Hawker [J. Acoust. Soc. Am.65, 675–681 (1979)] derived the acoustic field of a slowly moving point source with constant horizontal velocity in a uniform waveguide. The acoustic field for sources moving with arbitrary but small horizontal velocities, a more general result, is obtained in this paper. The wave equation is solved via a temporal Green’s function, and the ensuing acoustic field is naturally expressed in terms of retarded times familiar in relativity theory and electrodynamics. This contrasts sharply with conventional solutions in acoustics that are expressed in terms of contemporary time. For a given source motion, the solution may be recast entirely in terms of contemporary time. In the special case of a slowly moving source with constant horizontal velocity, the new solution reduces to that of Hawker. An example is given to illustrate the form of the new solution for a point source in circular motion in a horizontal plane.