Page 26 - Summer 2006

Fig. 13. Construction of a hybrid surface_left, porous absorber; middle, the mask; and right, cloth. (After Cox and D’Antonio15)
been optimized to be both asymmetrical, and yet to have identical symmetrical edges so that the surface can be rotat- ed and tiled in any direction. Consequently, architects can now manipulate the appearance and trade this off against acoustic performance. They can chose a periodic design, and accept the performance cost of the grating lobes, or they can use a more random appearance knowing that the acoustic performance will be enhanced. An example of this 2-dimen- sional bicubic waveform is shown in a ceiling application in Fig. 12 (bottom).
Hybrid diffusers
While it might appear that optimization is the answer to all possible diffuser designs, there is still interest in using number theories since the optimization problem becomes prohibitively large to solve when the diffuser has a large number of wells. However, number theory has suggested a different kind of diffuser—a hybrid surface. The construction of a hybrid surface is shown in Fig. 13. It consists of a piece of porous absorbent material that is covered with a perforat- ed mask. The mask may be hidden from view by a thin piece of acoustically transparent cloth or exposed in wood or metal. This is essentially a Helmholtz absorber, but with an uneven distribution of the holes. At some mid-frequency, high absorption results that decreases as the frequency increases. At these upper frequencies where only partial absorption occurs, the uneven distribution of the holes caus- es reflected energy to be diffused. To get good dispersion, a pseudo-random binary sequence that has an autocorrelation function similar to a delta-function is used. When zero occurs in the sequence a hole is drilled in the mask. When one occurs in the sequence, the mask is left untouched. Any repetition in the sequence will lead to lobes, so sequences are needed that are dissimilar from shifted versions of itself. Again, number theory can provide many different sequences.
Angus11 first examined the performance of these devices using maximum length sequences. These are the same sequences that were used originally to modulate Schroeder diffusers and also used by Schroeder in his first paper on dif- fusers. A problem that occurs is that maximum length sequences are a one-dimensional string of ones and zeros. For hybrid surfaces, a two-dimensional array of numbers is required. Again, there are a number of techniques for form- ing two-dimensional binary arrays12 that can be exploited. One of the commonly used techniques is referred to as the Chinese remainder theorem.
An example of a Chinese remainder problem was posed
13 by Sun Tsu Suan-Ching in the 4th century AD .
“There are certain things whose number is unknown. ... Divided by 3, the remainder is 2; by 5 the remainder is 3; and by 7 the remainder is 2. What will be the number?”
(One answer to the above problem is given at the end of the article.)
From this rather strange start, a method for sequence folding can be generated that has been used in coding sys- tems, cryptology, and x-ray astronomy. The mask shown in Fig. 13 is a maximum length sequence of length 1023 that has been folded into a 31x33 array using this process.
The problem with maximum length sequences is that they are devised for systems that are bipolar, consisting of plus ones and minus ones. The hybrid surfaces produce no reflections (reflection coefficient ≈ 0) and reflections (reflec- tion coefficient ≈ 1) and so are inherently unipolar. This can be a problem when designing diffusers. Most electronic sys- tems have bipolar capabilities that produce signals of the opposite sign. This is often exploited to reduce the out-of- phase autocorrelation function. Fiber optic systems, on the other hand, are intrinsically unipolar because the light is either on or off. These optical sequences can also be exploit- ed in hybrid diffusers; however, the number of sequences with the right balance of 0s and 1s are rather small.
A problem with planar hybrid surfaces is that energy can
only be removed from the specular reflection by absorption. If
it were possible to exploit interference by reflecting waves out
of phase with the specular energy, then it would be possible to
diminish the specular energy even further. One solution is to
bend or corrugate the surface, breaking up the specular reflec-
tion component. This type of design is proving to be very pop-
ular in studio control and listening rooms. More recently it has
been shown that the specular reflection can also be dispersed
by using a diffuser based on a ternary sequence that nominal-
ly has surface reflection coefficients of zero, minus 1, and plus
14
one . These reflection coefficients are made using wells,
absorbent patches and rigid sections respectively.
Figure 14 shows the scattering from two hybrid absorber- diffusers compared to a plane surface. The hybrid surfaces provide dispersion, with the performance of the ternary sequence being best because of its ability to generate more obliquely propagating sound, reducing the specular energy by
exploiting wave superposition as well as absorption.
Summary
Much has been learned about the design of room
Fig. 14. Scattering from three diffusers: Black: binary diffuser; Orange: ternary dif-
18 fuser showing significantly more lateral scattering, and Green: plane surface .
24 Acoustics Today, July 2006