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Join Date: Sep 2009
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# Speed of Sound in Gases

03/01/2020 8:42 AM

Can anyone help me to calculate speed of sound in any gas without the use of the adiabatic index [or component]. If anyone can offer a formula it will be much appreciated.

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Guru

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#1

### Re: Speed of sound in gases

03/01/2020 10:39 AM

Sorry but the adiabatic constant of the gas is one of the necessary values for calculating the speed of sound in a gas. Now to determine the adiabatic constant one must know the degree of freedom for the molecular motion.

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Join Date: Sep 2009
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#2

### Re: Speed of sound in gases

03/01/2020 10:43 AM

Ian Purdie

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#3

### Re: Speed of sound in gases

03/01/2020 2:21 PM

The adiabatic index can be computed by the number of degrees of freedom, f, of a gas, where γ = (f+2) / f, so I suppose you could plug in f for γ in the formula for the speed of sound (if that counts ).

http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/souspe3.html#c1

"Since the adiabatic constant γ for a gas is the ratio of the specific heats as indicated above, it depends upon the effective number of degrees of freedom in the molecular motion. It can in fact be expressed as γ = (f+2)/f where f is the number of degrees of freedom in the molecular motion. For a monoatomic gas like helium, f=3 and γ = 5/3. For diatomic molecules like N2 and O2, you include two degrees of rotational freedom, so f=5 and γ = 1.4 . Since almost all of the atmosphere is nitrogen and oxygen, γ = 1.4 can be used for air in such calculations as the speed of sound. For polyatomic molecules, there are three degrees of rotational freedom and this along with the three translational degrees of freedom would give γ = 4/3. But in the specific heats of polyatomic molecules, there is evidence of contribution by vibrational degrees of freedom, and this would further reduce the value of γ."

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