Measurement of Correlation Coefficients in Reverberant Sound Fields

TLDR

Reverberation chambers for acoustic measurements require fully random sound fields. The study describes an instrument for measuring and recording the cross‑correlation coefficient R over time. The authors define R as the normalized cross‑correlation of sound pressures and present an instrument that uses a recorder’s servomechanism to measure the ratio of two DC voltages to obtain R over time. In a random sound field, R equals (sin k r)/(k r), and the instrument’s measurements confirm this relationship in reverberant chambers.

Abstract

Reverberation chambers used for acoustical measurements should have completely random sound fields. We denote by R the cross-correlation coefficient for the sound pressures at two points a distance r apart. R = 〈p1p2〉Av/(〈p12〉Av〈p22〉Av)12, where p1 is the sound pressure at one point, p2 that at the other, and the angular brackets denote long time averages. In a random sound field, R = (sinkr)/kr, where k = 2π/(the wavelength of the sound). An instrument for measuring and recording R as a function of time is described. A feature of this instrument is the use of a recorder's servomechanism to measure the ratio of two dc voltages. The results of correlation measurements in reverberant sound fields are given.