🚀 go-pugleaf

Most of the formulae I have seen posted here for the speed of sound in 
air are wrong.  In fact, some of them are not even dimensionally 
correct.  

Here's what Resnick and Halliday (a well-known freshman physics text) 
have to say.  

The formula for the speed of sound in an elastic medium (either liquid 
or gas) is 

		c = sqrt (B/rho) 

where B is the bulk modulus of the material (the ratio of the change 
in pressure to the resulting fractional change in volume) with units 
of newtons/m^2 or, equivalently, kg/(m.sec^2), and rho is the density 
with units of kg/m^3.  

If the material is a solid, the formula is quite similar, but the bulk 
modulus is replaced by Young's modulus Y.  

Therefore, the more dense the material, the slower the speed of sound.  
Also, the higher the bulk modulus the more difficult it is to compress 
the material and the higher the speed of sound.  So the people who have
said that the speed of sound depends on the density of the air are
correct, but that is not all there is to it.  The bulk modulus of air
also varies and must also be considered.  

For an ideal gas, the formula for the speed of sound is given by 

		c = sqrt(gamma*P/rho) 

where it is assumed that the passage of a sound wave through a gas is 
an adiabatic process.  Here, gamma is the ratio of specific heats 
(Cp/Cv), P is the pressure, and rho is the density.  Except of course
for the factor gamma, this formula could have been derived by using a
simple dimensional analysis. 

Let us now look at the well-known ideal gas formula: 

		PV = nRT 

where n is the number of moles enclosed in a volume V, T is the absolute
temperature in Kelvin (K), and R is the universal gas constant, units 
of joules/(mole*K).  Solving for P gives 

		P = (n/V)RT 

The factor n/V is the number of moles per cubic meter.  Substituting 
this into the formula for the speed of sound in a gas, we get 

		c = sqrt( gamma*(n/(V*rho))RT ) 

The factor n/(V*rho) is simply the inverse of the molecular weight of 
the gas (MW), so the formula for the speed of sound in a gas is 

		c = sqrt( gamma*R*T/(MW) ) 

The ratio of specific heats is for all practical purposes a constant.  
R is a universal constant of nature, so the speed of sound depends 
only on the absolute temperature and on the molecular weight of the 
gas.  

Since the temperature of the air decreases with altitude in the 
troposphere, the speed of sound decreases with altitude.  

Hope this helps.  

Joe Baugher			**************************************
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