Schroeder presented methods of designing concert hall ceilings that
could avoid direct reflections into the audience. In 1975, he provided
a way of designing highly diffusing surfaces based on binary
maximum-length sequences, and showed that these periodic sequences
have the property that their harmonic amplitudes are all equal
[SchroederSchroeder1975]. He later extended his method and proposed surface
structures that give excellent sound diffusion over larger bandwidths
[SchroederSchroeder1979]. This is based on quadratic residue sequences of
elementary number theory, investigated by A. M. Legendre and
C. F. Gauss. These sequences are defined by
The quadratic residue diffuser, or Schroeder diffuser, is implemented by having periodic wells of different depths proportional to with period over the surface. Figure 1 shows a cross section through the diffusing surface based on the quadratic residue sequence with .
picture(6216,2424)(418,-3523) (6526,-1936)(0,0)[lb] % (5101,-3361)(0,0)[lb] % (3001,-3061)(0,0)[lb] %
The width of each well is determined by the design wavelength
, and the depths of the well are defined as
Strube did empirical and numerical analyses on scattering characteristics of Schroeder's diffuser [StrubeStrube1980a,StrubeStrube1980b], and design techniques of concert halls were provided by Ando using Schroeder's diffuser [AndoAndo1985].