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### Author Topic: Why speed of sound is faster at high temperature?  (Read 44711 times)

#### Doctor Kiki

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##### Why speed of sound is faster at high temperature?
« on: 19/11/2007 22:46:49 »
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.

#### daveshorts

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##### Why speed of sound is faster at high temperature?
« Reply #1 on: 19/11/2007 23:26:42 »
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

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##### Why speed of sound is faster at high temperature?
« Reply #2 on: 20/11/2007 03:51:26 »
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

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##### Why speed of sound is faster at high temperature?
« Reply #3 on: 20/11/2007 11:30:29 »
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.

« Last Edit: 20/11/2007 11:33:39 by daveshorts »

#### lyner

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##### Why speed of sound is faster at high temperature?
« Reply #4 on: 20/11/2007 13:01:24 »
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.
Quote
The speed of sound c = √(p/ρ)  where p=pressure and ρ=density
Where did this come from?

#### daveshorts

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##### Why speed of sound is faster at high temperature?
« Reply #5 on: 20/11/2007 13:13:06 »
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.

Quote
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
« Last Edit: 20/11/2007 13:16:07 by daveshorts »

#### lyner

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##### Why speed of sound is faster at high temperature?
« Reply #6 on: 20/11/2007 14:12:08 »
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

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##### Why speed of sound is faster at high temperature?
« Reply #7 on: 20/11/2007 16:55:01 »
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

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##### Why speed of sound is faster at high temperature?
« Reply #8 on: 20/11/2007 18:27:06 »
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

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##### Why speed of sound is faster at high temperature?
« Reply #9 on: 20/11/2007 19:15:33 »
So why does sound travel faster in solids and liquids than in gases?

#### Bored chemist

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##### Why speed of sound is faster at high temperature?
« Reply #10 on: 20/11/2007 19:36:33 »
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

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##### Why speed of sound is faster at high temperature?
« Reply #11 on: 20/11/2007 22:05:35 »
Quote
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

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##### Why speed of sound is faster at high temperature?
« Reply #12 on: 20/11/2007 23:39:51 »
Ok, so a high temperature gas would be possibly just two balls...this would take much longer...I still don't get it.

#### lyner

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##### Why speed of sound is faster at high temperature?
« Reply #13 on: 21/11/2007 10:22:27 »
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

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##### Why speed of sound is faster at high temperature?
« Reply #14 on: 21/11/2007 10:30:31 »
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

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##### Why speed of sound is faster at high temperature?
« Reply #15 on: 21/11/2007 18:25:33 »
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.
« Last Edit: 21/11/2007 18:27:29 by sophiecentaur »

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##### Why speed of sound is faster at high temperature?
« Reply #15 on: 21/11/2007 18:25:33 »