# The Naked Scientists Forum

### Author Topic: Why does sound travel more slowly in colder air?  (Read 1488 times)

#### chris

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##### Why does sound travel more slowly in colder air?
« on: 08/03/2014 15:07:18 »
Colder air conducts sounds more slowly than warm air. Intuitively one might think that it would be the other way around, since colder air is denser air, and denser media, like water, or metal, conduct sounds far more rapidly than air...?

#### RD

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##### Re: Why does sound travel more slowly in colder air?
« Reply #1 on: 08/03/2014 16:11:43 »
The denser the gas the more molecular collisions will occur per unit length.
Collisions of gas molecules will result in spinning the molecules to some degree rather than exclusively passing-on rectilinear motion.
So the more collisions the more energy is "wasted" on spinning molecules rather than transmitting the sound energy rectilinearly : the straight-line speed is reduced as a consequence of any rotation, (conservation of momentum).
So the denser the gas the slower the speed of sound because of the greater number of collisions per unit length and consequently the more energy wasted in spinning molecules   [ I think [?] ].
« Last Edit: 08/03/2014 16:27:19 by RD »

#### evan_au

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##### Re: Why does sound travel more slowly in colder air?
« Reply #2 on: 10/03/2014 15:08:41 »
As I understand it, the average energy of gas particles is proportional to temperature (temperatures measured in degrees absolute).

The kinetic energy* of one gas molecule is E=1/2mv2

This means that the average velocity of the gas molecule v is proportional to the square root of the temperature.

Quote from: Wikipedia
Sound generally travels at about 70% of the mean molecular speed in gases

Thus the speed of sound in air is roughly proportional to the square root of temperature (see green curve); the lower the temperature, the slower the speed of sound.

*The total thermal energy of diatomic gases like O2 and N2 is slightly more than the kinetic energy of the molecules, as various rotational and vibrational modes also share the energy. But these extra modes don't contribute to linear propagation of sound waves.

More details at: http://en.wikipedia.org/wiki/Speed_of_sound#Practical_application_to_air
« Last Edit: 10/03/2014 19:36:33 by evan_au »

#### alancalverd

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##### Re: Why does sound travel more slowly in colder air?
« Reply #3 on: 10/03/2014 17:58:18 »
The speed of a compression wave c=sqrt(K/d) where K is the elastic modulus of the medium and d is its density. The initial observation that water and metals are 3 - 10,000 times denser than air is obviously correct but their elastic modulus ("stiffness") is even greater, so sqrt(K/d) is 5  - 10 times that for air.

Cold air has similar compressibility to warm air but a greater density, so c decreases with temperature at constant pressure.

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##### Re: Why does sound travel more slowly in colder air?
« Reply #3 on: 10/03/2014 17:58:18 »