In this paper, the covariance function of noise at two points in a sound‐carrying medium is derived for an arbitrary distribution of noise generators when the noise suffers attenuation and spreading loss. The analysis is then applied to the cases of a volume and a plane distribution of omnidirectional sources. It is shown that the effect of attenuation on covariance is generally negligible in the volume case but is ordinarily important in the plane case. For the plane distribution, an asymptotic expansion is derived that holds for small values of an attenuation parameter. This expansion is then used to study the effect of attenuation on covariance as a function of receiver separation, receiver‐line orientation, and time delay.