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The behavior of a pulse whose frequency sweeps through the resonance of a linear system, although first studied in spin resonance, is widely applicable to many wave phenomena. A frequency-swept optical pulse transmitted through a resonant medium develops intensity oscillations, which are the result of heterodyning the input pulse with the field radiated by the resonant system. This self-induced heterodyne signal allows the determination of the relative phase between the input pulse and the single frequency field radiated by the resonant system. A simple approximate model which very accurately describes the time evolution of the output pulse is given a physical and mathematical basis. Results for the optically thin case are extended to include the effects of propagation, revealing phenomena which have no spin-resonance analogy.