Thermoacoustic systems are self-oscillating due to the fact that a constant input (fuel rate in gas turbine combustors for example) yields an asymptotically oscillatory response. This behavior arises due to the interaction between combustion and acoustics, resulting in thermoacoustic oscillations. This paper provides a numerical and experimental investigation of retrospective cost adaptive control (RCAC) for adaptively suppressing thermoacoustic oscillations under sampled-data control.