I found on Wikipedia that the equation for primary/secondary wave speed in solids in 3D is
C_{solid,p} = sqrt((K+4/3*G)/rho)
C_{solid,s} = sqrt(G/rho)
where K is the bulk modulus, and G is the shear modulus of the elastic material, and rho is the material density.
It's as Yuriy says. You can also find these solutions in a chapter of "Theory of Elasticity" by Timoshenko & Goodier (Wiley, 1970).
These are plane wave solutions, wave travels in x direction and
p wave: displacements u=f(x,t), v=0, w=0 and the stiffness term comes from \sigma_x=(K+4/3G)\epsilon_x
s wave displacements, u=0, v=g(x,t), w=o and the stiffness term comes from \tau_xy=G\gamma_xy
These equations are derived for 1D wave propagation. For 2D wave propagation, even the radial damping should be taken into account to determine these velocities. Any standard textbook on Geotechnical Engineering can give you idea about the derivations.
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