The transfer function of the title is derived first for the case of a stationary source‐receiver and a stationary target, with each in the far field of the other. Then, a quasi‐transfer‐function is constructed for the case in which the two bodies, separated as before, are moving at speeds which are small relative to the speed of sound, the flow around them being assumed to be derivable from velocity potentials. In both cases, the problem is formulated in terms of Helmholtz‐Kirchhoff integrals. Conditions related to the distance to boundaries are deduced through the method of images. Theorems due to Blokhintsev and Oestreicher are used to treat the radiation, scattering, and reception of sound by a moving body.