Consider a shock tube problem with where the pressure and temperature ratios are p4/p1 = 2 and T4/T1 = 1. Use Roe's Methods. Plot p/p1, T/T1 and u/a1 versus x/a1t. Include the numerical values of the critical points (x, y axis values) : shock, contact surface, expansion fan endpoints (as relevant). The fluid is standard air.