Efficient computational models that retain essential physics of the associated continuous mathematical models are important for several applications including acoustic horn optimization. For heterogeneous wave propagation models that are naturally posed on unbounded domains, a crucial physical requirement is that the scattered fields are radiating and satisfy a radiation condition at infinity. We describe and implement an efficient high-order coupled computer model for acoustic wave propagation in an unbounded region comprising bounded heterogeneous media with several obstacles. Our unbounded and heterogeneous media computer model retains the radiation condition exactly and hence is readily applicable for the celebrated acoustic horn problem. This approach is more suitable than using a standard low-order approximation of the radiation condition. Using parallel computing environments, we demonstrate the high-order algorithm with extensive numerical experiments and computational analysis, including the model horn problem with several material property parameters. Our efficient computer models and validation in this work lead to some interesting mathematical and numerical analysis problems for the acoustic system defined on unbounded and heterogeneous media comprising smooth, non-smooth, horn, impenetrable, and penetrable obstacles. (C) 2016 Elsevier B.V. All rights reserved.