A mathematical model investigating the dispersions of Rayleigh wave on an inhomogeneous rotating half-space with magnetic field influence, impedance and variable amplitudes of corrugation is presented. Normal mode approach and non-dimensionalization principles were employed to the equations of motion. Derivations of the analytical solutions of the stresses and displacement components occasioned by the wave on the material were achieved. Variable amplitudes of corrugation due to a linear function incorporated as the amplitude of the trigonometric Fourier series and the impedance conditions enriches the material characterizations and paved way in formulating the structure or nature of corrugation at the boundary. Thus, dispersion relations of Rayleigh waves due to homogeneous impedance and inhomogeneous impedance were analytically given and graphically depicted with the variations of the physical parameters.