By J. F. Allard (auth.)
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Extra resources for Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials
Example text
52) and a is an arbitrary constant. 46) yields the three components of the velocity v . 53) V3(XI> Xz, X3, t) ak3/kN . 53). 8 IMPEDANCE AT OBLIQUE INCIDENCE AT THE SURFACE OF A FLUID EQUIVALENT TO AN ANISOTROPIC POROUS MATERIAL The layer of porous material is fixed to a rigid, impervious wall, on its rear face, and is in contact with air on its front face, as shown in Fig. 11. The acoustic field in the air is homogeneous and the angle of incidence () is real. The formalism is the same if () is complex.
These two quantities cannot be the geometrical projections of a vector on the Xl and Xz axes unless complex angles are used to take into account the phase difference between the components. Plane waves with distinct equiphase and equiamplitude planes are called inhomogeneous plane waves. 3) can always be used to define the three complex components nl' nz and n3 of a unit vector n such that ni + n~ + n~ = 1. In the following, we will be concerned only with waves with a vector velocity parallel to a coordinate plane, for instance X3 = 0 if k3 = O.
33) This expression depends only on X3. 17). 2 Impedance at Oblique Incidence For a Layer of Finite Thickness Backed by an Impervious Rigid Wall The layer is represented in Fig. 4 in the incidence plane with the incident and the reflected waves. The angles are real or complex. For instance, fluid 2 can be a non-dissipative medium with a real wave number k and fluid 1 a dissipative medium with a complex wave I rL __ Fluid 2 Fluid 1 d FiG. 4. A layer of fluid of thickness d backed by an impervious rigid wall.