Combustion dynamics in a linear, semi-bounded channel were studied to characterize injection, mixing, and ignition processes in a two dimensional analogue of a rotating detonation wave combustor. The linear channel was developed to operate using natural gas and oxygen and to provide large optical accessibility in support of high-fidelity diagnostics at thermal power density levels representative of rotating detonation wave combustors over a broad range of flow conditions. Measurements of pressure and heat release were performed using an array of high-frequency dynamic pressure probes and OH*-chemiluminescence, respectively. Self-sustained, periodic generation of detonation waves was observed. These traveling combustion waves were initiated from low amplitude deflagrative fronts and steepened as they traveled through the combustion channel. The sensitivity of this instability to changes in acoustic boundary conditions was explored to determine the origin of the high-amplitude dynamics. The change in acoustic boundary at the end-wall affected the transverse acoustic mode frequency as expected, but had no effect on the detonation wave initiation. The detonation wave dynamics were found to be correlated with resonant frequencies in the propellant manifolds. It was determined that the frequency of the self-sustained chamber dynamics depends on which manifold has the strongest injection pressure ratio. OH*-chemiluminescence and pressure measurements indicate that the observed transition to detonation is linked to the auto-ignition of the reactants and that the auto-ignition event is coupled with the fluctuation in reactant mass flow associated with the manifold dynamics.