Acoustically treated, lined ducts are used in a wide range of applications, one of which is a transmission-line loudspeaker (TLL), which consists of a long, acoustically-lined, folded duct attached to the rear of the loudspeaker driver. Consequently, knowledge and understanding of sound propagation within acoustically treated ducts is essential in order to be able to create and analyse designs for the intended applications. The lowfrequency driver of a loudspeaker creates pressure fluctuations on both sides of the diaphragm. Therefore, a loudspeaker cabinet of some sort is required to control the sound radiation from the rear of the driver and to prevent the unwanted interference of those sounds with that radiated from the front of the loudspeaker. The transmission-line loudspeakers are however, designed and optimized to control this rear driver radiations by redirecting the pressure at the back of the driver and use them to extend the overall low-frequency response of the loudspeaker system. Transmission-line loudspeakers rely on the use of sound absorbing materials and, although attempts at modelling the performance of these have been reported in the literature, most transmission-line loudspeakers are designed empirically, using a combination of experience and trial-and-error. This project is concerned with creating and evaluating an engineering method of accurately modelling the sound propagating inside the transmission-line loudspeaker waveguides. Loudspeaker systems inherently suffer from an insufficient low-frequency response, due to their inefficiency at low-frequencies. Therefore, TLL rely on the use of sound absorbing materials added on their internal boundaries to extend their overall response of the loudspeaker at the lowfrequency region. The acoustic load on the driver and the sound radiated from the open end of the TLL duct both depend upon the propagation of sound through the duct; and the physical length of the duct determines the frequencies that can propagate within it. The addition of sound absorbing materials along the interior boundaries of the TLL reduces the speed of propagating sound within it, causing the TLL to respond such as having a much longer internal waveguide, consequently accommodating far lower frequencies within the TLL duct, extending the overall response of the loudspeaker system. The characteristics of sound propagation through a variety of two-dimensional and three-dimensional acoustically lined ducts at low-frequencies have been analyzed. Analytical models of straight ducts have been compared with the developed numerical models. In this research dissipative mufflers, that consist of ducts lined on the inside with an acoustically absorptive material, have been considered. Starting with the propagation of sound within hard-walled boundary condition ducts, this investigation moves to the modelling of waveguides treated with locally-reacting acoustic liners and next into the analysis of ducts treated with bulk-reacting acoustic absorbent materials; two kinds of excitations have been considered, namely pistonic and non-uniform excitation. The impedance mismatch and acoustic dissipation between the sound absorbing layer and the free propagation within the duct has been modelled numerically, and the results have been compared with the in-situ measurements conducted on a range of acoustically treated and purpose built transmission-line loudspeakers. A wide range of sound absorbing materials, namely fibrous and porous absorbers, have been characterized using their low-resistivity and acoustic impedance. Based on their individual characteristics, acoustical optimization was applied on a simple geometry U-shaped TLL duct.