Pulsed wire technique is a fast and accurate method for the measurement of first and second field integrals of undulators used in free-electron lasers and synchrotron light sources. In this paper, we present a theoretical analysis of this technique by finding out the analytic solution of the differential equation for the forced vibration of the wire taking dispersion due to stiffness into account. Method of images is used to extend these solutions to include reflections at the ends. For long undulators, the effect of dispersion of the acoustic wave in the wire could be significant and our analysis provides a method for the evaluation of the magnetic field profile even in such cases taking the effect due to dispersion into account in an exact way.