  We report first principles linear response calculations on NaCoO$_2$. Phonon
frequencies and eigenvectors are obtained throughout the Brillouin zone for two
geometries with different Na site occupancies. While most of the phonon modes
are found to be unsensitive to the Na site occupancy, there are two modes
dominated by out-of-plane vibrations of Na giving very different frequencies
for different geometries. One of these two modes, the A$_{2u}$ mode, is
infrared-active, and can be used as a suitable sensor of Na
distribution/ordering. The longitudinal-transverse splitting of the zone-center
optical-mode frequencies, Born effective charges and the dielectric constants
are also reported, showing considerable anisotropy. The calculated frequencies
of Raman-active modes generally agree with the experimental values of
corresponding Na de-intercalated and/or hydrated compounds, while it requires
better experimental data to clarify the infrared-active mode frequencies.
