Speed of Sound Formula [v=sqrt (B/p)]

[blazinfury]

I am trying to understand the speed of sound formula [v=sqrt (B/p)] where v= speed of sound; B=restoring force/molecular Kinetic energy; p= molecular inertia/density. Sound travels fastest through solids than liquids and gases. Aren't solids denser than the other phases (except for water where liquid is denser than ice)? If so, then shouldn't denser materials transmit sound better? Also, what does the Restoring Force variable (B) represent on a molecular level and how should I think about it conceptually to make sense? Thanks.

[Crimson Sunbird]

[latex]B[/latex] is a quantity called the bulk modulus of the material through which the sound is travelling; it is a measure of the material’s resistance to uniform compression and is defined by

[latex]B=-V\frac{\mathrm dp}{\mathrm dV}[/latex]

where [latex]V[/latex] is volume and [latex]p[/latex] is pressure. Think of it as the (infinitesimal) ratio of the increase in the external pressure applied to the relative decrease in volume produced.

Edited February 18, 2013 by Crimson Sunbird

[Enthalpy]

Solids use to be slightly denser than liquids but seriously stiffer (bulk modulus), and this makes for faster sound.

 

For one same compound, all those I can think of are stiffer when solid.

 

Even with different compounds: few liquids are stiffer than some solids. I spent weeks searching both for technological uses, and they're scarce. You get ~4GPa from liquid glycerine if not too hot nor wet and ~0.7GPa from some silicone rubbers, while (solid) ceramics achieve 500GPa.

 

This is at 1 atm pressure. Stiffness increases with pressure, logically enough - as you don't expect shrinkage to zero volume at a finite pressure. 300b, a typical pressure for hydraulics circuitry, are enough to raise the bulk modulus by 30% for instance. Temperature and impurities matter also, like salt in sea water (important for the path of sonar waves due to refraction), and of course bubbles.