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Acousto-electromagnetic wave interaction occurs when an electromagnetic wave scatters from an object under seismic or acoustic illumination. The vibration of the object under acoustic excitation gives rise to a frequency modulated scattered field which depends on both the object and electromagnetic and acoustic source parameters. The objective of this study is to accurately calculate the Doppler spectrum of the bistatic scattered field which is usually orders of magnitude smaller than the fundamental component of the scattered field (the stationary target response). In this analysis the recently developed sheet boundary conditions are used to set up a duplicate problem of a stationary object having time varying sheet impedance and admittance accounting for the object vibration. The problem is formulated using the two-dimensional finite-difference time-domain (FDTD) method in an iterative scheme in order to find the broadband response of the scattered field Doppler component. Two-dimensional analytical solutions for a canonical geometry are used to verify the FDTD simulation results.