Civil Engineering Reference
In-Depth Information
R
being given by Equation (6.26). The wave numbers
k
a
and
k
a
are represented by the
same curve in Figure 6.6. It should be noticed that at low frequencies this wave is strongly
damped, the imaginary part and the real part of
k
a
being nearly equal. The characteristic
impedance
Z
a
related to the propagation of the airborne wave in the air in the material
is represented in Figure 6.7.
The related characteristic impedance
Z
2
for the same material with a rigid frame is
given by
( ρ
22
R)
1
/
2
φ
Z
2
=
(6.87)
This evaluation is represented by the same curve in Figure 6.7.
The ratio modulus
|
µ
b
|
of the velocities of the frame and the air for the frame-borne
wave decreases from 1
·
0at50Hzto0
·
82 at 1500 Hz. The frame-borne wave, as indicated
in Section 6.5.3, induces a noticeable velocity of the air in the material. On the other
hand, the wave number
δ
b
and the characteristic impedance
Z
b
, evaluated by Equation
(6.67) at high frequencies and Equation (6.77), are very close to the wave number and
the characteristic impedance for longitudinal waves propagating in the frame in vacuum
ω
ρ
1
K
c
δ
1
=
(6.88)
=
ρ
1
K
c
Z
1
(6.89)
K
c
being the elasticity coefficient of the frame in the vacuum given by Equation (1.76).
6
4
Re
2
0
−
2
Im
−
4
−
6
8
−
−
10
0
0.25
0.5
0.75
1
1.25
1.5
Frequency(kHz)
Figure 6.7
The normalized characteristic impedance
Z
a
/Z
0
related to the propagation
of the airborne wave in the air in the fibrous material.
