Statistical characteristics of some standard reverberant sound field measurements

Abstract

The space and time fluctuations of 1 3 - octave band sound pressure level and reverberation time measurements in hard-walled chambers have been investigated experimentally with the aim of determining characteristic probability density functions and typical variances. The basic random variables observed (that is, the mean square pressure and the reverberation time estimates) are acceptably described by a gamma distribution given in a paper by D. Lubman. A specific sampling procedure has been used for the experiments: the samples were taken in randomly chosen discrete positions and a time averaging performed in each position so that the time variances thus obtained were much smaller than the spatial variances. Such a sampling procedure leads to the statistical characteristics of the random variables being independent of any specific equipment used. With the aid of the basic probability density function, statements of precision with regard to time and space fluctuations can be made from the data obtained in this way. Confidence intervals for standard measurements of sound pressure level, reverberation time, sound pressure level difference, sound power level and transmission loss are presented. The typical variances in various possible situations are not always well-known, which means that one has to use estimated values of the variances in the derivation of the respective confidence statements. This fact causes some uncertainty, and one must regard the confidence statements thus obtained as approximate only. From the results obtained in these investigations, it appears that the degree of this uncertainty would be quite acceptable in a normal measurement situation.