Chapter 11, Problem 13Q

To determine

Explain why the speed of sound in most solids is somewhat greater than in air, yet the density of solids is much greater (10³ to 10⁴ times).

Answer to Problem 13Q

Solution:

The sound velocity is usually larger in solids than in liquids and usually larger in liquids than in gases is because of the elastic constants of the material.

Explanation of Solution

Sound can be defined as a local disturbance whose propagation is facilitated by the collisions between particles; this disturbance propagates in a longitudinal wave.

Generally, sound travels faster in solids than in liquids or gases. This is because the speed of these waves is determined by a relationship between the elastic properties of the medium (the elastic modulus)in which they propagate and the mass density of the material.

Solid materials have a high modulus of elasticity,therefore, when an external force is applied, they recover quickly (much faster than gases and liquids)without deforming. The density is greater, but the elasticity factor wins and therefore the sound spreads faster.

Conclusion:

The velocity with which the sound spreads is proportional to the elastic constant of the material.