Miyashita T.

Among numerical methods adopted recently for evaluations of room acoustics, finite difference time domain (FDTD) method is prominent in ability to visualize and to investigate numerically sound waves in various materials of an arbitrary structure as they propagate. The method has, however, restrictions due to capacity of memory and CPU speed of the workstations. Our investigations are limited to two-dimensional wave propagations. Therefore, a precise representation of the fine structures of the objects in the room should be adequately considered for the FDTD calculation. We have used an elastic FDTD program developed by us, and the number of grid points per wavelength was 40. The numerical dispersion error induced by this grid size was estimated as 0.00052 times the period or the wavelength. The temporal sampling interval was 10.10 microseconds. We report here (1) what can be analyzed by the FDTD method using continuous waves, burst ones, or an impulsive acoustic wave in structured objects. The physical quantities are sound pressure of longitudinal waves, particle velocity, acoustic energy flow, and shear stress of transverse waves in solid materials. (2) Propagations of sound waves in concert halls, especially shoebox-shaped hall of 40.8 m times 18.7 m and small fan-shaped, or diamond-shaped, hall of 27.6 m times 27.6 m. Both are reasonably considered by two-dimensional propagations of sound waves. (3) Echo-time patterns at representative positions in the halls up to 1.0 sec. The average delay-time of the first arriving reflected sound waves were between 20 ms to 30 ms. It is shown that this method of analysis can give reasonable and useful results about fundamental acoustic properties of rooms and concert halls.