Civil Engineering Reference
In-Depth Information
6.5.2.1
Formulas for calculation. Examples
One should not be surprised, taken the complexity of the task to even calculate the sound
reduction index of a single homogeneous wall between two rooms, that a number of
formulas are cited in the literature. A number of these are found in EN 12354-1, in
which Equation
(6.103)
is given for the transmission factor. The dimensions of the wall
are given by the quantities
a
and
b
, η
tot
is the total loss factor, σ and σ
f
are the radiation
factor for resonant and non-resonant transmission, respectively. The latter is expressed
by the formula by Sewell (Equation
(6.49)
), whereas the corresponding one for σ is a
little more involved than the one given in section
6.3.4.2.
2
⎡
)
2
⎤
(
ab
+
2
⎛
Z
⎞
f
σ
0
c
⎢
⎥
τ
=
2
σ
+
⋅
f
<
f
,
⎜
⎟
f
c
2
2
π
fm
⎢
f
η
⎥
ab
+
⎝
⎠
tot
⎣
⎦
2
⎡
2
⎤
⎛
Z
⎞
πσ
0
τ
=
f
=
f
,
(6.103)
⎢
⎥
⎜
⎟
c
π
fm
2
η
⎢
⎥
⎝
⎠
⎣
⎦
tot
2
⎡
2
⎤
⎛
Z
⎞
πσ
f
0
c
τ
=
f
>
f
.
⎢
⎥
⎜
⎟
c
π
fm
2
f
η
⎝
⎠
⎣
⎢
⎥
⎦
tot
For rough estimates one may make some simplifications. For forced transmission (
f
<
f
c
),
the simple mass law, given in Equation
(6.102)
, is often sufficient. A slightly better
alternative is to neglect the contribution from the resonant transmission but to include a
slightly simplified area effect. Fahy (1987) has suggested that for the range
f < f
c
one
should use the following expression:
⎡
2
⎤
⎡
⎤
⎛
⎞
⎛
⎞
2
π
f
f
⎢
⎥
RR
=−⋅
10 lg ln
⋅
b
+⋅
20 lg 1
−
,
(6.104)
⎢
⎥
⎜
⎟
⎜
⎟
f
0
c
⎢
f
⎥
⎢
⎥
⎝
⎠
⎝
⎠
⎣
⎦
0
c
⎣
⎦
where index f on the reduction index indicates that we are dealing with forced
⎡
2
⎤
⎡
⎤
⎛
⎞
⎛
⎞
2
π
f
f
(
)
⎢
⎥
R
≈⋅
20 lg
m
⋅
f
−⋅
10 lg ln
⋅
ab
+⋅
20 lg 1
−
−
42 dB.
(6.105)
⎢
⎥
⎜
⎟
⎜
⎟
f
c
⎢
f
⎥
⎢
⎥
⎝
⎠
⎝
⎠
⎣
⎦
0
c
⎣
⎦
In the frequency range above the critical frequency we may set σ ≈ 1, and when using the
last entry in
(6.103)
, we obtain
⎡
⎤
f
R
=⋅
20 lg(
m
⋅
f
)
+⋅
10 lg 2
η
−
47 dB
f
>
f
.
(6.106)
⎢
⎥
tot
c
f
⎣
⎦
c
This expression is identical to the one given for a plate of infinite size (see Equation
(6.101))
. Below, we shall present several examples where we compare measured and
calculated data. In all cases we shall use the complete set of equations given in Equation
