The problem of gas motion inside a resonance tube, closed at one end by a plug and fitted at the other with an oscillating piston is treated analytically and numerically. An analytical model is derived for arbitrary piston motion and gas oscillations about the first resonance frequency, where the gas flow is characterized by a shock wave travelling periodically back and forth in the tube. The model is obtained by a perturbation analysis in terms of a small-amplitude parameter $\varepsilon$. All the hydrodynamic properties of the gas are predicted with accuracy up to the second-order terms of $\varepsilon$. Isentropic and adiabatic problem formulations are addressed. Expressions for spatial distributions of the time-averaged hydrodynamic gas properties are derived for any frequency within the resonance band. It is shown that they are determined by the gas adiabatic exponent $\gamma$ and the law that governs the motion of the piston. The analytical model is verified by comparison with a numerical solution, showing good agreement.