Timeline for Why are sound waves adiabatic?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 19, 2016 at 14:02 | history | edited | Greg Lyons | CC BY-SA 3.0 |
Corrected a sign error in the equations.
|
| Mar 18, 2016 at 21:17 | history | edited | Greg Lyons | CC BY-SA 3.0 |
Fixed grammar.
|
| Mar 18, 2016 at 20:40 | history | edited | Greg Lyons | CC BY-SA 3.0 |
Edited to formally correct the previous mathematical argument about the conduction being negligible.
|
| Mar 18, 2016 at 20:25 | comment | added | Greg Lyons | The equation is the inviscid Fourier-Kirchhoff-Neumann energy equation for quasi-static processes and constant thermal conductivity. You're right about this lhs - rhs business, though, and I'm editing now. | |
| Mar 18, 2016 at 20:07 | history | edited | Greg Lyons | CC BY-SA 3.0 |
Included mention of attenuation at high frequency and improved citation.
|
| Mar 18, 2016 at 20:06 | comment | added | Thomas | Actually, I just noticed that there is something wrong with your equation (it violates the second law). Should be $(\nabla T)^2$. What I meant is: You write ".. make the rhs negligible to the left ..", but this does not make sense, there is an = sign. What you mean is that the lhs (=rhs) is small compared to $\rho T s/T_P$, where $T_P$ is the period. | |
| Mar 18, 2016 at 16:21 | comment | added | Greg Lyons | 2) Absolutely, the effects of attenuation from viscosity and conduction, as well as molecular relaxation, are typically dominant in the supposed isothermal regime. But this isn't altogether obvious physically (at least not to me) and requires a lot more work to show. I think it should be included as an edit, though. | |
| Mar 18, 2016 at 16:10 | comment | added | Greg Lyons | 1) Not sure I'm clear on your meaning. For linear acoustics those quantities will be equal in magnitude, since advection is second order. $\kappa$ is thermal conductivity above. The formal argument I'm familiar with proceeds by linearizing the equation and then assuming harmonic waves. | |
| Mar 18, 2016 at 15:54 | comment | added | Thomas | Veru good: Two minor comments. 1) Last sentence. Obviously the lhs is equal to the rhs, What you mean is that the time averaged value of $ds/dt$ is small compared to $\omega s$. 2) For standard sound waves large $\kappa$ does not make them isothermal, it makes them strongly damped. There are some cases where you can achieve large heat transport without dissipation, for example radiative transport in space plasmas. | |
| Mar 18, 2016 at 2:01 | comment | added | Greg Lyons | You can thank my acoustics professor for drilling that one into my head. I'm drawing from Allan Pierce's book, Acoustics: An Introduction to Its Physical Principles and Applications, Chapter 1, Section 10 specifically. It's a great text, but can be difficult if you don't have a mathematical background. Fundamentals of Acoustics by Kinsler et al. is maybe more accessible, but I don't know if it contains this discussion. | |
| Mar 18, 2016 at 1:51 | comment | added | user109867 | Thanks a lot for the really good answer, just what I was looking for. Do you have a source for details? I'm really interested. | |
| Mar 18, 2016 at 1:49 | vote | accept | CommunityBot | ||
| Mar 18, 2016 at 1:16 | history | answered | Greg Lyons | CC BY-SA 3.0 |