# Why does a higher density slow down sound in air?

• dragon-kazooie
In summary, the conversation discusses the relationship between humidity and the density of air, and how it affects the speed of sound. The main reason for the difference in speed is the lower mass of water molecules, not the spacing between them. The speed of sound in solids, on the other hand, depends on stiffness and mass density. The conversation also mentions the ideal gas law and provides a link for further information.
dragon-kazooie

## Homework Statement

Sorry, it's not an actual problem, it's just a statement I don't understand from my text - "The density of water vapor is less than that of dry air. Therefore, the higher the humidity (that is, the more water vapor there is in the air), the lower the density of the air. For this reason, sound travels through the air more rapidly in damp weather than in clear weather."

But why?

## Homework Equations

/ 3. The Attempt at a Solution [/B]
Earlier we learned that in solids, denser materials make for faster movement of sound through them, because the molecules are closer so they can transmit the energy faster. Why wouldn't it be the same for air? I think it would matter more for air because the molecules are even farther apart.

If you are familiar with the ideal gas law PV = NkT, then you can rearrange it to get an expression for the number of molecules per unit volume:

N/V = P/(kT)

This shows that the number of molecules per unit volume depends only on the pressure and temperature and not on the particular type of gas. Thus, the number of molecules per unit volume in dry air is the same as for moist air for a given pressure and temperature. This means that the average spacing between the molecules will be the same for the two gases.

The main reason that the speed of sound in moist air is greater than in dry air is that a water molecule has significantly less mass than a nitrogen or oxygen molecule. Roughly speaking, the smaller inertia of the water molecules allows them to transmit a disturbance in the gas more quickly.

You can find more information, including formulas, with a web search. For example
https://pages.mtu.edu/~suits/SpeedofSound.html

phinds
dragon-kazooie said:
Earlier we learned that in solids, denser materials make for faster movement of sound through them, because the molecules are closer so they can transmit the energy faster.
That sounds like complete rubbish. The speed of sound in solids depends on stiffness (the stiffer the faster) and mass density (the denser, the slower).

https://en.wikipedia.org/wiki/Speed_of_sound#Speed_of_sound_in_solids

TSny said:
If you are familiar with the ideal gas law PV = NkT, then you can rearrange it to get an expression for the number of molecules per unit volume:

N/V = P/(kT)

This shows that the number of molecules per unit volume depends only on the pressure and temperature and not on the particular type of gas. Thus, the number of molecules per unit volume in dry air is the same as for moist air for a given pressure and temperature. This means that the average spacing between the molecules will be the same for the two gases.

The main reason that the speed of sound in moist air is greater than in dry air is that a water molecule has significantly less mass than a nitrogen or oxygen molecule. Roughly speaking, the smaller inertia of the water molecules allows them to transmit a disturbance in the gas more quickly.

You can find more information, including formulas, with a web search. For example
https://pages.mtu.edu/~suits/SpeedofSound.html

Oooooooh! So the density difference is because the mass is lower, not because the molecules are closer! It makes sense now. Thank you for explaining that so clearly and linking more info!

jbriggs444 said:
That sounds like complete rubbish. The speed of sound in solids depends on stiffness (the stiffer the faster) and mass density (the denser, the slower).

https://en.wikipedia.org/wiki/Speed_of_sound#Speed_of_sound_in_solids

Huh. I will have to go back to that section and see if it is written incorrectly or if I just understood it wrong. Thank you!

## 1. Why does a higher density slow down sound in air?

Higher density slows down sound in air because it increases the number of molecules in a given volume of air. This leads to more collisions between the molecules, causing the sound waves to travel at a slower speed.

## 2. How does density affect the speed of sound in air?

Density is directly proportional to the speed of sound in air. This means that as density increases, the speed of sound also increases, and vice versa.

## 3. What is the relationship between density and the speed of sound in air?

The relationship between density and the speed of sound in air is described by the equation: speed of sound = √(elasticity/density). This means that as density increases, the speed of sound decreases.

## 4. Why does sound travel faster in solids and liquids compared to air?

Sound travels faster in solids and liquids because they have a higher density compared to air. This means that there are more molecules present to transmit the sound waves, resulting in a faster speed.

## 5. How does temperature affect the density of air and in turn, the speed of sound?

As temperature increases, the density of air decreases. This is because the molecules in warmer air have more energy and are more spread out. As a result, the speed of sound also increases with higher temperatures due to the decrease in density.

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