The paper illustrates the applicability of the Laguerre spectral method to solving a one-dimensional problem of the dynamics of a saturated porous medium. A one-dimensional non-stationary problem of a pulsed action on a saturated porous medium is investigated taking into account the effects of electromagnetoacoustics. The features of the acoustic response to a pulsed electromagnetic action in such a system are numerically discovered. The dependence of the amplitudes of trans- verse acoustic waves arriving at a boundary of the porous medium on the external magnetic field for various parameters of the porous medium is revealed.