Civil Engineering Reference
In-Depth Information
π
π
2
2
⎡
2
⎤
∫
∫
α
=
2(
αϕ ϕ ϕϕ
) sin s
d21
=
−
R
sin s
ϕ ϕϕ
d.
(3.79)
stat
p
⎢
⎥
⎣
⎦
0
0
⎡
() ()
2
2
⎤
(
)
′
′′
′
′
z
−
z
′′
z
z
1
z
2
α
=⋅
8
⎢
1
− ⋅ + + + ⋅
ln 1
2
zz
′
⋅
rctg
⎥
.
(3.80)
stat
2
2
′′
2
′
z
1
+
z
⎢
⎥
z
z
z
⎣
⎦
The symbol
z
is the surface impedance normalised by the characteristic impedance
Z
0
of
the medium, i.e.
Z
Z
⎧
⎫
⎧
⎫
g
g
zz
=+⋅ =
′
j
z
′′
e
+⋅
j Im .
(3.81)
⎨
⎬
⎨
⎬
Z
Z
⎩⎭
⎩⎭
0
0
impedance. A comparison with
Figure 3.11
generally shows that the statistical absorption
coefficient is higher than the normal incidence factor, but also that the absolute
maximum is slightly lower; (α
stat
)
max
≈ 0.95 at
z
'
≈ 1.6.
15
0
.259
10
5
0
.864
0
.432
0
.605
0
.519
0
.346
0
-5
-10
0
.173
0
.0864
-15
0
5
10
15
20
Real Z
Figure 3.14
Statistical absorption factor as a function of the normalized impedance components, (
Z
=
Z
g
/
Z
0
).
3.5.3
Oblique sound incidence. Boundary between two media
A general treatment of the case of plane wave's incident on a locally reacting surface was
given in the previous section. Implicitly, this means that we presuppose the impedance
Z
g
