Turbulent mixing due to hydrodynamic instabilities occurs in a wide range of science and engineering applications such as supernova explosions and inertial confinement fusion. The experimental, theoretical and numerical studies help us to understand the dynamics of hydrodynamically unstable interfaces between fluids in these important problems. In this paper, we present an increasingly accurate and robust front tracking method for the numerical simulations of Richtmyer-Meshkov Instability (RMI) to estimate the growth rate. The single-mode shock tube experiments of Collins and Jacobs 2002 [1] for two incident shock strengths $(M = 1.11$ and $M = 1.21)$ are used to validate the RMI simulations. The simulations based on the classical fifth order weighted essentially non-oscillatory (WENO) scheme of Jiang and Shu [2] with Yang’s artificial compression [3] are compared with Collins and Jacobs 2002 shock tube experiments. We investigate the resolution effects using front tracking with WENO schemes on the two-dimensional RMI of an ${\rm air}/SF_6$ interface. We achieve very good agreement on the early time interface displacement and amplitude growth rate between simulations and experiments for Mach number $M = 1.11.$ A 4% discrepancy on early-time amplitude is observed between the fine grid simulation and the $M = 1.21$ experiments of Collins and Jacobs 2002.