Speed of sound as the sqrt(elasticity/density) and why it must always be < C

[pyrotix]

The question in the title. Speed of sound in a medium obviously must be less than the speed of light. Speed of sound is usually given by the equation sqrt(c/p). Wondering what causes this to always be less than the speed of light.

Gar. Just realized something as I'm typing this. Now that I think about it, in the relativistic limit the equation would be different. As the particles in the wavefront started moving at a speed close to the speed of light they would gain mass. As they approached the speed of light the density would approach infinity.

I think I'll try and derive out what the actual equation is.

Leaving this up here in case people have interesting comments.

 

[henry_m]

An interesting question this one. The particles traveling at relativistic speeds won't save you! Linear waves can have an amplitude as small as you like and still propagate at the same speed, so the speed of individual particles can be made tiny. As you say, you have to use full relativistic equations, and these will be important if you've got some really amazing equation of state with massive pressures or something. I'm not quite sure exactly what it is physically that'll save us. I guess the best way to work it out is to do perfect fluids first and see what happens. I might do a calculation later; I'll post what I find.

 

[pyrotix]

after thinking about it you're right. I got confused. The speed of particles depends on du/dt and can -> 0 without any effect on the c^2 term.

Maybe the trick is when doing the hooke's law derivation of the wave is to compensate for the fact that the "springs" do not react instantly but only at the speed of light.

Atlernately there might be some density elasticity dependency that saves you.

I'll think about it some more.