In the challenging world of wave propagation on materials, models built to describe phenomena on irregular inhomogeneous impedance boundaries are much rare in the literatures despite the huge importance they generally play in the transfer or deciphering of information from one system to another. Consequently, this study conceptualizes a wave-mechanics for the dispersion equation of Rayleigh wave in a rotating inhomogeneous material under magnetic effect and impedance-irregular boundary conditions which underscores scenarios of dispersion equations for homogeneous impedance and inhomogeneous impedance characterizations of the modeled problem. The irregular condition at the boundary of the rotating inhomogeneous material under magnetic effect is wavy (corrugated or grooved) in nature. This wavy or grooved-like phenomenon is expressed mathematically as a trigonometric series at the boundary of the material. Thus, using the stress-strain relation of a fibre-reinforced material and the Maxwell’s principle of electromagnetism, the dynamic equations for the model is derived. Through these, dispersions relations for both the homogeneous impedance and inhomogeneous impedance for an inhomogeneous fibre-reinforced material are derived analytically and presented graphically, especially after utilizing the normal mode solution approach whilst deriving, also, the fields’ distributions of the stresses and displacement components of the wave on the material. In addition, these graphics illustrates the impact of the contributing physical parameters of rotation, irregular parameters (wave number and amplitude of grooved boundary), inhomogeneity and magnetic field on the two dispersions relations; homogeneous impedance and inhomogeneous impedance of the fibre-reinforced inhomogeneous material, respectively. We observe that both dispersion relations were impacted by the contributing physical parameters. While the rotation of the medium decrease the dispersion relations when increased, the magnetic fields tend to push both dispersion relations in an upward trend when increased. The impact of the horizontal and vertical impedance on both dispersion relations cause a near resistant-like effect on the propagating wave on the inhomogeneous fibre-reinforced material. However, the dispersion relation due to the homogeneous impedance tend to have reduced amplitude of dispersion of the wave on the rotating grooved inhomogeneous material under magnetic effect as compared with the dispersion relation occasioned by the inhomogeneous impedance characterizations on the inhomogeneous fibre-reinforced medium. This work should be invaluable in some engineering applications where Rayleigh wave propagation could be utilized for non-destructive testing and the construction of actuators and sensors. Moreover, utilization of surface waves with some rotation and magnetic field play a host to influence reinforced materials such as in the forging and failure analysis of rotating machinery components especially in rotor blades, etc.