I had a question regarding phonon spectrum in condensed matter.

Consider a cubic lattice with '$p$' atoms per primitive cell. Consider the lattice plane used for derivation of the phonon spectrum to be the face of the cube and consider only nearest neighbour interactions. Consider the force on the plane to be directly proportional to the nearest neighbour distance with that of the neighbouring planes. Using this prescription (described in Introduction to Solid State Physics by Charles Kittel for example) we get $\omega$ versus $k$ curves depending on the value of $p$ . My question is how do you classify these curves into 'acoustic' and 'optical' modes? On what basis is the nomenclature of 'optical' and 'acoustic' used? Further, why are there only 3 acoustic modes be it any '$p$' value?