We present a study of the far-infrared reflectance anisotropy spectra for (001) surfaces of Ge and alpha-Sn in the (2 x 1) asymmetric dimer geometry, which exhibit a resonance structure associated with the excitation of surface phonon modes. We have employed a theoretical formalism, based on the adiabatic bond-charge model (ABCM), for computing the far-infrared reflectance anisotropy spectra. In comparison with previous theoretical results for silicon and diamond surfaces, the resonance structure in the reflectance anisotropy spectrum for Ge(001)-(2 x 1) turns out to be similar to that observed in the spectrum for the Si(001)-(2 x 1) surface, whereas the spectrum for a-Sn(001)-(2 x 1) surface is noticeably different from the others. We have established a trend of far-infrared reflectance anisotropy spectra for IV(001) surfaces: the weaker dimer strength, the stronger resonances of low-frequency surface phonons. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim