A technique is developed for treating each of the waves generated by an arbitrary current source in a partly ionized gas with no steady magnetic field. Starting with Maxwell's equations and three sets of coupled hydrodynamic equations (for the electrons, ions, and neutral molecules), it is shown that one can obtain a separate inhomogeneous wave equation for each type of wave in the plasma, with the source term for the transverse and longitudinal waves dependent, respectively, on the curl and divergence of the current source.