A formula for the cross-correlation function of pressure fluctuations
of thermal acoustic radiation in a sound-absorbing liquid is derived o
n the basis of hydrodynamic fluctuation theory. A model of a two-eleme
nt interferometer consisting of two piezoelectric transducers is used
in the derivation. The resulting formula is an acoustical variant of t
he van Cittert-Zernike theorem of optics. It relates the degree of coh
erence of pressure fluctuations to the depth of penetration of the ove
rlap region of the transducer directivity patterns into the liquid und
er study.