[Doctor Kiki (OP)]

Why speed of sound is faster at high temperature?
for example,speed of sound at 20°C is faster than speed of sound at 0°C.
Anyone can please help me!!

[daveshorts]

One way of thinking about it is that the molecules in hot air are moving around faster so will expand quicker into an area of lower pressure. This means that a change in pressure will propagate faster, so the speed of sound is higher in hot air than cold air where the molecules have less energy and are moving more slowly.

[Mr Andrew]

The speed of sound is greater in colder air.  Just as sound travels faster in a solid than through air, it travels faster through the more dense air (colder) than the less dense air (warmer).  This has to do with the probability of collisions in relation to density...after all, pressure is the sum of many molecular collisions and sound is a pressure wave.  This is why the two cups on the ends of string works; the sound travels better through the solid string than through the air.

[daveshorts]

The speed of sound is greater in colder air.  Just as sound travels faster in a solid than through air, it travels faster through the more dense air (colder) than the less dense air (warmer).  This has to do with the probability of collisions in relation to density...after all, pressure is the sum of many molecular collisions and sound is a pressure wave.  This is why the two cups on the ends of string works; the sound travels better through the solid string than through the air.

No this is wrong

The speed of sound is greater in hot air.

The speed of sound c = √(p/ρ)  where p=pressure and ρ=density

if you increase the pressure you also increase the density so this has no effect on the speed of sound. But if you increase the temperature you increase the pressure without increasing the density so the speed of sound increases.

[lyner]

Mr Andrew is right.
The speed of sound in a gas increases with density, all other things being constant.
Demonstrated by the funny voice you get when you breathe Helium.
At atmospheric pressure, if you increase the temperature, the air will expand (unless you keep it in a container) so the density will decrease - so the speed of sound will decrease.
I think you have not really specified the conditions for your original statement. It depends on what you choose to keep constant.
We all know that the speed of sound is a lot less at low pressure -it's easier to 'break the sound barrier' at high altitude.

The speed of sound c = √(p/ρ)  where p=pressure and ρ=density

Where did this come from?

[daveshorts]

No I am afraid he isn't.

If you keep the pressure constant and alter the density of a gas without changing the temperature by altering the mass of the gas molecules  you can alter the speed of sound propagation, but the higher the density the lower the speed. To a pretty good approximation though at a constant temperature a gas will have a constant speed of sound whatever the pressure.

Where did this come from

sorry, technically c² = ∂p/∂ρ
but what I say still holds.

it is coming from the general result that a speed of wave propagation = sqrt(stiffness/density) which you can find by solving the wave equation.

http://en.wikipedia.org/wiki/Speed_of_sound

[lyner]

Yes, Daveshorts - you are right about that. I even got the helium thing wrong.
I was thinking of the higher speed in water and was extrapolating - dodgy.
Liquids are  more dense and the speed of sound is much higher. But it must be because there is a 'discontinuity' , once the gas becomes a liquid because the bulk modulus increases more than the density.

[Mr Andrew]

Wait...I thought the speed of sound followed directly from the KMT of gases?!  More dense means more collisions per unit time and thus faster propagation of sound!!!

[lightarrow]

Wait...I thought the speed of sound followed directly from the KMT of gases?!  More dense means more collisions per unit time and thus faster propagation of sound!!!

But it's not important if you have 1 or 100 particles colliding with a wall (for ex.); what counts is their speed: higher temperature --> higher speed.

[Mr Andrew]

So why does sound travel faster in solids and liquids than in gases?

[Bored chemist]

Because they are stiff.
The forces that hold them together are strong so, if they get pushed out of place, they spring back quickly and push or pull the next molecule quickly.

[lyner]

So why does sound travel faster in solids and liquids than in gases?

Imagine a Newton's cradle. The end ball moves away 'almost' instantaneously, when the first ball is hit.  This is like a solid - no gaps - just very resilient balls (molecules)
Now imagine a cradle with spaces between the balls. This is like molecules in a gas.
Say you left one ball out and spaced them out to cover the same distance as the first cradle- for a fair test.
After an impact, each ball would move away ' instantaneously'  but would have to travel, at the same speed as the original ball, across the gap to the next ball - then the next ball would move away. It would take longer for the impact to transmit from one end to the other along the cradle with the spaces because of the time to move across the gaps.
That's an analogy - Continuous line of balls - solid: line of balls with gaps - gas.

[Mr Andrew]

Ok, so a high temperature gas would be possibly just two balls...this would take much longer...I still don't get it.

[lyner]

My Newton's cradle thing is just to demonstrate the difference between solids - no gaps and  gases - with gaps.
If you want the complete kinetic theory explanation for sound transmission in gases, go to Wiki. The sums show it all happening.
Your 'more dense means more collisions' idea is not relevant. 
Two different gases at the same temp will have the same number of molecules per unit volume - the density will depend on the mass of the molecules. The more massive molecules will be traveling slower because both types will all have the same KE - that will mean the speed of the wave is less - they will take longer to communicate with the adjacent molecules..
To be totally convinced, you'll have to follow the sums, which include all the factors.

[daveshorts]

The newton's cradle is quite a nice analogy
 
If you have a newton's cradle with large gaps, the time it takes for the energy to move will be proportional to the speed the balls are moving at not the number of the balls, as the the huge majority of the time is spent with the balls moving, the impacts are essentially instantaneous and don't make a lot of difference because in a gas they don't move the energy much further on.

So the speed of sound is related to the speed of the molecules not their density.

[lyner]

Can't agree there - the total distance that needs to be covered by each flying ball is very much dependent upon how many balls there are in the cradle and how much total space there is  in between them. This is because the speed of the first ball is whatever you give it and the others are stationary. If there were only one ball, the whole distance would have to be covered by a flying ball  while, if only one ball were missing, the total distance for 'ball-flight' would only be 1/nth. So the propagation speed would be influenced by the 'density' in that case.
I don't think that the newton's cradle is a good enough model to analyse sound through a gas unless the balls were already vibrating.  In any case, it doesn't model an ideal gas at all - infinitely small molecules etc.
It serves well to show the difference between solid and gas, tho.

[jben]

Two facts about sound I did not see reflected in this discussion string: Air is a compressible medium, whereas water, steel, and other solids are not. Also, air molecules don't travel: the wave energy does the molecules move back and forth the sound wave reciprocation, bumping up against the molecules nearest to them. Yes, sound travels faster in warm air than in cold air, but it travels farther in cold air.
Due to the increased elasticity of the air in warm temperatures, there is more attenuation over a certain distance than in cold air. In other words, the rarefaction at higher temperatures of the medium dampens the travel of the energy wave, especially with sound of shorter wavelengths, i.e., higher frequencies. Also, sound waves are not sinusoidal, but alternating fronts of compression and rarefaction. This is why the Doppler effect works: the pitch of an approaching source of sound is higher than the pitch of the same source standing still, because the speed of the approach compresses the air ahead of it, thus bringing the alternating pressure bands closer, thus shortening the wavelength, thus raising the pitch.
Another thing to consider, is that hot air with moisture is a more efficient transfer medium for sound, since water is an uncompressible medium, which reduces the attenuation normally due to dry air's higher compressibility.
One more thing: if liquids and solids were compressible like air, then ultrasound would not work at all. Definition high enough to form imagery requires very short wavelengths, which require high medium density, which air at any temperature simply does not have.

[Bored chemist]

Two facts about sound I did not see reflected in this discussion string: Air is a compressible medium, whereas water, steel, and other solids are not.

You missed it.

speed of wave propagation = sqrt(stiffness/density)

The stiffness is the inverse of the compressibility.
Also, since sound travels in solids and liquids they are compressible.
Not easily- and that's why the speed of sound in them is high.