Flows in a ramjet inlet is simulated for the study of the rocket-ramjet transition. The flow is unsteady, two-dimensional axisymmetric, compressible and turbulent. Double time marching method is used for the unsteady calculation and HLLC method is used as a higher order MUSCL method. As for turbulent calculation, $kappa-omega$ SST model is used for more accurate viscous calculations. Sinusoidal pressure perturbation is given at the exit and the flow fields at the inlet is studied. The cruise condition as well as the ground test condition are considered. The pressure level for the ground test condition is relatively low and the effect of the pressure perturbation at the combustion chamber is small. The normal shock at the cruise condition is very sensitive to the pressure perturbation and can be easily detached from the cowl when the exit pressure is relatively high. The sudden decrease in the mass flux is observed when the inlet flow becomes subcritical, which can make the inlet incapable. The amplitude of travelling pressure waves becomes larger as the downstream pressure increases, and the wavelength becomes shorter as Mach number increases. The phase difference of the travelling perturbed pressure wave in space is 180 degree.