Modelling Room Acoustics Using Transmission Line Matrix Method

The primary objective of the project is to model room acoustics using Transmission Line Matrix Method (TLM). The method approximates acoustic wave propagation by Huygen's principle. It is best suited for equidistant nodes and fixed time steps coupled to the spatial distance of the nodes. The TLM method was applied to a one-dimensional (1-D) case of an air column. The results were validated using a model generated by Finite Difference Method (FDM). The results indicate no spurious peaks or built up errors. Accuracy of the plot could be made more fine by varying mesh size and propagation velocity while keeping time-step constant. In the two-dimensional (2-D) TLM model of a square plane considered on the surface of water, new issues were observed. The simulation creates dispersion effects. It was observed that this effect occurs when the wave pattern is sharp beyond a particular level. After making corrections, the TLM method was applied to other 2-D cases. In modelling moving sources, two methods were explored. The first implied the direct movement of the source by one node for some pre-defined number of time-steps i.e. moving source at some finite value of speed. The results indicate distortion in the radial propagation and sharp ends at the source. The second method requires dividing the intervening space into n sub-units and taking the corresponding weighted mean of the amplitudes at the two nodes. The obtained results were explained using Doppler effect. The TLM method was extended to model acoustic beam-steering using phased arrays. The applications of this are usually in radio communications. A rigid wall was used as the reflector. The pulses coming from each of the five sources were kept in a temporary store and at the next iteration, these values were used as the incident pulses. Thus superposing the effect of the five sources at each node in the grid. The beam can be propagated in a specific direction by varying the phase difference. The boundary conditions were varied and perfectly reflecting, perfectly absorbing and partially absorbing-partially reflecting boundaries were considered. The reflection coefficient values used at the boundaries are as follows: ? = 1 for rigid walls, ? = -1 for open ends and ? = 0 for impedance boundaries. By varying the values of frequency, standing waves were generated in 1-D and 2-D cases. In 2-D waves were captured at the transition state. Three dimensional (3-D) room acoustics was simulated using TLM. Modelling in 3-D was lot more different from the rest as large computation time and computational power was required. There are numerous methods available to model 3-D case like triangular meshing, Cartesian meshing, tetrahedral meshing etc. Cartesian method was used for this project as it is the natural extension of 2-D TLM code. The wave propagation was captured on three perpendicular planes parallel to the coordinate planes. Open, rigid and impedance boundaries were also modelled. The results were found to be satisfactory. From the results obtained, it can be concluded that TLM is equivalent to FDM in terms of its usefulness. Despite the computational time and power being higher than FDM, the results are more accurate and the simulation itself runs without any hindrances. Compared to the problems of instability or very high noise, that are frequently encountered in FDM, TLM stands as the better solution.