The velocity of a sound wave is generally higher in more dense materials because the density of a material affects its elasticity, which in turn affects how quickly sound can propagate through it. Elasticity refers to the ability of a material to deform and then return to its original shape when a force is applied to it.
In a more dense material, such as a solid, the particles are packed more closely together, resulting in stronger intermolecular or interatomic forces. These stronger forces contribute to a higher degree of elasticity in the material. When a sound wave travels through a solid, it can rapidly transmit energy by causing small vibrations in the closely packed particles, and these particles can quickly pass on the vibrations to neighboring particles due to the strong intermolecular forces. As a result, sound waves can travel faster in denser materials.
In contrast, in less dense materials like gases, the particles are more spread out and have weaker intermolecular forces. Consequently, the particles are less tightly bound, which reduces the material's elasticity. Sound waves have to overcome weaker forces and encounter more gaps between particles, leading to a slower propagation speed.
It's important to note that the relationship between density and sound velocity is not a direct proportionality in all cases, as other factors like the material's compressibility and bulk modulus also come into play. However, generally speaking, denser materials tend to have higher sound velocities due to their increased elasticity.