The application of the Hershcel-Quincke (HQ) tube as a noise reduction device for one-dimensional plane-wave sound fields has been studied in great detail in previous years. In this thesis, an analytical technique is developed to investigate the potential of the HQ tube concept to control higher-order duct modes. This analytical method involves modeling the tube-duct interfaces as finite piston sources, which couple the acoustic field inside the main duct with the acoustic field within the HQ tube(s). The acoustic field within the HQ tube is modeled as plane-waves and the acoustic field within the main duct is modeled by expanding the sound field in terms of the higher-order modes. This model is then used to investigate the noise reduction mechanisms behind the attenuation of higher-order modes. These mechanisms involve both the reflection of the incident wave as well as the reconstruction and recombination of the modal content of the incident disturbance into other modes. The effects of the modal content of the disturbance along with the HQ tube geometric parameters, such as tube axial position, length, distance between interfaces, and cross-sectional area, are studied with respect to the frequencies of attenuation and the reduction obtained. These results show the potential of the Herschel-Quincke tube concept to reduce higher-order modes in ducts.