This paper presents the results of an investigation that focuses on the stochastic wave propagation that occurs within an elastic medium when the thermoelectric properties are taken into consideration. It has been found that there is a clear association between the characteristics of electrical conductivity and thermal conductivity. As a result, the current topic focuses on the influence a magnetic field has on the variable thermal conductivity and electrical conductivity that exists within a material. This is done within the context of dual phase lag thermoelasticity. Several parameters are incorporated into the governing equations, which exhibit coupling. Thermal shock has been applied to the boundary of the medium that represents the non-traction barrier. At the border of the problem, stochasticity is imposed in order to make the problem appear more realistic. Within the boundary conditions, it is presumed that the white-noise function is present. Utilizing the Laplace transform method is the approach that is taken to address the issue. It is possible to determine the inverse transformations using numerical approximation approaches. Both graphical and visual analyses are performed on the dataset. In conclusion, graphical representations are utilized in order to make comparisons between the deterministic and stochastic solutions of all physical fields