Re: [Phys-l] speed of sound

[John Mallinckrodt <ajm@csupomona.edu>]

>          The temperature correction is to first order independent  
> of the
> gas used:
> V(T) = V + 0.606T
>          Where V is the speed at a known temperature and T is the
> difference in temperature between that temperature and temperature  
> wanted
> in Celsius.

That's incorrect.  The empirical formula given above will work near 0  
degrees Celsius for a gas whose speed of sound is 331 m/s at 0  
degrees Celsius, e.g. air, but not for arbitrary gases or for  
arbitrary reference temperatures.

To a good degree of approximation, within a somewhat restricted range  
of temperatures and frequencies, the speed of sound in a gas is  
proportional to the square root of the absolute temperature.  This  
would seem to apply to the case you are describing, so you should be  
able to use

    v(T) = v(T_ref)*sqrt(T/T_ref)

[Note that 331*sqrt(274/273) = 331 + 1*(.606), that 331*sqrt(283/273)  
= 331 + 10*(.601), and that 331*sqrt(303/273) = 331 + 30*(.590)]

John Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://outlawsofphysics.com>




> Gary
>
>
> At 02:27 PM 4/16/2007 -0400, you wrote:
> > I know how the speed of sound varies with temperature in air, and am
> > wanting the speed of sound in carbon dioxide. I've searched the  
> > web with
> > no luck. Only found the speed to be 258 m/s at 0 °C. Wanted to  
> > know other
> > values for a speed of sound lab I'm trying soon (with water,  
> > tuning fork,
> > Alka-Seltzer, etc.).
> >
> > Can someone guide me to a web site or a formula for the speed of  
> > sound in
> > CO2 from 0 °C to 100 °C? I don't have a CRC Handbook, but am  
> > wondering if
> > this book might have the information I need.
> >
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>
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A. John Mallinckrodt                 mailto:ajm@csupomona.edu
Professor of Physics                 http://www.csupomona.edu/~ajm
Physics Department                 office:  Building 8, Room 223
Cal Poly Pomona                      voice:  909-869-4054
Pomona, CA 91768-4031       fax:  909-869-5090