THE SPATIAL VARIABILITY OF RANDOM NOISE IN A REVERBERANT SPACE

The spatial variability of a frequency band of random noise in a reverberant space is a contributor to the uncertainty of the measurement of sound insulation. This paper looks at the theory for predicting the spatial variance of a frequency band of random noise in a reverberant space and compares the theory with experimental measurements. In the mid-frequency range, the relative spatial variance is well predicted by the well-known formula, 3*ln(10)/(B*T60), where B is the statistical bandwidth of the random noise and T60 is the reverberation time of the room. This formula under predicts the experimental results at low frequencies in all reverberant rooms. This paper gives a formula, derived from a formula for the pure tone spatial relative covariance in a reverberant space, which predicts the measured results surprisingly well. It depends on the modal overlap of the reverberant space. The formula given above also underestimates the measured spatial variance in larger rooms at high frequencies, and the measured spatial variance is greater when the sound source is more directional. Lubman's theory, which depends on the directivity of the sound source, gives a better estimate of the spatial variance in large rooms at high frequencies. Interestingly, this increase in spatial variance at high frequencies in large rooms does not occur when the sound field is decaying. This is indication that the properties of the sound source affect the steady state variance at high frequencies in large rooms. Another interesting observation is that a rotating diffuser reduced the spatial variance of third octave band reverberation time measurements but had almost no effect on the spatial variance of steady state third octave band random noise levels in a reverberant space. The paper also gives the history of the development of the theory for predicting the spatial variance.