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

256 11. Acoustics of Enclosed Spaces: Architectural Acoustics11.9 Reverberation as Affected by Sound Absorptionand Humidity in AirWe have previously not considered the effect of absorption of sound and humidity inair on reverberation times. The volume of air contained in very large auditoriumsor a place of worship can absorb an amount of acoustic energy that cannot beneglected as in the case with smaller rooms. If a room is small, the number ofreflections from the boundaries is large and the amount of time the sound wavespends in the room is correspondingly small. In this situation acoustic energyabsorption in the air is generally not important. In very large room volumes thetime a wave spends in the air between reflections becomes greater to the extentthat absorption of energy in air no longer becomes negligible. The reverberationequations must now include the effect of air absorption, particularly at higherfrequencies (>1 kHz).Sound waves lose some energy through viscous effects during the course oftheir propagation through a fluid medium. The intensity of a plane wave lessenswith distance according to the equationI = I 0 e −2βx = I 0 e −mx .Here m = 2β represents the attenuation coefficient of the medium. Some texts useα rather than β to denote the attenuation constant of the medium; we eschew itsuse in order to avoid confusion with α used in this chapter to denote the absorptioncoefficient of a surface. During time interval t, a sound wave travels a distancex = ct, and the preceding equation may be revised to read(β/4V +m)ctI = I0 eThe expression for the reverberation time becomesT = 0.161V(11.18)A + 4mVwhere the constant mis expressed in units of m –1 . The total surface absorption Ais given either by Equation (11.3) or (11.17) depending whether that room fits intothe category of being an acoustically live or dead chamber. As the room volume Vbecomes larger, the second term in the denominator of Equation (11.18) increasesin magnitude, as air absorption becomes more significant, due to increasing pathlengths between the walls. Since m also increases with frequency, air absorptionalso becomes more manifest at higher frequencies (above 1 kHz) than at lowerfrequencies. The values of m are given in Figure 11.7 1 as a function of humidityfor various frequencies at a normal room temperature of 20 ◦ C. More details, alsogiven in tabular form, for a range of air temperatures and humidities are givenin the NASA report (1967), prepared by Cyril M. Harris, listed at the end of thischapter. It is seen from Figure 11.7 that the effect of humidity reaches a maximum1 The plot of Figure 11.7 applies to indoor sound propagation, not to outdoor propagation that includesmeteorological effects not present indoors.