# Temperature and the Speed of Sound

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

• Observe the demonstrations below and explain the differences in the speed of sound when the temperature is changed.
 Temperature Speed of Sound (m/s) 358.0 343.6 330.4

## Temperature and the speed of sound

Temperature is also a condition that affects the speed of sound. Heat, like sound, is a form of kinetic energy. Molecules at higher temperatures have more energy, thus they can vibrate faster. Since the molecules vibrate faster, sound waves can travel more quickly. The speed of sound in room temperature air is 346 meters per second. This is faster than 331 meters per second, which is the speed of sound in air at freezing temperatures.

The formula to find the speed of sound in air is as follows:

$v=331m/s+0.6 \frac{m/s}{C}\times T$

v is the speed of sound and T is the temperature of the air. One thing to keep in mind is that this formula finds the average speed of sound for any given temperature. The speed of sound is also affected by other factors such as humidity and air pressure.

## Air Density and Temperature

Suppose that two volumes of a substance such as air have different densities. We know the more dense substance must have more mass per volume. More molecules are squeezed into the same volume, therefore, the molecules are closer together and their bonds are stronger (think tight springs). Since sound is more easily transmitted between particles with strong bonds (tight springs), sound travels faster through denser air.

However, you may have noticed from the table above that sound travels faster in the warmer 40$^{\circ}$ C air than in the cooler 20$^{\circ}$ C air. This doesn't seem right because the cooler air is more dense. However, in gases, an increase in temperature causes the molecules to move faster and this account for the increase in the speed of sound. This will be discussed in more detail on the next page.

### Review:

1. The speed of sound is faster when temperatures are higher.