Geometrically structured surfaces

Geometrical structures

Geometrical structures for the generation of diffuse reflections.
gs: structure period

Geometrical structures reflect incident sound diffusely if their dimensions are in the order of magnitude of the sound’s wavelength.

The small sticks of wood contained in an ingrain wallpaper, for example, have a thickness of about 1 mm. A wavelength of 1 mm corresponds to a frequency of 340 kHz, so diffuse reflection will only take place in the ultrasonic frequency range. In the audible frequency range, however, the ingrain wallpaper has the same effect as a plane, rigid wall, which reflects an incident wave geometrically.

The surface of a sound mixer neither acts as a diffusor in the audible frequency range. The many knobs and pan pots have a height of about 1 cm which corresponds to a frequency of about 34 kHz.

Apart from the height of the surface irregularities, their length and width are important as well. This can be illustrated by the following example where geometrical instead of diffuse reflection is desired. To improve acoustics in concert halls, sound is frequently directed into certain areas of the auditorium by means of baffles. Their plane, rigid surface only reflects sound geometrically down to a certain lower limiting frequency below which the baffle acts as a scattering body. Consequently the baffles must be of a minimum size.

In recording studios, on the other hand, interfering geometrical reflections from windows or technical equipment often cause problems. Here it makes sense to keep such surfaces as small as possible so that instead diffuse reflections occur in important frequency ranges. Or the surfaces must be inclined in such a way that geometrical reflections are directed into parts of the room where they do not disturb the sound engineer.

Meyer and Bohn investigated the scattering coefficient of rectangular, prismatic, and cylindrical structures. Fasold, Sonntag and Winkler give a good summary of the results. The structures can be made from battens or folded sheets, for example. The figure on the left shows their cross-sections. The length after which the structure is repeated is called structure period. Unfortunately, the structures’ effectiveness as diffusely reflecting surfaces is limited to a rather narrow frequency range. For rectangular structures it is even smaller than for cylindrical or prismatic structures. If the proportions of the structures are comparable to the proportions shown in the figure to the left, a maximum scattering coefficient is attained at the wavelength corresponding to between a half and a full structure period.