Building Acoustics

Sound absorbers 193

When both lengths are relatively large and of equal size the absorption
characteristic is similar to the ones found for ordinary mineral wool products. By
decreasing values of Λ, however, the characteristic resembles the ones found for certain
types of plastic foam materials (see next section).

Figure 5.28 Normal incidence absorption factor of a porous material of 50 mm thickness with hard backing
predicted by the Allard/Johnson model. The curve parameter is the characteristic viscous length Λ (μm). Other
data are: r – 20000 Pa⋅s/m^2 , σ − 0.95, ks − 2.0, Λ′ − 100 μm.

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5.5.5 Models for materials having an elastic frame (skeleton)

The models are getting even more complicated where we cannot assume that the frame
stays motionless under the sound field impact. There will be a coupled motion of the
frame and the air in the pores, which may give pronounced effects in certain frequency
ranges. Up to now we have tacitly assumed that that there will be just one wave type
propagating in the medium, i.e. a compressional wave. Now we will have three types of
wave: two compressional waves denoted a fast and a slow wave, respectively, together
with a shear wave. These waves will have quite different properties depending on the
coupling between the fluid and the frame.
In common porous materials, where the fluid is air, there is a weak coupling
between the frame and the fluid. In the audio- and ultrasound frequency range one of the
compressional waves will mainly propagate in the air contained in the pores leaving the
frame motionless. The second one will propagate in both media, having a velocity
approximately equal to the velocity of a compressional wave in the frame situated in
vacuum. One then gets a situation where the motion or vibration of the frame results in a
corresponding motion of the air in the pores.
A movement in the air will, on the other hand, not affect the frame in the same way,
as the latter is much heavier. The air will move in the frame without affecting it. One
should then envisage that we could talk about an airborne and a frame-borne wave, but