The dispersion of small-amplitude, impulsively excited wave trains propagating along a magnetic flux tube is investigated. The initial disturbance is a localized transverse displacement of the tube that excites a fast kink wave packet. The spatial and temporal evolution of the perturbed variables (density, plasma displacement, velocity, ...) is given by an analytical expression containing an integral that is computed numerically. We find that the dispersion of fast kink wave trains is more important for shorter initial disturbances (i.e., more concentrated in the longitudinal direction) and for larger density ratios (i.e., for larger contrasts of the tube density with respect to the environment density). This type of excitation generates a wave train whose signature at a fixed position along a coronal loop is a short event (duration 20 s) in which the velocity and density oscillate very rapidly with typical periods of the order of a few seconds. The oscillatory period is not constant but gradually declines during the course of this event. Peak values of the velocity are of the order of 10?km s–1 and are accompanied by maximum density variations of the order of 10%-15% the unperturbed loop density.
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