We present a study of the temporal changes in the sensitivities of the frequencies of the solar p-mode oscillations to corresponding changes in the levels of solar activity during Solar Cycle 23. From MDI and GONG++ full-disk Dopplergram three-day time series obtained between 1996 and 2008 we have computed a total of 221 sets of m-averaged power spectra for spherical harmonic degrees ranging up to 1000. We have then fit these 284 sets of m-averaged power spectra using our WMLTP fitting code and both symmetric Lorentzian profiles for the peaks as well as the asymmetric profile of Nigam and Kosovichev to obtain 568 tables of p-mode parameters. We then inter-compared these 568 tables, and we performed linear regression analyses of the differences in p-mode frequencies, widths, amplitudes, and asymmetries as functions of the differences in as many as ten different solar activity indices. From the linear regression analyses that we performed on the frequency difference data sets, we have discovered a new signature of the frequency shifts of the p-modes. Specifically, we have discovered that the temporal shifts of the solar oscillation frequencies are positively correlated with the changes in solar activity below a limiting frequency. They then become anti-correlated with the changes in activity for a range of frequencies before once again becoming positively-correlated with the activity changes at very high frequencies. We have also discovered that the two frequencies where the sensitivities of the temporal frequency shifts change sign also change in phase with the average level of solar activity.