The combustion dynamics in a laboratory-scale non-premixed half-dump combustor of rectangular cross-section is investigated over a wide range of operating conditions. The fuel (methane) is injected just upstream of the dump plane. Acoustic measurements and high-speed imaging of the CH chemiluminescence and schlieren of the flow field in the flame zone are performed. For short lengths of the combustor, the acoustic signals have broadband peaks at what can be identified as the Strouhal frequency of vortex shedding and the natural acoustic mode of the duct. For the largest combustor length tested, the two broadband peaks move closer to each other and form a single sharp peak of very high amplitude as the air flow is increased, signaling a transition from combustion noise to instability-like behavior. The excitation of noise is accompanied by roll-up of large-scale vortices, which in turn contain several small-scale vortices. Three blow-off regimes occur for the large combustor length, namely, a fuel-rich limit, an intermediate limit, and a fuel-lean limit. The fuel-lean limit coincides with the excitation of the high-amplitude discrete tones. The blow-off limits are explained based on the oscillations prevailing in the combustor, taking into account the oscillatory fuel-air mixing and its phase delay with the oscillations.