Speed of sound in sodium at absolute zero?

[quarky2001]

I don't need help with a numerical solution here - mostly a concept check.

I've been asked to calculate the speed of sound in metallic sodium at T = 0 K using Fermi-Dirac statistics.

After doing so, I get a speed of 14.5 meters per second, which is, well, really slow.

I would have expected sound to travel much more quickly than in air at that temperature. Is my answer likely to be right? If so, could someone explain why the result is so counter-intuitive?

 

[espen180]

From what I have read, the speed of sound is roughly proportional to the speed of the molecules if it is a gas. I think it is intuitive to assume that the speed of sound is dependent in a similar fashion to the vibarational states of the molecules in a solid, and thus increase with increasing temperature.

For the air comment, remember that at T=0K, air cannot exist. Everything is a solid at T=0, right?

 

[quarky2001]

Ah, I suppose that makes sense. Thanks.