When is velocity of sound directly or inversely related to density?

[Jeff85]

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I've seen the fact that sound travels faster in water because it is more dense, but I've also seen the equation that v=B/p, where B=young's modulus and p=density.
When does that equation apply? Can someone shed some logic to that equation conceptually?

 

[RogueUnicorn]

The reasoning is quite complex from what I've seen, and involves bulk modulus and other things completely out of MCAT scope. Do know that across mediums, sound will travel faster in a denser medium (e.g. faster in solids than gases) but within a medium, less dense means faster sound (e.g. thin air has faster sound than thick air)

 

[Vanguard23]

I've seen the fact that sound travels faster in water because it is more dense, but I've also seen the equation that v=B/p, where B=young's modulus and p=density.
When does that equation apply? Can someone shed some logic to that equation conceptually?

Density actually slows the waves down. It just happens that denser mediums also happen to be more elastic. *that* is where the increased velocity comes in.
Sort of like in a circuit. Decreasing the resistance increases the power output, even though the equation is P= i^2R. The resistance decrease actually decreases the power output; the increase comes from the current increase, which compensates.

 

[lorenzomicron]

Just think of what sound is: a vibration through material that compresses and rarefracts. From a less physics point of view, it seems to make sense that sound, i.e. vibration, would proceed faster in a denser (closer packed) medium because the molecules need to move statistically less to transmit their vibration to the other discrete particles. The mathematics for this would involve the details of the bulk modulus B, which can be used to show that the pressure would be more than the density as B increases, thus ensuring a higher speed for a denser material.