Civil Engineering Reference
In-Depth Information
Ta b l e 6 . 1
Values of parameters
α
∞
,
ρ
1
,
σ
,
φ
,
N
and
ν
for the glass wool 'Domisol
Coffrage'.
Tortuosity
Density
Flow
Porosity
Shear
Poisson
α
∞
φ
of frame
resistivity
modulus
coefficient
ρ
1
σ
N
ν
(kg m
−
3
)
−
4
s)
(N cm
−
2
)
(
1
·
06
130
·
0
40 000
0
·
94
220(1
+
j0
·
1)
0
The bulk modulus
K
f
of the air in the fibrous material,
G(ω)
, and the parameters
P
,
Q
and
R
are evaluated using Eqs (5.38), (5.36), (6.28), (6.27) and (6.26), respectively. The
subscripts
a
and
b
will be used to specify the quantities related to the airborne wave and
the frame-borne wave. At high frequencies, for the airborne wave, the ratio
µ
a
of the
velocities of the frame and the air is
µ
2
given by Equation (6.71), and the wave number
is
δ
2
given by Equation (6.68). At frequencies lower than 495 Hz, the airborne wave is
related to
µ
1
and
δ
1
.
The quantity
|
|
is larger than 40 for frequencies higher than 50 Hz. The velocity
of the frame is negligible, compared with the velocity of the air, and this wave is very
similar to the one that would propagate if the material were rigidly framed. The wave
number
k
a
is represented in Figure 6.6. The wave number
k
a
for the same material with
a rigid frame is given by
µ
a
ω
ρ
22
R
1
/
2
k
a
=
(6.86)
50
40
30
Re
k
a
20
10
0
−
10
−
20
Im
k
a
−
30
−
40
0
0.25
0.5
0.75
1
1.25
1.5
Frequency (kHz)
Figure 6.6
The wave number
k
a
of the airborne wave in the fibrous material.
