ACOUSTIC SCATTERING: FRACTALS AND DIFFUSION
 
 

Diffusing surfaces can be used to model phenomenon in atmospheric and underwater acoustics, and have applications in several sub-fields of acoustics, including architectural acoustics and noise control. Specifically, diffusers are often used in performing arts spaces and sound recording studios as a means for controlling echoes and providing an even distribution of sound energy. The accurate quantification of surface diffusivity is imperative when taking a holistic approach to the design of acoustically sensitive spaces. The sound diffusion from these types of surfaces can also provide attenuation of the sound buildup in urban street canyons where high sided buildings form a semi-enclosed space leading to unacceptable sound levels. Additionally, diffusers can be used to augment the effectiveness of highway noise barriers, as well as increase the speech intelligibility in spaces ranging from subway stations to classrooms.

The type of diffuser typically used in these applications utilizes surface irregularities in a narrow range of characteristic dimensions, which ensues in a constricted frequency range of diffuse reflections. The need for diffusion often breaches this limited frequency response, which causes design limitations when using diffusing surfaces. One design modification available for addressing this issue is the incorporation of fractals in the diffuser.

 
 

The concept of fractals was developed by Mandelbrot to describe structures exhibiting self-similar characteristics, wherein the geometric structure is maintained through scale transformation. These structures possess small scale copies of the large geometry; as the structure is magnified, a similar looking structure can be found. As applicable to diffusers, the scale invariant nature of fractal structures plays an important role in the frequency range of diffusivity. The ability of a surface to reflect sound energy in a diffuse manner is dependent on the relationship between the wavelength in question and the surface irregularity dimensions.

Since certain fractal objects possess perturbations at various scales, a wide range of wavelengths are affected, resulting in a broad frequency response from diffusers utilizing this structure type. This behavior is in opposition to typical diffusers, and thus can provide an solution to the limited bandwidth of scattering.

The research in this area focuses on classifying the effects of the fractal inputs on diffusion properties based on experimental measurements.

The experimental work iscomplimented by a theoretical prediction method based on the Helmholtz-Kirchhoff integral equation. Verifying an accurate prediction method for fractal diffusors will aid in incorporating these types of surfaces into computer modeling schemes for predicting sound fields in enclosed spaces. Additionally, the ability to predict the scattering behavior of fractal diffusors would allow for the pre-knowledge necessary to design these types of surfaces as they are used in real spaces.