M. R. SCHROEDER
INCIDENT WAVE
o
SPECULAR
REFLECTION
Figure 2. Scatter diagram of reflection grating shown in Fig. 1, obtained with
sound waves at three times the "design" frequency. With p = 17, the
grating scatters effectively over a frequency range o f l t o p - 1 = 16 (four
musical octaves).
4. Wave diffraction and primitive roots
In some applications, including concert hall acoustics, it may be desirable
to attenuate the specular reflection (the "zeroeth diffraction order'') relative to
the other diffraction orders. Are such "super scattering" phase gratings
possible? The answer is yes and it comes, again, from number theory.
Instead of quadratic residues the author [2] has suggested powers of
primitive roots to construct reflection coefficients. Specifically (3) is replaced
by
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