Acoustically coupled combustion instabilities can result in large-scale, potentially catastrophic pressure oscillations in aerospace propulsion systems, including liquid rocket engines (LREs) and gas turbine engines. A fundamental understanding of the interactions among flow and flame hydrodynamics, acoustics, and reaction kinetics is essential to determining combustor stability and controlling combustion processes. This dissertation focuses on a range of fundamental experiments that can shed light on combustion instabilities and their dynamical signatures, including (1) exploration of the effects of nanoparticulate additives on liquid fuels during acoustically-coupled combustion and (2) the effects of acoustic excitation on gas phase combu...