Why is velocity of sound inversely proportional to square r

AI Thread Summary
The velocity of sound is influenced by the medium through which it travels, with sound propagating faster in solids due to closely packed molecules that facilitate rapid collisions. The relationship between sound velocity and density is mathematically expressed as being inversely proportional to the square root of density. This means that as density increases, the speed of sound decreases. For a deeper understanding, mathematical derivations can be found through online resources. The discussion emphasizes the need for a mathematical basis to explain this relationship.
Ajit Kumar
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A. Sound is nothing more than a local disturbance whose propagation is facilitated by the collisions between particles

B. The distances between molecules in solids are very small, i.e., solids are more dense - as compared to liquids and gases. Because they are so close, than can collide very quickly.

So why is velocity of sound inversely proportional to square root of density?
 
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You want a reason for a mathematical relationship so the derivation must be mathematical. A search on Google for Speed of sound derivation gives many hits. This link seems to look OK.
 

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