Sound Speed Clarification

[oxelhs]

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I was going through TBR which states that the stronger the force between any two molecules, the greater the restoring force and ultimately greater sound speed.

How come then, the speed of sound increases in hotter air? Isn't hotter air less dense (i.e. more space amongst the individual particles)?

 

[TexasSurgeon]

I was going through TBR which states that the stronger the force between any two molecules, the greater the restoring force and ultimately greater sound speed.

How come then, the speed of sound increases in hotter air? Isn't hotter air less dense (i.e. more space amongst the individual particles)?

Yeah you're right. The speed increases due to greater energy interaction between particles.

 

[TexasSurgeon]

I was going through TBR which states that the stronger the force between any two molecules, the greater the restoring force and ultimately greater sound speed.

How come then, the speed of sound increases in hotter air? Isn't hotter air less dense (i.e. more space amongst the individual particles)?

That's why the speed increases, since more hot particles are colliding faster so the transmission is faster

 

[oxelhs]

I see - thanks!

 

[dcamkl1]

I'm fairly certain that cold air is more dense than warm air.

If you look at the formula for the speed of a sound wave in a gaseous media in TBR, "v" is inversely proportional to the square root of density, and directly proportional to the square root of temperature.

So, cold air (more dense) has a smaller speed, and warm air (higher T) has a bigger speed.

Also, "v" is proportional to the square root of the restoring force or molecular kinetic energy (like you wrote in your post). And since according to the kinetic theory of gases, temperature is a measure of KE for a gas, high T = faster speed of sound. I think the restoring force best applies to situations where you are comparing two different mediums (i.e. solid and liquid).

 

[TexasSurgeon]

.

 

[milski]

Impossible. Think practically- hot air rises. This is why hot air balloons have a gas lamp inside so that when you pull that weird string, hot air fills the balloon, causing a decrease in altitude because well, hot air is more dense.

Your formula shows that cold air has a lower speed because the rate of molecular interaction is less than hot air. As a result, it is less dense.

Hot air rises precisely because it is less dense. That's easy to see from PV=nRT if you rewrite it as n/V=P/(RT)=ρ

 

[TexasSurgeon]

I'm fairly certain that cold air is more dense than warm air.

If you look at the formula for the speed of a sound wave in a gaseous media in TBR, "v" is inversely proportional to the square root of density, and directly proportional to the square root of temperature.

So, cold air (more dense) has a smaller speed, and warm air (higher T) has a bigger speed.

Also, "v" is proportional to the square root of the restoring force or molecular kinetic energy (like you wrote in your post). And since according to the kinetic theory of gases, temperature is a measure of KE for a gas, high T = faster speed of sound. I think the restoring force best applies to situations where you are comparing two different mediums (i.e. solid and liquid).

Hot air rises precisely because it is less dense. That's easy to see from PV=nRT if you rewrite it as n/V=P/(RT)=ρ

Yeah you're right. I didn't see it like that.