How to calculate or find the compressional stress wave velocity, Cp for a rock
See page 2 here for example: https://pangea.stanford.edu/courses/gp262/Notes/8.SeismicVelocity.pdf . 

What you refer to as Cp (as far as I can gather from your linked paper), is in the geophysics world generally referred to as the P-wave velocity (P stands for the primary/pressure/compressional wave; separating it from the S-wave which is the slower secondary/shear/transverse wave mode). It kind of depends on the specific mineralogy, compaction, depth, ... to determine exactly what the velocity is for any given rock. Note that the range of velocities is not particularly great (all values lie within one order of magnitude for typical rocks), so if your method is not particularly dependent on getting the P-wave velocity exactly right, you shouldn't have too much of a problem taking some average value for your rock! If, on the other hand, it is very sensitive to this value, you'll have to make an accurate measurement on your sample (which is not a trivial thing to do at all!).