Within the framework of static scattering, scattering-induced spectral changes in the forward-scattered component of polychromatic Gaussian beams transmitting through an insulating plate with rough surface are discussed. It is shown that the spectrum may be red-shifted and blue-shifted in comparison with the source spectrum, and the spectral switch may also take place. The H-parameter (the maximum deviation of the surface profile from the mean surface line) influences spectral behavior greatly. The spectrum remains unchanged if H=0. The phenomenon of scattering-induced spectral switches of polychromatic Gaussian beams in the far zone belongs to the effect in singular optics.