Low-frequency longitudinal (compressional) and transverse (shear) modes of phonons in Debye-Yukawa complex plasma crystals are studied. The general dispersion relations obtained for two-dimensional modes [Wang, Bhattacharjee, and Hu, Phys. Rev. Lett. 86, 2596 (200 1)] are applied to the long-wavelength phonon regime with the wavenumber k -> 0, and the shielding parameter kappa -> 0 to calculate the acoustic velocity of phonons in complex plasma crystals. Our analytic work confirms earlier numerical results. (c) 2005 Elsevier B.V. All rights reserved.