How many acoustic and optical modes are there in a 3D crystal with p atoms?

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Homework Statement


For a given wavelength, how many acoustic and optical modes are there in a three dimensional crystal with p atoms in its basis?

Homework Equations

The Attempt at a Solution


Since it's 3D, I assume there's at least 3 acoustic modes and 3 optical modes? After all, the soundwaves/phonons must be able to travel in all directions.

Further on, I know both longitudinal and transverse modes are possible, but I don't know how this affects the count..
 
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Nobody knows? Perhaps something in my question is unclear?
 
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