Zwitterionic L-alanine forms crystals containing strong hydrogen-bonding and methylmethyl interactions. Well-defined low-frequency lattice vibrations exist in the crystals involving correlated intermolecular motions on the picosecond timescale. A characterization of these vibrations is expected to provide useful information on the nature of nonbonded interactions in peptides and proteins. We examine some of the vibrations using coherent inelastic neutron scattering and computer simulation techniques. The neutron scattering measurements are used to determine phonon dispersion relations for the acoustic and some low-frequency optic modes in the crystal. There is evidence for interaction between the two lowest frequency optical phonons and the longitudinal acoustic mode. The velocity of sound is anisotropic and can be correlated with the hydrogen-bonding arrangement in the crystal. Corresponding phonon dispersion relations are derived from normal mode analyses of the crystal using the program CHARMM. Although some calculated vibrational frequencies are somewhat too high, the form of the calculated dispersion relations are in good agreement with experiment.