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