The far infrared absorption spectra measurements were performed on the CdxHg1-x Te samples with x=0.18 to 0.45 in the wavenumber region of 15-500 cm-1 at the temperatures from 4.5 to 300 K. In addition to the absorption structures of two phonon combination on both sides of the reststrahlen band of the material, a low frequency absorption band has been observed for the first time between 20-50 cm-1 in all the measured samples. By comparison with the phonon spectra of the mixed crystals CdxHg1-x Te which have been estimated by means of the ab initio density functional calculations of planar force constants, we have attributed the low frequency absorption band to the TA band modes induced by the disorder and "doping" effects resulting from by the crystalline mixing in the material.