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Schroeder Diffusers

Often called reflection phase gratings, these panels scatter sound waves. A Schroeder diffuser is a structure comprising a number of wells of different, carefully chosen depths. As a soundwave strikes the irregular surface, instead of bouncing off it like a mirror, it bounces out of each well at a slightly different time. The result is many small reflections, spread out in both time and space. The frequencies at which such structures operate as diffusers depend upon their dimensions. For example, the lower limit is that frequency where the deepest well is a quarter-wavelength. The result is a richer, livelier sound with an enhanced sense of space. Listeners claim that the panels seem to make the walls disappear. A small room takes on the air of a great hall. The secret lies in the varying depths of a panel’s wells. With depths based on specific sequences of numbers rooted in number theory, the wells scatter a broad range of frequencies evenly over a wide angle.

The scientist who pioneered the ideas responsible for this development is Manfred R. Schroeder, a University Professor of Speech and Acoustics at the University of Goettingen, Germany. In the 1970s, Schroeder and two collaborators undertook a major acoustical study of more than 20 famous European concert halls. One of their findings was that listeners like the sound of long, narrow halls better than that of wide halls. Perhaps the reason for this, Schroeder reasoned, is related to another finding that listeners prefer to hear somewhat different signals at each of their two ears.

Schroeder discovered that number theory can be used to determine the ideal depth of the notches, resulting in an acoustic grating that’s analogous to diffraction gratings used to scatter light. The operating range of a single diffuser is limited to about four octaves because, if the deepest well is deeper than about fifteen times its width, it begins to behave as an absorber. The well depths are most commonly given by: where d is the depth of the diffuser, h is the well number, N is the prime number on which the sequence is based, and L is the wavelength of the lowest operating frequency.

Mathematical analysis shows that for such an arrangement, the spectrum of energies scattered into different directions is essentially flat, meaning that roughly equal amounts of energy go in all directions.

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