Periodic waveguides may be analyzed using dispersion diagrams, which plot the wavenumbers as functions of frequency. Imaginary wavenumbers mean propagation is not possible and, therefore, normal modes cannot build up. Muffler design has traditionally explored periodicity, but usually not using dispersion analysis. In this work, we show how to model one-dimensional acoustic waveguides with plane wave assumption using spectral elements (SE), how to obtain dispersion diagrams and, using semi-infinite elements, transmission loss from an SE model. The technological challenge consists in opening band gaps at low frequencies with a limited size muffler, and SE models are handy for low cost parameter optimization. For arbitrary shapes, this work uses scaled SE models or, alternatively, a state-space formulation recently developed by the authors. Additive manufacturing is an enabling technology for the implementation of the designed mufflers. In this work, we show experimental results for simple periodic mufflers built using 3D printing. The proposed simulation methodology is simple and can be used for quick design of 3D-printed polymer mufflers.