By Tonkin S. F.
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Additional info for Amateur Telescope Making Advanced (Book Two) (1952)(en)(650s)
Scattering objects can be seen as coupling together the local modes of the empty room, giving rise to hybrid versions of the original mode shapes (Morse and Ingard, 1968). These hybrid versions no longer have the symmetrical sound pressure ﬁelds associated with individual local modes in an empty box-shaped room. In the limit, as the room shape becomes increasingly irregular (or sufﬁcient scattering objects are placed inside a box-shaped room) and the room surfaces have a random distribution of acoustic surface impedance, we can effectively consider all the room modes to be some form of oblique mode.
15 that this can be achieved by creating a lattice in Cartesian coordinates where the x, y, and z axes represent kx , ky , and kz (Kuttruff, 1979). This lattice of eigenvalues in k-space is shown in Fig. 12, where each intersection in the lattice represents an eigenvalue indicated by the symbol •. The length of the vector from the origin to an eigenvalue equals kp,q,r . e. all eigenvalues excluding those on the axes and the coordinate planes) represent oblique modes. From Eq. 52 it is evident that the distance between adjacent eigenvalues in the kx , ky , and kz directions are π/Lx , π/Ly , and π/Lz respectively.
However, the sound ﬁeld does not always bare a close resemblance to a diffuse ﬁeld over the entire building acoustics frequency range. In the low-frequency range this is primarily due to the fact that sound waves arriving at any point come from a limited number of directions. In the mid- and high-frequency ranges, waves arriving at any point tend to come from many different directions. In the central zone of typical rooms it is often reasonable to assume that there is a diffuse ﬁeld in the mid- and high-frequency ranges.