  As an alternative to atomistic calculations of long-wavelength acoustic modes
of atomically thin layers, which are known to converge very slowly, we propose
a quantitatively predictive and physically intuitive approach based on
continuum elasticity theory. We describe a layer, independent of its thickness,
by a membrane, characterize its elastic behavior by a $(3{\times}3)$ elastic
matrix as well as the flexural rigidity. We present simple quantitative
expressions for frequencies of long-wavelength acoustic modes, which we
determine using 2D elastic constants calculated by {\em ab initio} Density
Functional Theory. The calculated spectra accurately reproduce observed and
calculated long-wavelength phonon spectra of graphene and phosphorene, the
monolayer of black phosphorus. Our approach also correctly describes the
observed dependence of the radial breathing mode frequency on the diameter of
carbon fullerenes and nanotubes.
