Understanding Sound and Bulk Modulus: Formula, Interplay, and Phase Dependence

[oracleoflight]

I am trying to understand what the formula v=sq rt( Bulk Modulus/density).

I understand that Bulk Modulus is indicative of a Pressure force and shows how much an object resists being compressed. So if we take a solid, it will have a greater Bulk Modulus than a liquid and so sound will travel faster through a solid. Sound also travels faster through a solid because the molecules are closer together.

Density is an intrinsic property of an object. Except for water, solids have the highest density and gases have the lowest because the molecules are concentrated over a smaller area in a solid.

However, I am having trouble discerning how both Bulk Modulus and density interplay with one another and if one of these terms predominated more than another in a given situation? Also, are both of these terms dependent on phases in anyway?

Thanks so much.

 

[sophiecentaur]

If you consider a very simplified model of a solid, consisting of a one dimensional line of masses, connected by springs. In a purely qualitative way, you could imagine how stiffer springs would pass a disturbance faster along the chain and larger masses would slow it down. You could obtain a given propagation speed with many different combinations of stiffness and mass.
Transfer that idea to a three dimensional structure and you have the modulus and density.
That's about as arm-waving as I can go!.