We have developed a theory for the generation and detection of coherent phonons in carbon based nanotstructures such as single walled nanotubes (SWNTs), graphene, and graphene nanoribbons. Coherent phonons are generated via the deformation potential electron/hole-phonon interaction with ultrafast photo-excited carriers. They modulate the reflectance or absorption of an optical probe pules on a THz time scale and might be useful for optical modulators. In our theory the electronic states are treated in a third nearest neighbor extended tight binding formalism which gives a good description of the states over the entire Brillouin zone while the phonon states are treated using valence force field models which include bond stretching, in-plane and out-of-plane bond bending, and bond twisting interactions up to fourth neighbor distances. We compare our theory to experiments for the low frequency radial breathing mode (RBM) in micelle suspended single-walled nanotubes (SWNTs). The analysis of such data provides a wealth of information on the dynamics and interplay of photons, phonons and electrons in these carbon based nanostructures.