The development of new acoustics prediction algorithms
The success of concert halls, public spaces and working environments is often dependant on their acoustics. Hence the need for fast, accurate algorithms to predict room acoustics during the design phase. Ongoing research in this department aims to make full use of increasingly powerful computer hardware to develop new, faster and more accurate methods to predict the propagation of sound in architectural spaces. In particular the 'adaptive beam tracing algorithm' was developed to faithfully reproduce the spread of a propagating sound field without gaps or overlaps by taking into account exact areas of beam illumination.Previous Methods
The most popular models to predict sound propagation in architectural spaces involve the tracing of rays, images or beams.
- Ray Tracing - creates a dense spread of rays, which are subsequently reflected around a room and tested for intersection with a spherical detector. The energy attenuation of the intersecting rays and distances travelled are used to construct an echogram. Although relatively simple to implement the algorithm has inherent systematic errors where by spurious reflections can be created due to using a non point detector whilst other valid reflections missed as the rays diverge.
- The Image Method - overcomes these problems by instead calculating images of the sound sources in reflecting walls. Higher order images are in turn calculated and so on until an echogram is produced. Although initially much faster than ray tracing the image method slows exponentially with increasing orders of reflection as the number of possible though not necessarily valid images increases. Invalid images must be eliminated with validity and visibility tests. Some applications use a hybrid of the two methods to improve speed and accuracy, however it still requires a large number of rays initially and suffers from missing images later on.
- Beam Tracing - models sound propagation as conical or triangular beams. Beams are reflected around a room and tested for illumination of the detector. These algorithms provide the speed of ray tracing with the accuracy advantages of being able to use a point detector. However since cones and triangles represent approximations of the propagating sound field, overlaps and missing reflections can happen and so have to be compensated for statistically.
The adaptive beam tracing algorithm was developed to faithfully describe the specular propagating sound field without holes or overlaps. The shape of reflecting beams is based on the exact sections of illumination of previous beams on reflecting plane surfaces, not triangular or conical approximations. Hence, the algorithm finds valid sound images as faithfully as the image method but without generating an exponential number possibilities to be eliminated with visibility tests. The adaptive beam tracing algorithm also facilitates a convenient way to calculate energy upon reflection by providing exact areas of illumination by beams on walls with respect to time. Diffuse energy imparted on walls can then be re-radiated and exchanged between walls so creating a diffuse echogram. Specular and diffuse components can then be combined so eliminating the need for empirical and statistical adjustments.
I. A. Drumm, Y. W. Lam, The adaptive beam tracing algorithm, J. Acoust. Soc. Am. 107, 1405 (2000)