This paper describes a numerical study on wave interactions following the emergence of a supersonic projectile released from the open-end of a shock tube into ambient air. The Euler equations, assuming axisymmetric flows, were solved using a dispersion-controlled scheme implemented with moving boundary conditions. The numerical results show that not only does the leading shock due to the second blast overtake the projectile but also the gas behind the projectile does so when the initial pressure ratio behind and ahead of the projectile is high. Subsequently, the projectile will overtake them again. The second blast becomes tightly coupled with the first.