Experimental and analytical studies were conducted to investigate key physical mechanisms responsible for flame-acoustic coupling during the onset of acoustically driven combustion instabilities in liquid rocket engines (LREs). Controlled experiments were conducted in which a turbulent hydrogen-oxygen (GH2-GO2) diffusion flame, established downstream of a two-dimensional model shear coaxial injector was acoustically forced by a compression driver unit mounted in a transverse direction and excited through a broad range of frequencies (200Hz-2000Hz) and amplitudes. Characteristic interactions between flame and acoustics visualized through OH* and CH* chemiluminescence imaging and dynamic pressure measurements obtained using high frequency dynamic pressure transducers indicated that small acoustic disturbances could be amplified by flame-acoustic coupling under certain conditions leading to substantial modulation in spatial heat release fluctuations. Density gradient between fuel and oxidizer was found to significantly affect the way acoustic waves interacted with density stratified flame fronts. The particular case of an asymmetric flame front oscillation under transverse acoustic forcing indicated that baroclinic vorticity, generated by the interactions between misaligned pressure gradient (across the acoustic wave) and density gradient (across the fuel oxidizer interface) could further amplify flame front distortions. Asymmetric interaction between flame and acoustics is shown to occur preferentially on flame fronts where controlled waves from the compression driver travel from lighter fluid to denser fluid and the amount of interaction between flame and acoustics is shown to depend strongly on the density ratio between the fluids on either sides of the flame front. This observation is in agreement with the baroclinic vorticity mechanism and a variant of the classical Rayleigh-Taylor instability mechanism. The results provide the first known experimental evidence that baroclinic vorticity could play a role in triggering flame-acoustic interactions associated with LRE shear coaxial injectors. Parametric studies investigating the sensitivity of flame-acoustic interaction on key physical parameters that govern shear coaxial injector operations (including density ratio, velocity ratio, momentum ratio and chemical composition of the fuel) were conducted by varying the parameter of interest independently while holding the other parameters relatively constant. Density ratios ranging from 1 to 16, velocity ratios ranging from 3.02 to 5.27, momentum ratios ranging from 0.67 to 2.12 and fuel mixtures ranging from pure hydrogen to 10%-90% GH2-GCH4 combination were tested. It is shown that in the ranges considered, flame-acoustic interaction is most sensitively affected by density ratio changes. Spectral measurements of flame front oscillations using local chemiluminescence measurements further revealed the non-linear nature of the interaction process : a flame system forced at 1150 Hz gave rise not only to 1150 Hz oscillations but also triggered flame oscillations occurring at substantially lower frequencies. Analytical models were developed to interpret and predict acoustic modes of a combustion chamber containing a density stratified flowfield subjected to transverse acoustic disturbances. Incorporating both the known phenomenon of jet mixing length and the new experimental result of preferential excitation, the models allow different resonant behaviors to occur for separate regions of the combustor bounded by sudden changes in density. For isothermal experiments where the flow temperature was known, calculated Eigen frequencies were in good agreement with measured frequencies. Overall, the identification of fuel-oxidizer density ratio as a critical parameter and the identification of baroclinic vorticity as a potential mechanism in flame acoustic coupling are significant because a reduction in the density gradient between fuel and oxidizer can be used as a control mechanism to improve flame stability in liquid rocket engines.