Helmholtz Solver Wave impedance boundary conditions

Numerical methods and mathematical models of Elmer
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CrocoDuck
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Helmholtz Solver Wave impedance boundary conditions

Post by CrocoDuck » 12 Aug 2016, 14:16

Hi guys, I just want to check a thing with you. Sorry I am bombarding the forums with questions but I find hard to grasp everything from tutorials and documentation, especially for Acoustics related problems. Once all of this will be clear to me I think I will try to contribute with tutorials and guides.

So, if a Boundary is made of a given material it has a specific acoustic impedance z measured in rayls. However, Elmer describes the wave impedance as Z, which has units of meters per second (see equation (9.6)). Specific acoustic impedance not only depends on the material but also on the wave, being, for example, rho * c for plane waves and a complex function of distance from source and frequency for spherical waves, in which the therm rho * c is still present, with rho the density of the medium and c the phase speed of sound.

I get that Z is impedance associated to wave propagation in a certain medium. As such, is it correct to obtain it from z by division by rho?

Z = z / rho

It makes sense given that the impedance Z for plane wave outlets appears to be c. Up to now I always used z straight into Z and got results that made sense to me, also if compared to other solvers. Probably the reason is that rho = 1.205 ~ 1 kg m^-3 for air at room temperature. I have started running my Comsol VS Elmer comparison again with Z = z / rho and that seems to be making the agreement even better, hinting that I am on the right track.

Am I right on this?

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