Answer to 1st question is no. As for the 2nd question, if you can obtain the acoustic wave speed and density for the material, the relation to bulk modulus of compressibility is:
K = rho*c^2
where
K = bulk modulus of compressibility
rho = density
c = acoustic wave speed (compression waves)
Generally, it is much easier to measure density and acoustic wave velocity experimentally and calculate bulk modulus of compressibility than it is to directly measure bulk modulus of compressibility.
