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Wave propagation in a fuel line bounded on one end by a pressure regulator creating a constant head and on the other by a single fuel injector creating a time dependent flow rate is studied. It is found that a model consisting of a linearized wave equation and a linearized injector/fuel line boundary condition (including lumped damping) is convenient for analytical work. A general closed form solution of the pertinent equations can be found in terms of a recursion relation which holds for any injection history. Representative solutions are reported for sinusoidal and step function (sudden injector opening or closing) injection histories. Solutions for step function histories are superimposed to create predictions for a variety of periodic (but nonsinusoidal) injection histories. It is found to be possible to extract limiting steady state solutions from these general transient results.