Speed of sound question

[mariposas905]

Advertisement - Members don't see this ad

What does this mean?

"sound travels faster in medium that is more resistant to compression."
"sound travels slower in medium with greater density."

Aren't those two contradicting each other because a medium that is more resistant to compression (like a solid) would also have greater density (solids have more density than liquids or gases)??

 

[Altius Premier Tutor]

Hi @mariposas905. I am a current Altius tutor starting medical school this fall and took the MCAT last June. The speed of sound in different mediums is related to the stiffness/rigidity and density of the medium. The more rigid or stiff a medium, the faster the sound waves through the medium. This is due to individual molecules within the medium having strong IMFs between them. This is why sound waves travel faster in a solid compared to a gas. A more dense medium will result in slower sound waves. Density can be related to inertia so something that is more dense has more inertia and so harder to propagate the mechanical sound waves. Now the equation that relates both of these factors is v = sqrt(B/rho) where B is the bulk modulus of the material aka how stiff it is and rho is the density of the medium. Now, to get to your question about the contradiction, the bulk modulus is usually the factor that affects the velocity more. So with your example with solid (a piece of metal) vs gas (air) with a solid, you would expect higher bulk modulus so higher velocity but also higher density which would indicate lower velocity but your bulk modulus overpowers the density increase which is why the piece of metal would have faster sound waves. Hope this helps! Feel free to private message if you need further clarification!