It is shown that the mathematical solution of problems involving the propagation of noise is materially aided by the introduction of the space correlation function ψ(x1,x2, τ), defined as the average, overt, ofp(x1t)p(x2t−τ),pbeing the acoustic pressure in the noise field. The differential equations satisfied by ψ are derived. Its relation to Ψ(α, β, γ) is discussed, α, β, γ being the propagation vector of a sinusoidal wave, and Ψ/2ρc2being the density of potential energy in the α, β, γ space.The theory of uniform noise fields, both isotropic and anisotropic, is developed in detail. The anisotropy caused by a reflecting plane is discussed. The radiation of noise by a vibrating plane is discussed, neglecting the reaction of the radiation on the motion of the surface. In particular, it is shown that to this approximation the sea surface cannot radiate subsonic energy into the high atmosphere because the velocity of the surface gravity waves is less than the velocity of sound in air.The theory of noise, as here developed, is analogous to the theory of turbulence, and the relation between noise and turbulence is briefly discussed.