Probability Density Function of the Time Average of Sound Pressure Level Measurements in a Reverberant Room Excited by Random Noise
Douglas J. Ingalls · The Journal of the Acoustical Society of America · 1973
The probability density function of the time average of the sound pressure levels (measured in decibels) of a reverberant room excited by a finite bandwidth of random noise is (approximately) Gaussian for a stationary source and stationary receiver. The mean of the distribution for a finite integration time is less than the mean for an infinite integration time. The difference (in decibels) is given by 4.8/BT, where B is the bandwidth in hertz and T the integration time in seconds. The normalized variance of the distribution is given by 19/BT. The results imply that narrow-band measurements in a reverberant room need to be carefully defined if errors in the measurement due to finite integration times are to be minimized.