A theoretical study of the sound power density field radiated from a simple source, a doublet source, a single point source before a totally reflecting plane (free as well as rigid), and a piston vibrating in an infinite fixed wall have been investigated. Formulae are worked out to allow the computation of percent of total radiation flowing through a given area. By interpolation of the graphs plotted from these equations, the streaming or flow of energy for the above radiation fields is shown. In connection with this work the numerical integration of the definite integral ∫z′Pm(z)Pn(z)dz, in which the P's are the Legendre polynomials, was carried out for all the even values of m and n from 0 to 20, and for the argument z taking thirteen different values in the interval 0⩽z⩽1. In case these computations are not published, they are available from the authors upon request.