Concept: Earthquake waves are mainly of two body-wave types: P-waves and S-waves. P-waves can travel through solids, liquids, and gases, but S-waves can travel only through solids.
Step 1: Understand S-waves.
S-waves are secondary waves. They move the ground perpendicular to the direction of wave travel.
\[
S\text{-waves} = \text{Shear waves}
\]
Step 2: Understand why S-waves cannot travel through liquids.
S-waves need rigidity or shear strength to travel. Liquids and gases do not have enough shear strength.
\[
\text{Liquids and gases} \Rightarrow \text{No shear rigidity}
\]
Step 3: Select the correct medium.
Since S-waves travel only through solid parts of the Earth, option A is correct.
\[
S\text{-waves} \rightarrow \text{Solid medium only}
\]
Therefore, the correct answer is A Only.