Acoustic Radiation in Semi-Infinite Rigid Ducts: A Revisited Study

This study investigates the acoustic radiation phenomena from semi-infinite waveguides with rigid outer surfaces by considering different boundary conditions and wall thicknesses. The work is organized into two main parts. In the first part three configurations are analyzed under the assumption of an infinitely thin wall with a single radius a. The inner surface is rigid in the first problem, soft in the second, and coated with an acoustically absorbing lining in the third. The results of the third configuration can reproduce those of the first two cases through variations in physical parameters. In the second part the effect of wall thickness is introduced by defining an inner radius a and an outer radius b. Since the lined configuration in the thin wall case already generalizes the other two, only the thick walled lined case is investigated. Comprehensive analyses are carried out for a wide range of physical parameters and the results are systematically compared across different configurations in order to reveal the effects of boundary conditions and wall thickness on acoustic radiation characteristics. The results provide quantitative theoretical support for the design and optimization of acoustic linings in exhaust and ventilation systems, particularly by clarifying the roles of boundary conditions and wall thickness in shaping far-field radiation characteristics.