  A simple empirical model and approach are introduced for calculation of the
vibrational spectra of arbitrary single wall carbon nanotubes. Differently from
the frequently used force constants description, the model employs only
invariant quantities such as variations of lengths and angles. All the salient
qualitative features of vibrational spectra of nanotubes naturally follow from
the vibrational Hamiltonian of graphene upon its isometric mapping onto a
cylindrical surface and without any ad hoc corrections. A qualitative
difference with previous results is found in a parabolic, rather than a linear,
long wavelength dispersion of the transverse acoustic modes of the nanotubes.
The parabolic dispersion is confirmed and elucidated in the provided continuum
analysis of the vibrations. We also discuss and use an alternative definition
of the nanotube unit cell with only two carbons per cell that illustrates a
"true" longitudinal periodicity of the nanotubes, and of the corresponding
Brillouin zone.
