Velocity of P and S-waves...

P-waves:
The velocity of P-waves can be calculated from elastic constants of material through which the wave is traveling - one formula is:

v_p =

where K is the bulk modulus, m the shear modulus and r is the density

S-waves:
The velocity of S-waves is given by the formula:

v_s =

Question: Why can't S-waves travel through fluids?
In a fluid, rigidity (measured by ) is zero, therefore v_s must also be zero.

Question: Why are P-waves always faster than S-waves?

Because K and are always positive numbers, the ratio of v_p to v_s will always be greater than 1.