An investigation of the interactions between waves and steady flow fields was stimulated by the problem of combustion instability in rocket engines. A one‐dimensional analysis of traveling acoustic waves in flows of an inviscid nonconducting perfect gas, containing mass and heat sources, reveals the existence of a coupling between acoustic waves and nonhomogeneous steady flow fields. This coupling results in either amplification or attenuation of the waves, depending on the gradients of the steady flow variables, phase relationships between oscillations in mass/heat sources and flow field, and injection conditions. A portion of this amplification or attenuation is a result of energy transport between the waves and the flow field, while the remainder is a result of variations in group velocity and impedance. In addition higher‐order effects, such as the generation of backward‐moving acoustic waves and entropy waves by forward‐moving acoustic waves, can occur. Results of experiments with nonuniform velocity fields are in agreement with theoretical predictions. In particular, an air jet discharging into a straight organ pipe and a converging air flow through a tapered pipe are found to attenuate acoustic waves propagating through the pipes.