Several authors studied experimentally the motion of a column of air in a long pipe, closed at one end and driven at the other by an oscillating piston. At resonance, they observed shock waves traveling in the tube. The paper presents a simple theoretical analysis of the motion, based on discontinuous linearized solutions and a secular equation. This equation guarantees that the motion remains periodic in spite of the cumulative effects of the nonlinear terms. For an inviscid gas, the amplitude at resonance is found to be finite and to be determined by nonlinear effects. This differs from previous results of Frederiksen. Friction can be taken into account and is included in the final results, which are presented in the form of a chart.