Discussion
If P-wave and S-wave were to go from a solid to a liquid medium, what would happen to their velocity ?
Answer: C
The P-wave velocity would decrease and the S-wave velocity would decrease to zero.
P-waves depend on both the bulk and shear moduli, while S-waves depend only on the shear modulus:
\[ \begin{aligned} V_{P} &= \sqrt{\frac{K + \frac{4}{3}\mu}{\rho}} \\ V_{S} &= \sqrt{\frac{\mu}{\rho}} \end{aligned} \]
A liquid has no rigidity (μ = 0), so S-waves cannot travel through it at all, and the P-wave velocity falls because the shear term drops out. This is why S-waves do not pass through the Earth's liquid outer core and why P-waves slow sharply at the core-mantle boundary.
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