Re: How does sound travel faster in a less dense medium and fastest in solids?

This situation seems odd at first, but happens because the velocity depends
on two different properties of a material, one being the density but the
other is a material's "elasticity" or tension.  There is a pretty good
description of this at the "Physics Classroom" Lesson on Sound 
( http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/u11l2c.html
) 
and a brief discussion about this in a different MadSci question 
( http://www.madsci.org/posts/archives/may2002/1021570053.Ph.r.html
).  

Generally, sound speed depends on elasticity and density according to:

	(velocity)^2  =   "elasticity" / "density".   

Where the elasticity of an object is similar to how tension in a string
alters the frequency of the sound that the string will produce.  For the
same tensions, strings made out of different materials (therefore different
densities) will have different sounds.  Similarly, for materials that have
a similar elasticity, the sound velocity will depend inversely on the
material's density.

Solids are held together by significantly stronger forces than liquids,
which give solid objects their characteristic property of a definite shape.
 Liquids, though their shape is somewhat easier to change, still have
inter-atomic forces holding the material together.  The molecules of a gas,
however, are not bound at all to each other.  This gives rise to a very
large spread in elasticity between solids, liquids, and gases.  I couldn't
find a good, numerical reference, but here are a few numbers I found,
measured in terms of pressure (psi):

	Solids ( http://www.engineeringtoolbox.com/young-modulus-24_773.html
):
		Iron	~ 1 x 10^7
		Steel ~ 3 x 10^7
		Aluminum ~1 x 10^7

	Liquids ( http://www.engineeringtoolbox.com/bulk-modulus-elasticity-21_585.html
)
		Gasoline ~ 2 x 10^5
		Mercury ~ 4 x 10^5
		Water ~ 3 x 10^5

You can see that these liquids have about 100 times less elastic strength
than the solids, but the values for different solids are roughly the same
as are those for different liquids.  This large jump in elasticity makes it
so that the velocity of sound in solids is generally greater than in
liquids, which are both greater than that in gases, regardless of density.

For a more mathematical derivation of a wave’s relationship with a
materials density and elasticity, take a look at “Physics for Scientists
and Engineers” by Fishbane, Gasiorowics, and Thornton (pgs 380-385).

Eric Gauthier