The stability of stratified air-water flow under the influence of periodic disturbances in the liquid level is investigated numerically for a horizontal pipe. One-dimensional two-fluid model is used for flow simulation. Conservation equations for mass and linear momentum are discretized for both phases using a finite volume method. Coupling between equations is achieved by sequentially solving a modified version of PRIME method. Controlled disturbances are introduced in the flow by oscillating the liquid level at the pipe inlet. The evolution of the generated disturbances along the pipe is analyzed and the results are compared with predictions given by a model based on linear theory of Kelvin-Helmholtz (KH). An excellent agreement is obtained for velocity, frequency and wave number of the perturbations. This indicates that both approaches are capable to predict the fundamental characteristics of the waves. Amplifications rates predicted by simulation and model have been also compared and the results show a reasonable agreement. It is found that the frequency of the perturbations plays a role in the amplification rate. For increasingly higher frequencies the disturbances tends to be more unstable. The analysis is extended for long pipes, in such cases the growth rates changes at locations far from the inlet. It is conjectured that non linear mechanisms are related to observations.