Small angle and large-angle Brillouin scattering have been used to measure the sound velocity and damping of longitudinal waves propagating along (C, and perpendicular to (C'J the incommensurate axis in Ba,NaNb,O,, . For each mode strong dispersion is observed, with relaxation time 2 m of order 1.3 x lo-" s near T. For C , , T (~ satisfies with 2nr, = (1.08 & 0.13) x lo-'' s;2zr1 = (8.5 + 0.7) x lo-" s; and thediffusivity D = 1.3 cm'/s. This approximately 65 times larger than the thermal diffusivity of entropy fluctuations and implies a dynamic "central mode" for right-angle geometry light scattering of -60GHz. This mode is ten times the width observed for phason (soliton) diffusion by Lyons et al. in BaMnF,; it is not directly observed in the present work. For LA sound waves perpendicular to the incommensurate axis r;i(T) = T ; ' + Dq';that is, T, and D are the same as for C , , but ro' is neligible. T,, is interpreted as due to amplitude mode-acoustic mode interaction; T, and D are interpreted as interaction of acoustic modes with mobile defects, presumably soliton-like kinks in the incommensurate structure. +This paper summarizes the