This study investigates the axial wave propagation characteristics of functionally graded, variable cross-section, and porous rods in the axial direction. The exponential variation of material properties and rod cross-sectional area along the rod length is modeled using a combined dimensionless gradient parameter. Wave equations are derived analytically; closed-form expressions are obtained for mechanical impedance, phase velocity, and group velocity. Numerical analyses demonstrate the influence of gradient intensity and porosity on wave dispersion and stop-band behavior, highlighting the system's potential as a tunable acoustic filter. The findings provide a robust theoretical framework for the dynamic design and acoustic insulation of advanced engineering structures.