-j\,\kappa _{m}x}}+C_{m}\cdot e^{{+j\,\kappa _{m}x}}}\right]\cdot\cos\,\left({m\pi\left({\frac{z_{\nu}}{a}-\frac{1}{2}}\right)}\right)}$$
(1)

with

$$\kappa _{m}=\left\{{\begin{array}[]{@{}l}\sqrt{k_{0}^{2}-({m\pi}\mathord{\left/{\vphantom{{m\pi}a}}\right.}a)^{2}}\geq...

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(2008). Plane Wall with Wide Grooves. In: Mechel, F.P. (eds) Formulas of Acoustics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76833-3_38

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