Speed of sound in sodium at absolute zero?

In summary, the conversation discusses the calculation of the speed of sound in metallic sodium using Fermi-Dirac statistics at T=0K. The result is found to be surprisingly slow and the question is raised about its accuracy. The relationship between the speed of sound and the speed of molecules in gases and solids is also mentioned. It is pointed out that at T=0K, air cannot exist and everything is a solid.
  • #1
quarky2001
34
0
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?
 
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  • #2
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?
 
Last edited:
  • #3
Ah, I suppose that makes sense. Thanks.
 

1. What is the speed of sound in sodium at absolute zero?

The speed of sound in sodium at absolute zero is approximately 0 meters per second. At this temperature, the particles in sodium are not moving and therefore cannot transmit sound waves.

2. How is the speed of sound in sodium affected by temperature?

The speed of sound in sodium is directly proportional to temperature. As temperature increases, the particles in sodium have more kinetic energy and can vibrate faster, resulting in a higher speed of sound.

3. What factors affect the speed of sound in sodium?

Aside from temperature, the speed of sound in sodium is also influenced by the density and elasticity of the material. These properties determine how quickly sound waves can travel through a substance.

4. How does the speed of sound in sodium compare to other materials?

The speed of sound in sodium is relatively low compared to other materials, such as solids like steel and liquids like water. This is due to the relatively low density and elasticity of sodium.

5. Is the speed of sound in sodium the same at all temperatures?

No, the speed of sound in sodium varies depending on temperature. As temperature increases, the speed of sound in sodium also increases. However, at extremely low temperatures approaching absolute zero, the speed of sound approaches zero as well.

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