## Topic: Velocity of sound and air density (Read 5098 times)previous topic - next topic

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Velocity of sound and air density
##### 23 May, 2013, 09:35:12 PM
Having started at the beginning, there are plenty of articles quoting the velocity of sound at sea level, and how the velocity of sound increases due to temperature rise and the corresponding reduction air density. Not being entirely happy with this concept I have found another view point.
http://www.sengpielaudio.com/calculator-speedsound.htm
I’m thinking that the latter is probably correct.
Please correct me if this is not so.
Paul

apologies if this is not the correct forum

• saratoga
Velocity of sound and air density
##### Reply #1 – 23 May, 2013, 09:48:30 PM
Having started at the beginning, there are plenty of articles quoting the velocity of sound at sea level, and how the velocity of sound increases due to temperature rise and the corresponding reduction air density. Not being entirely happy with this concept I have found another view point.
http://www.sengpielaudio.com/calculator-speedsound.htm
I’m thinking that the latter is probably correct.
Please correct me if this is not so.
Paul

The speed of sound depends on density, and the ideal gas law says that PV=nRT.  So yes, it depends on both pressure (P) and temperature (T).

Why do you care?  Planning on building spacecraft or listening to music in a cryotank?  Usually the speed is quoted at room temp and sea level, since thats about where most people live.

Velocity of sound and air density
##### Reply #2 – 23 May, 2013, 09:56:22 PM
Having started at the beginning, there are plenty of articles quoting the velocity of sound at sea level, and how the velocity of sound increases due to temperature rise and the corresponding reduction air density. Not being entirely happy with this concept I have found another view point.
http://www.sengpielaudio.com/calculator-speedsound.htm
I’m thinking that the latter is probably correct.
Please correct me if this is not so.
Paul

The speed of sound depends on density, and the ideal gas law says that PV=nRT.  So yes, it depends on both pressure (P) and temperature (T).

Why do you care?  Planning on building spacecraft or listening to music in a cryotank?  Usually the speed is quoted at room temp and sea level, since thats about where most people live.

My thinking was going along the lines that if velocity increases with rarity, then taken to the nth degree.....but not so simple eh

• Rotareneg
Velocity of sound and air density
##### Reply #3 – 23 May, 2013, 10:01:31 PM
Quote
For a given ideal gas the sound speed depends only on its temperature. At a constant temperature, the ideal gas pressure has no effect on the speed of sound, because pressure and density (also proportional to pressure) have equal but opposite effects on the speed of sound, and the two contributions cancel out exactly
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• drewfx
Velocity of sound and air density
##### Reply #4 – 24 May, 2013, 02:24:07 PM
If you take the formula given in the link:

c=(γ*p/ρ)1/2

and combine it with:

pV=nRT

you end up getting T and a bunch of constants:

c=(γ*R*T/M)1/2

where
γ = the adiabatic constant, characteristic of the specific gas (about 1.4 for air).
R = the Ideal Gas Constant (8.3144621)
T = temperature in °K
M = the Molecular mass (about .02896 kg/mol for air)

[EDIT: oops, I transcribed things wrong -

M is given in kg/kmol which is ~28.96 for air, but I wanted kg/mol so I divided by 1000. But I should have done that in the formula:

c=(γ*R*T*1000/M)1/2

]