The figure shows that specular reflections occur at the boundaries. We can clearly see the symmetry in the wave propagation pattern, and the energy is concentrated at some regions in the mesh after some time has passed. On the other hand, the mesh with one of its boundaries being replaced with Schroeder's diffuser reveals very different reflection characteristics as shown in Figure 6. The wave propagates in the same pattern at the beginning as in the plain mesh, but it starts to diffuse in the third plot as it approaches a boundary with Schroeder's diffuser. This diffusion from the the uneven boundary disturbs the symmetric wave propagation pattern seen in the plain mesh, and in the last plot, we can see the energy is evenly distributed all over the mesh after a very short period of 4.5 milliseconds.
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The comparison between the plain mesh with specular boundaries and the
mesh with a diffusing boundary becomes more obvious if we use an
incident plane wave as their initial excitation. Even before looking
at the animated results, we may expect that the plain mesh with flat
surfaces will show a specular reflection pattern; i.e., the plane wave
will reflect with equal angles of incidence and reflection as light is
reflected in the mirror. Figure 7 shows this
specular reflection of the plane wave when the angle of incidence is
. The plane wave is reflected with the same angle
as its angle of incidence, and keeps the same specular reflection
pattern, resulting in the propagation pattern similar to diamond
shape, whereas the wave propagation pattern shown in Figure
8 is totally different. The plane wave is diffused
as it reaches the diffusing surface in the second plot, and it starts
to propagate in many directions as shown in the next plot. Finally, in
the last plot, we can see the sound energy is evenly distributed on
the mesh without any visible concentration on specific regions.
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Figure 9 shows the scattering characteristics of
two different meshes by using a plane wave normal to the boundary as
an excitation source (i.e., incidence angle of ), and by
picking up the output at various angles. This polar response clearly
shows that the sound energy is evenly scattered at every angle at the diffusing
boundary whereas only specular reflection occurs at the flat surface.
Note that sound examples and Matlab generated movies which clearly visualize wave propagation are available from the WWW URL address: http://www-ccrma.stanford.edu/~kglee/2dmesh_QRD/