Abstract
The resonant oscillations of a gas in a closed-end tube are treated. The time-periodic motion is given by a regular perturbation method in which the expansion parameter is the Mach number of the resulting flow. The solution at the first order exhibits a shock traveling in the tube, but, to this order, the waves do not interact. The interaction of the waves is calculated at the second order. The perturbation procedure proceeds systematically by an application of the Fredholm alternative at each stage.
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