Cavity ringdown spectroscopy is an efficient gas-sensing method, but improvement in measurement speed is required before this method can be applied to the analysis of fast phenomena. We present a new continuous-wave cavity ringdown design, involving fast tuning of the laser frequency and a rapidly swept optical cavity, to allow high-speed sensing with spectral resolution refinement. This approach, which provides a simple and versatile instrument, is investigated numerically and experimentally. By performing detection of a forbidden transition of molecular oxygen near 766 nm during a 2-ms single sweep of the laser frequency, we show that our system fulfils the requirements for probing rapid chemical processes.