Relative fundamental frequency (RFF) is a promising assessment technique for vocal pathologies. Herein, we explore the underlying laryngeal factors dictating RFF behaviours during phonation offset. To gain physical insights, we analyze a simple impact oscillator model and follow that with a numerical study using the well-established body-cover model of the vocal folds (VFs). Study of the impact oscillator suggests that the observed decrease in fundamental frequency during offset is due, at least in part, to the increase in the neutral gap between the VFs during abduction and the concomitant decrease in collision forces. Moreover, the impact oscillator elucidates a correlation between sharper drops in RFF and increased stiffness of the VFs, supporting experimental RFF studies. The body-cover model study further emphasizes the correlation between the drops in RFF and collision forces. The numerical analysis also illustrates the sensitivity of RFF to abduction initiation time relative to the phase of the phonation cycle, and the abduction period length. In addition, the numerical simulations display the potential role of the cricothyroid muscle to mitigate the RFF reduction. Last, simplified models of phonotraumatic vocal hyperfunction are explored, demonstrating that the observed sharper drops in RFF are associated with increased pre-offset collision forces.