# The Speed of Sound in Other Materials

### After reading this section you will be able to do the following:

• Explain whether or not the speed of sound is constant for all materials.
• Describe what elasticity and density are and what relationship they have to the speed of sound.

Imagine you are in a long mining tunnel deep under the earth. You have a friend that is several thousands of feet away from you in the tunnel. With a walkie talkie you tell your friend to yell and clang on the pipes on the tunnel floor at the same time. Press the play button below to find out what happens.

## Speeds of Sound

 Material Speed of Sound Rubber 60 m/s Air at 40oC 355 m/s Air at 20 oC 343 m/s Lead 1210 m/s Gold 3240 m/s Glass 4540 m/s Copper 4600 m/s Aluminum 6320 m/s

## What happens when there is a change in the material through which the sound travels?

The speed of sound is not always the same. Remember that sound is a vibration of kinetic energy passed from molecule to molecule. The closer the molecules are to each other and the tighter their bonds, the less time it takes for them to pass the sound to each other and the faster sound can travel. It is easier for sound waves to go through solids than through liquids because the molecules are closer together and more tightly bonded in solids. Similarly, it is harder for sound to pass through gases than through liquids, because gaseous molecules are farther apart. The speed of sound is faster in solid materials and slower in liquids or gases. The velocity of a sound wave is affected by two properties of matter: the elastic properties and density. The relationship is described by the following equation.

$V=\sqrt{\frac{C_{ij}}{\rho}}$

Where Cij contains the elastic properties and $\rho$ is the density.

## Elastic Properties

The speed of sound is also different for different types of solids, liquids, and gases. One of the reasons for this is that the elastic properties are different for different materials. Elastic properties relate to the tendency of a material to maintain its shape and not deform when a force is applied to it. A material such as steel will experience a smaller deformation than rubber when a force is applied to the materials. Steel is a rigid material while rubber deforms easily and is a more flexible material.

At the particle level, a rigid material is characterized by atoms and/or molecules with strong forces of attraction for each other. These forces can be thought of as springs that control how quickly the particles return to their original positions. Particles that return to their resting position quickly are ready to move again more quickly, and thus they can vibrate at higher speeds. Therefore, sound can travel faster through mediums with higher elastic properties (like steel) than it can through solids like rubber, which have lower elastic properties.

The phase of matter has a large impact upon the elastic properties of a medium. In general, the bond strength between particles is strongest in solid materials and is weakest in the gaseous state. As a result, sound waves travel faster in solids than in liquids, and faster in liquids than in gasses. While the density of a medium also affects the speed of sound, the elastic properties have a greater influence on the wave speed.

## Density

The density of a medium is the second factor that affects the speed of sound. Density describes the mass of a substance per volume. A substance that is more dense per volume has more mass per volume. Usually, larger molecules have more mass. If a material is more dense because its molecules are larger, it will transmit sound slower. Sound waves are made up of kinetic energy. It takes more energy to make large molecules vibrate than it does to make smaller molecules vibrate. Thus, sound will travel at a slower rate in the more dense object if they have the same elastic properties. If sound waves were passed through two materials with approximately the same elastic properties such as aluminum (10 psi) and gold (10.8 psi), sound will travel about twice as fast in the aluminum (0.632cm/microsecond) than in the gold (0.324cm/microsecond). This is because the aluminum has a density of 2.7gram per cubic cm which is less than the density of gold, which is about 19 grams per cubic cm. The elastic properties usually have a larger effect that the density so it is important to both material properties.

### Review:

1. The speed of sound is faster in solid materials and slower in liquids or gases.
2. The speed of a sound wave is related to the elastic properties and density of the medium it is in.
3. Elastic properties relate to the tendency of a material to maintain its shape and not deform when a force is applied to it.