VRIJE UNIVERSITEIT BRUSSEL Acoustics - the Dept. of ...

4.3. MEASURING THE ACOUSTIC ABSORPTION 73If the absorption coefficient a is small (a < 0.25) than a ≈ −ln(1 − a)and equation 4.24 :T = V6SA with A = ∑ ia i S i the total absorption (4.27)This last equation is called the model of Sabine (W.C. Sabine has found thisexpression experimentally [22]).Remark : Above theory belongs to what is called the statistical roomacoustics. It gives a certain global image of the reverberation of sound, andis based on many hypothesis and neglects many phenomena, so it does notdeliver full satisfaction to many theorists. The result is however useful andpractically well applicable.If the volume V and the reverberation time T of a space is measured, thetotal absorption can be determined with use of the law of Sabine : A = V . 6TFrom this one can determine ā SAB , the experimentally determined, averageabsorption coefficient of Sabine : ā SAB = A ∑i S i. One may thus assume, thatā SAB is a practically acceptable correct value (keeping in mind that it is aspatial and experimental average, defined by the model of Sabine). Thusin practice, the absorption coefficient shall be experimentally determined forvarious absorbing materials, making use of the model of Sabine. Would wethen estimate the reverberation time of a certain space in which absorbingmaterials are used, it can be done with the following practical model:T =V6 ∑ i S ia SAB,i(4.28)wherein the values of a SAB,i be used which can be found in tables of measurementresults. In what follows in this course, we will simplify the notationby omitting SAB, in which we however remember that each absorption coefficienta that we encounter, was determined experimentally in the mannerdescribed above.Favorablereverberationtimesdependonthetypeandusageoftherooms:for a furnished living room : 0.5 sec, for a cinema and lecture hall : 0.7-1sec, theater : 0.9-1.3 sec, music hall : 1.7-2.3 sec.In principle, one should not interpret these numbers in a too ’mathematical’manner, as having an absolute value for the acoustics of a given space.One notes, however, that the rooms which have good acoustics, have a Tthat is about within the above range. Short reverberation time gives rise to’dry sound’ i.e. sound that does not reverberate because it is immediatelyabsorbed. Several sound (e.g. music) need reverberation for their subjective