The Speed of Sound: Exploring Temperature's Effect

[cobrastrike]

Speed of sound!

Why does sound travel faster through warm air then cold air?
-_-

 

[Vagn]

Why does sound travel faster through warm air then cold air?
-_-

If something is warm then it has a higher temperature, this means that the average kinetic energy of a molecule is higher, i.e. the gas particles are moving faster.

If they are moving faster, then they cover a greater distance, and so are more likely to collide, which allows sound to travel quicker, as all sound is, is an increase and decrease of the local pressure.

 

[Archosaur]

Err... I'm pretty sure sound travels faster in cold air.

For the same reason sound travels faster in iron; cold air is denser than hot air.

 

[JaredJames]

For every 1 degree celsius the temperature increases, the speed of sound increases by 0.6m/s.

 

[Archosaur]

I stand corrected. I suppose I should have done a little googling before posting.

But I think this is a more complicated problem than we're giving it credit. The speed of sound through a medium is directly proportional to the density and temperature of the medium, but density and temperature are inversely proportional to each other. But, if what I'm hearing is right, the increase in molecular velocity outweighs the decrease in speed.

 

[nasu]

The speed of sound decreases when the density increases.
This is generally true for all kind of media, gas, liquid, solid.
The speed increases with increased stiffness of the medium. For fluids this stiffness is usually measured by the bulk modulus; for solids by Young's modulus.
The reason sound propagates faster through metals even though they are denser than gases is that they can support larger restoring forces (they are stiffer).

 

[cobrastrike]

Thanks ppl!

 

[LURCH]

For every 1 degree celsius the temperature increases, the speed of sound increases by 0.6m/s.

...so long as pressure remains constant. My understanding of the theory would suggest that heating up air in an airtight enclosure (so that pressure increases according to Boyle's Law) would yield a much higher increase in the speed of soundwaves. Does anyone know of any experiments of this sort? Just want to make sure I've got the theory right.

 

[Archosaur]

The speed of sound decreases when the density increases.

What? Why is that? I see how "stiffness" would certainly carry sound faster, but I don't follow on this point.

EDIT: Ok, I got it. http://www.ndt-ed.org/EducationResources/HighSchool/Sound/speedinmaterials.htm" .

 

[cjl]

I stand corrected. I suppose I should have done a little googling before posting.

But I think this is a more complicated problem than we're giving it credit. The speed of sound through a medium is directly proportional to the density and temperature of the medium, but density and temperature are inversely proportional to each other. But, if what I'm hearing is right, the increase in molecular velocity outweighs the decrease in speed.

Actually, for an ideal gas, the speed of sound is largely independent of density, and it is proportional to the square root of the temperature.

 

[sophiecentaur]

Actually, for an ideal gas, the speed of sound is largely independent of density, and it is proportional to the square root of the temperature.

If you think of the time needed for one molecule to travel to the neighbouring molecule and then to transfer its momentum (crude mechanical idea but sufficient for this purpose). This tells you the speed at which the 'influence' of vibrations can pass through the air will increase as the molecules travel faster. If the gas density increases then a molecule will meet another molecule in a shorter time but that molecule will need to travel again before it meets a third molecule. The time for the actual 'influence' to travel over a certain distance will, thus, only depend upon the average speed of molecules and not how close they are together.

Furthermore, for solids, the speed of sound depends upon the stiffness (modulus) and the density. Faster for stiffer, slower for more dense. For two substances with the same stiffness, the more dense one will transmit sound slower. If this is counter-intuitive, it's because our experience is that more dense materials are usually / often more stiff.

 

[nowhat]

Hey guys just did some algebraic calculation and got a strange conclusion.

since speed of sound is related to speed of molecule, we can assume they are proportional to each others. Then, according to kinetic theory equation,

pV = 1/3 NMc ...(1)

where c is the rms speed of air molecules, N is number of air molecules, M is mass of each air molecule. i.e. NM = total mass of the gas

please notice that density of air = mass/volume, i.e. ρ = NM/V , where ρ is density
therefore, by rearranging the equation,

c = 3p/ρ

which basically means that the speed of molecule is inversely proportional to density, assuming change in pressure is negligible, which is against most of the arguments above.

 

[mfb]

If you increase the density with constant pressure, you cool the gas (or replace it by a gas with heavier molecules). A lower temperature gives a lower speed of sound. Where is the problem?

 

[Bob S]

Where is the problem?

the problem is, what is A above middle C? Concert pitch should (?) depend on ambient temperature.

 

[mfb]

As long as all instruments in the concert are roughly at the same temperature, this shouldn't be a big problem. A (large!) temperature difference of 5°C would be a relative change of ~1.5% of the absolute temperature, while the half-steps are about +-6% at the frequency.

 

[sophiecentaur]

But strings don't behave like wind instruments.

 

[cjl]

Hey guys just did some algebraic calculation and got a strange conclusion.

since speed of sound is related to speed of molecule, we can assume they are proportional to each others. Then, according to kinetic theory equation,

pV = 1/3 NMc ...(1)

where c is the rms speed of air molecules, N is number of air molecules, M is mass of each air molecule. i.e. NM = total mass of the gas

please notice that density of air = mass/volume, i.e. ρ = NM/V , where ρ is density
therefore, by rearranging the equation,

c = 3p/ρ

which basically means that the speed of molecule is inversely proportional to density, assuming change in pressure is negligible, which is against most of the arguments above.

I'm not sure where you got that equation, but it appears to be missing something. The speed of the molecules should be proportional to the square root of p/ρ, rather than directly proportional. My guess is that your equation (1) should have a c² rather than simply c. Also, you can't change the density without changing the pressure unless the temperature is also changed, and if you rearrange the density form of the ideal gas equation (P = ρRT), you'll find that T is proportional to P/ρ, so stating that the speed of sound is proportional to the square root of P/ρ (which is the correct relation) is identical to stating it is proportional to the square root of the temperature, as the only way you can change either P or ρ independent of each other is by changing the temperature (for an ideal gas).

 

[cjl]

But strings don't behave like wind instruments.

But the instruments all tune (using the same reference) at the beginning of the concert, so it doesn't really matter. Honestly, it doesn't even matter if the reference is perfectly on 440 Hz or not, so long as they're all tuned to the same reference (and as long as the reference is fairly close to correct).