$v_{solid} > v_{liquid} > v_{gas}$
Explanation
Sound is a mechanical longitudinal wave that propagates through a medium via the vibration of particles. The speed of sound ($v$) in a medium is governed by the properties of that medium, specifically its elasticity (modulus of elasticity, $E$) and density ($\rho$), according to the relationship $v = \sqrt{\frac{E}{\rho}}$.
Analysis:
- Solids: Particles in solids are tightly packed, and the intermolecular forces are very strong. This results in high elasticity. Although solids are denser than gases, their high modulus of elasticity dominates, allowing sound waves to travel fastest through them.
- Liquids: The particles are less tightly packed compared to solids, and the intermolecular forces are weaker. Consequently, the speed of sound in liquids is lower than in solids but higher than in gases.
- Gases: Particles in gases are far apart and have negligible intermolecular forces. Gases have the lowest elasticity among the three states of matter, resulting in the slowest propagation of sound.
For instance, the speed of sound is approximately 5,960 m/s in steel (solid), 1,482 m/s in water (liquid), and 343 m/s in air (gas).
Key Takeaway:
The speed of sound follows the order: Solid > Liquid > Gas, primarily because the elasticity of solids is significantly higher than that of liquids and gases.