The presence of multiple populations is now well-established in most globular clusters (GCs) 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 (<Pab>) between the two Oosterhoff groups. In our models, while matching the observed color-magnitude diagrams, the difference in <Pab> is naturally reproduced as the instability strip is occupied by different subpopulations with increasing metallicity. The instability strip in the metal-poor group II clusters is populated by second generation stars (G2) with enhanced helium and CNO abundances, while the RR Lyraes in the metal-rich group I clusters are mostly produced by first generation stars (G1) without these enhancements. This population shift within the instability strip 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 Oosterhoff group III clusters having RR Lyraes with longest <Pab> can also be reproduced, if more helium-rich third generation stars (G3) are present in these GCs.