Using direct observations via stroboscopic technique it is shown that in iron garnet crystals placed in an alternating magnetic field aligned perpendicular to the plane of the sample the dynamic magnetization reversal is carried out by the oscillations of the domain walls with their subsequent drift. For the first time the dependences of the maximum speed of domain walls motion during oscillations Vosc and of the domain walls oscillations amplitude Aosc in external oscillating magnetic field on amplitude of the external magnetic field H0 are obtained. It is shown that these dependences can be approximated by linear functions. Numerical simulations of domain walls motion in an alternating magnetic field were performed with parameters of the real sample. It is established that the experimental dependences Vosc(H0) and Aosc(H0) at different frequencies are in a qualitative agreement with the results of numerical simulations.