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This study focuses on investigating the propagation of acoustic waves in a cylindrical waveguide with higher‐order derivative‐based boundary conditions and a sound absorbent lining. The mode‐matching method is employed to solve the governing boundary value problem, utilizing continuity conditions for pressure and velocity at waveguide interfaces. The objective is to establish a theoretical framework for analyzing and optimizing the acoustic performance of the waveguide, considering the influence of crucial parameters. The study's findings hold significant practical implications in acoustic engineering and noise control, enabling accurate prediction of acoustic wave behavior and facilitating the design of effective noise reduction measures and optimized sound‐absorbing materials in various applications. Additionally, the numerical techniques developed here can be extended to address more complex waveguide geometries and boundary conditions. [ABSTRACT FROM AUTHOR]