Abstract
An array of identical carbon nanotubes mounted on a metallic plate in the presence of a vertical electric field executes collective vibrations parallel to the metallic plate. The dispersion relation for these vibrations is deduced. The characteristic parameters are the length, radius and Young's modulus of the tubes, the vertical electric field and the separation between the nanotubes. These modes are similar to one-dimensional acoustic modes in a solid. These modes can be detected by the Brillouin scattering of a laser.