# Does pressure affect the speed of sound in a solid?

1. May 2, 2004

### ShawnD

If I put a metal bar in a hydraulic press, will sound travel through the bar faster, slower, or the same speed as when the bar was not being crushed?

2. May 2, 2004

### arildno

I'd say it depends of whether the local Young's modulus changes as a result of the crushing procedure, since the (local) speed of sound should depend on the local density and Young's modulus values.
Don't know for a fact that the crushing procedure changes these values, but it seems rather likely..
(How it affects it specifically, I've no idea)

3. May 2, 2004

### VBPhysics

Funny I had a problem like this on my thermodynamics final.

Yes Presure affects the speed of sound(we'll call it u) in the material.
The equation follows

u^2 = d P/d Rho)s

The speed of sound squared is equal to the partial of Presure with respect to density at constant entropy.

4. May 2, 2004

### flexten

It does NOT change the velocity of sound more than say .01 %, and we can't get data or repeatability of material samples within this range so basically : NO.
( c^2=Y/rho). The speed of sound squared is equal to the Young's modulus divided by the density for isotropic solids. Of course if you run the press up until plasic flow then lots of things change; work hardening, grain structure, anisotropy, etc.
Or another way to say it: initial stress will not change the eigenvalues, it does pump up the potential energy but only by a static value. Then computing the peak stress we add them up. Linear Elasticity. From physical acoustics standpoint you could do as VBPhysics says and do non-linear, but it's second order the PV plot being pretty straight for solids in the linear range.
Would you do this isothermal or adiabatic ?