Civil Engineering Reference
In-Depth Information
2.5
2.25
2
1.75
1.5
1.25
1
0.75
0.5
0.25
0
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
Frequency (kHz)
Figure 7.3
Amplitude of the reflected wave calculated with Equation (7.6), material 1,
l
=
4cm,
z
1
+
z
2
=−
0
.
5m,
r
=
0.
4 cm. In this chapter, Equations (5.50), (5.52)
are used for the effective density and Equations (5.51), (5.55) for the bulk modulus.
Materials 1 and 2 could be ordinary porous sound absorbing materials. The modulus
of the exact reflected pressure calculated with Equation (7.6) for a layer of thickness
l
=
4cm at
θ
0
=
0and
z
1
+
z
2
=−
0
.
5 m is represented in Figure 7.3. The modulus
of the difference between the exact evaluation and the evaluation by Equation (7.20) is
represented in Figure 7.4, together with the modulus of the term
N/(k
0
R
1
)
.
The difference is much smaller than
|
N/(k
0
R
1
)
|
for frequencies higher than 500 Hz.
This shows the interest of the steepest descent method for large
k
0
R
1
. In Figures 7.5, 7.6
The thickness of the sample is
l
=
0.45
Added contribution
Error
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
Frequency (kHz)
Figure 7.4
Modulus of the difference between the exact evaluation and the evaluation of
the reflected pressure with the steepest descent method from Equation (7.20), and modulus
of the term
N/k
0
R
1
in Equation (7.20), material 1,
l
=
4cm,
z
1
+
z
2
=−
0
.
5m,
r
=
0.
