A range of analysis approaches, namely continuous wavelet, cross wavelet, and wavelet coherence analyses, are employed to clarify the phase relationship between the smoothed monthly mean sunspot number and solar 10.7 cm flux (F10.7). Analysis shows that there is a region of high spectral power sitting across the Schwabe cycle belt, where the two time series are in phase. However, analysis of the cross-wavelet transform and wavelet coherence unveils asynchronous behavior featured with phase mixing in the high-frequency components of sunspot activity and solar F10.7, which may explain the different activity properties of the photosphere and corona on a short time scale.