THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

254 11. Acoustics of Enclosed Spaces: Architectural AcousticsExample Problem 1: Reverberation PredictionA room 8 m long, 4 m wide, and 2.8 m high contains four walls faced with gypsumboards. The only exceptions to the wall area are a glass window1mby0.5mandaplywood-paneled door 2.2 m by 0.6 m. In addition the door has a gap underneath,1.5 cm high. In order to estimate the reverberation time of the room at 500 Hz wemake use of the data in Table 11.1. Predict the reverberation time T .SolutionThe absorption area (in m 2 ) is found as follows:A = Si α i = [2(8 × 2.8) + 2(4 × 2.8) − 2.2(0.6) − (0.015)(0.6) − 1.0(0.5)]× 0.05 + (2.2)(0.6)(0.17) + (0.015)(0.6)(1) + 1.0(0.5)(0.18)+ (4)((8)(0.81) + (4)(8)(0.81) = 32.70 m 2 .Applying Equation (11.14):0.161 × 8 × 4 × 2.8T = = 0.82 s.32.7The gap at the bottom of the door is treated as a complete sound absorber with acoefficient of unity. From the above estimated value of the reverberation time of0.44 s and a chamber volume of 89.6 m 3 , the room may be suitable for use as aclassroom according to Figure 11.4.11.8 Decay of Sound in Dead RoomsThe derivation of Equation (11.14) was based on the assumption that a sufficientnumber of reflections occur during the growth or decay of sound and also thatthe energy of the direct sound and the energy of the fractional amount of soundreflected were both sufficient to ensure a uniform energy distribution. In the caseof anechoic chambers, where the absorption coefficient of the materials constitutingthe boundaries is very close to unity, it is apparent that the derivations of thepreceding equations for growth and decay of sound are not applicable. The onlyenergy present is the direct wave emanating from the sound source. The reverberationtime must be zero, whereas application of Equation (11.14) would yielda finite reverberation time of 0.161V/S, where S is simply the total area of theinterior surfaces of the chamber. Thus, it is apparent that Equation (11.14) wouldbe increasingly in error as the average sound absorption coefficient increases. Ifthe average value of the absorption coefficient exceeds 0.2, Equation (11.14) willbe in error by approximately 10%.A different approach to ascertaining the decay of sound in a dead room, whichwas developed by Eyring (1930), is to consider the multiplicity of reflections as aset of image sources, all of which are considered to exist as soon as the real sourcebegins. Let ᾱ, found from the relationship ᾱ = ( ∑ α i S i )/ ∑ S i denote the average