# In acoustics is there something analogous to skin depth in EM?

Hi all

The reflection and transmission of a pressure wave at a boundary depends on the relative impedance of the two media.

I'm pretty new to acoustics but the textbook I've been looking at doesn't seem to specify that the such calculations are only valid when the medium is at least a few wavelengths thick.

Surely the reflection at a boundary with a material less than a wavelength thick will be very different from that of a material many wavelengths thick? Is there a specific technical term for such things in acoustics? Is there an analogous concept to skin depth in acoustics?

Thanks

## Answers and Replies

Pythagorean
Gold Member
Good question! When I worked in infrasound we used a lot of optical concepts like "aperture" and did ray-tracing of acoustical waves (temperature profiles act as lenses). It looks like the acoustic viscocity boundary layer is analogous:

I've seen it else where called the viscous skin depth.

Bobbywhy
Gold Member
Here are two papers that may have answers for you:

Journal of Computational and Applied Mathematics
Volume 51, Issue 1, 30 May 1994, Pages 15–36
“The acoustic boundary layers: a detailed analysis”

Abstract:
The viscosity of the medium plays an important role in defining the characteristics of sound wave propagation in ducts. This effect, due to the difficulty of analysis, has been either completely neglected in the literature or considered only approximately.

Keywords:
Acoustics boundary layers; Duct acoustics; Viscosity effect; Propagation and attenuation of sound waves
http://www.sciencedirect.com/science/article/pii/0377042794900914

Here is a thorough analysis of the response of a thin parallel boundary layer over a non-rigid boundary to small perturbations. The small perturbations may be acoustic, but may also be small perturbations to an incompressible fluid:
http://www.damtp.cam.ac.uk/user/ejb48/files/brambley-2011-jfm.pdf [Broken]

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Thanks Bobbywhy and Pythagorean.. I am still digesting those papers. I see the matter is not trivial