Civil Engineering Reference
In-Depth Information
11.6
Calculation of the acoustic indicators
11.6.1 Surface impedance, reflection and absorption coefficients
If a plane acoustic wave impinges upon a stratified medium illustrated by either
Figure 11.4 (absorption problem) or Figure 11.5 (transmission problem), at an incidence
angle
p(A)
/
v
f
3
(A), or
θ
, the surface impedance
Z
s
of the medium is written as Z
s
=
1
Z
s
]
V
f
(A)
[
−
=
0
(11.86)
Adding this new equation to the system of Equations (11.82) or (11.85), a new system
is formed with a square matrix:
−
V
1
Z
s
0
···
0
=
0
(11.87)
[
D
]
The determinant of this matrix is equal to zero, so
Z
s
is calculated by
det[D
1
]
det[D
2
]
Z
s
=−
(11.88)
where det[
D
1
] (resp. det[
D
2
]) is the determinant of the matrix obtained when the first
column (resp. the second column) has been removed from [
D
]. The reflection coefficient
R
and the absorption coefficient
α
are then given by the classical formulas:
Z
s
cos
Z
0
Z
s
cos
θ +
Z
0
θ −
R
=
(11.89)
and
2
α(
θ
)
=
1
−|
R
|
(11.90)
In case of a diffuse field excitation, the absorption coefficient is defined as follows:
θ
max
α(
θ
)
cos
θ
sin
θ
dθ
θ
min
α
d
=
(11.91)
θ
max
cos
θ
sin
θ
d
θ
θ
min
where
α
)
is the absorption coefficient at a given angle of incidence
θ
,asdefinedpre-
viously,
θ
min
and
θ
max
are the selected diffuse field integration limits, usually 0
◦
and 90
◦
.
θ
(
11.6.2 Transmission coefficient and transmission loss
When the multilayer is extended by a semi-infinite fluid medium, the transmission coef-
ficient
T
and the reflection coefficient
R
are related by
p(A)
1
+
R
−
p(B)
T
=
0
(11.92)
