An active control approach was developed to observe and control nonlinear effects for high-amplitude acoustic waves in a cavity. The acoustic medium was air at ambient pressure and temperature. A harmonic cavity was driven using a multi-frequency drive to selectively drive the fundamental mode and suppress nonlinear interactions between the fundamental and other modes. A semi-empirical model was developed using effective quadratic and cubic nonlinear coupling coefficients to predict resonator response. The cavity was also shown to act as an acoustic mixer. Typical acoustic pressure amplitudes were 1000 Pa (SPL 154 dBre: 20 μPa).