Does pressure affect the speed of sound in a solid?

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Discussion Overview

The discussion centers on the effect of pressure on the speed of sound in solids, particularly in the context of a metal bar subjected to a hydraulic press. Participants explore theoretical implications, mathematical relationships, and practical considerations regarding sound propagation under varying pressure conditions.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether sound will travel faster, slower, or at the same speed in a metal bar under pressure.
  • Another participant suggests that the effect on sound speed depends on whether the local Young's modulus changes due to the crushing, noting uncertainty about how this might specifically affect sound speed.
  • A different participant asserts that pressure does affect the speed of sound in materials, referencing a specific equation relating sound speed to pressure and density at constant entropy.
  • Another contributor argues that the change in sound velocity due to pressure is minimal (around 0.01%) and emphasizes that this change is not significant enough to yield reliable data. They discuss the implications of plastic flow and other factors like work hardening and anisotropy on sound speed.
  • There is a mention of linear elasticity and a question posed about whether the analysis should be conducted under isothermal or adiabatic conditions.

Areas of Agreement / Disagreement

Participants express differing views on the extent to which pressure affects sound speed in solids. While some acknowledge a potential effect, others argue that it is negligible. The discussion remains unresolved regarding the specific impact of pressure on sound speed and the conditions under which it may vary.

Contextual Notes

Participants highlight the dependence of sound speed on factors such as Young's modulus and density, and the discussion includes references to specific equations and conditions (isothermal vs. adiabatic) that may influence the outcomes. There is uncertainty regarding the changes in material properties due to pressure.

ShawnD
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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?
 
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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)
 
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.
 
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 ?
 

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