Rotating Detonation Combustion (RDC) has been under investigation recently for its thermodynamic efficiency advantage over traditional constant pressure gas turbine combustors. The main challenge in integrating RDCs with gas turbines for power and propulsion has been its operational stability, inducing pressure and gas speed fluctuations. In this study we conduct a detailed investigation of cycle-to-cycle detonation wave speed fluctuations in a RDC that appears to operate at steady conditions. Various methods to analyze high-speed video (HSV) images of the detonation wave and ion probe (IP) voltage data have been developed. First, a power spectra of steady-state operation is obtained using IP voltage data, which shows a spread of frequencies indicating wave speed fluctuations throughout the test. Then, a parametric computational study is conducted showing the effects of Chapman-Jouguet (C-J) velocity at varying equivalence ratios and inlet conditions to attribute the cause of the wave speed fluctuations to varying fuel-air inlet conditions. The IP voltage data are analyzed by a differential method and cross-correlation method, and the HSV images are analyzed manually and by digital processing. It is found that all data analysis techniques show macroscopic and microscopic time scale fluctuations in the detonation wave speed. The comparison between wave speed measured by IPs and HSV digital processing allow for the validation of the probe data by an optical technique. These speed fluctuations could be attributed to the fuel-air mixing fluctuations in the injector plate, pointing to the need for better design of the fuel-air injector plate systems. However, the main cause for the detonation wave speed fluctuations is the instability of supply gases entering the injector, and the coupled effect of these supply instabilities with the local equivalence ratio. The uncertainty involved in the various methods of analysis have been discussed. Additionally, a case study is conducted in which the previous method of obtaining the wave speed via the IPs is used for comparison and validation at a different test condition with a higher mass flux of reactants. Sound probe data are displayed and compared to the IP power spectra. Finally, high-speed transducer voltage data are compared with the power spectra of both the IP differential and the sound probe data. It was found that at higher mass fluxes, the wave speed fluctuations decreased by approximately 75 %. This dramatic reduction in wave speed fluctuations is caused by the reduction of inlet gas speed fluctuations by providing a more choked flow at the injector. In addition, the sound probe and PCB data show the same information about the detonation wave speed fluctuations as the IPs, but each measurement also provides its own unique information about an RDC experiment.