Why does a higher density slow down sound in air?

[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.

 

[TSny]

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

 

[jbriggs444]

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

 

[dragon-kazooie]

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!

 

[dragon-kazooie]

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!