The presence of multiple populations is now well-established in most globular clusters in the Milky Way. In light of this progress, here we suggest a new model explaining the origin of the Sandage period-shift and the difference in mean period of type ab RR Lyrae variables between the two Oosterhoff groups. In our models, the instability strip in the metal-poor group II clusters, such as M15, is populated by second generation stars (G2) with enhanced helium and CNO abundances, while the RR Lyraes in the relatively metal-rich group I clusters like M3 are mostly produced by first generation stars (G1) without these enhancements. This population shift within the instability strip with metallicity can create the observed period-shift between the two groups, since both helium and CNO abundances play a role in increasing the period of RR Lyrae variables. The presence of more metal-rich clusters having Oosterhoff-intermediate characteristics, such as NGC 1851, as well as of most metal-rich clusters having RR Lyraes with longest periods (group III) can also be reproduced, as more helium-rich third and later generations of stars (G3) penetrate into the instability strip with further increase in metallicity. Therefore, although there are systems where the suggested population shift cannot be a viable explanation, for the most general cases, our models predict that the RR Lyraes are produced mostly by G1, G2, and G3, respectively, for the Oosterhoff groups I, II, and III.