Civil Engineering Reference
In-Depth Information
(
)
2
2
ρ
ckSF
4
ρ
c
()
2
00
p
'
=
00
⋅
W
'
=
.
(6.119)
22
A
πω
A
m
The sound pressure
p
´ will then drive the plate, resulting in a velocity
u
P
that in the
linear case must be proportional to the applied pressure. Hence, we may write
(
2
2
P
ubp
=⋅
'
,
(6.120)
where
b
is a second factor of proportionality. Using Equation
(6.119)
we get
(
)
2
2
2
ρ
πω
ckS
u
00
P
2
=⋅
b
.
(6.121)
2
2
F
A
m
source and receiving point. From the principle of reciprocity, these equations shall then
be identical resulting in
(
)
2
2
ρ
ckS
22
2
a
Am
ω
ρ
ck
00
=
⋅
=
00
.
(6.122)
22
2
b
πω
A
m c S
8
ρ
4
π
00
From this follows that we may generally find the velocity of a structure placed in a
diffuse field (see Equation
(6.120))
, if we know the power radiated from the structure by
a point force excitation given by Equation
(6.114).
It should be noted that this
specifically applies to a given point-to-point relationship. The proportionality factors
a
and
b
will generally be space dependent.
6.6.2
Sound reduction index and impact sound pressure level: a relationship
Finally, we shall follow Cremer et al. (1988), giving an example on how to use Equation
(6.122)
to derive a simple functional relationship between the impact sound pressure
level of a massive floor construction and its sound reduction index. We shall assume that
the frequency is above the critical frequency, i.e. setting the radiation factor σ ≈ 1 is
applicable both for airborne and impact sound. We shall cast the impact sound pressure
⎧
pA
2
⎫
L
=⋅
10 lg
⋅
,
(6.123)
⎨
⎬
n
pA
2
0
⎩
⎭
0
where
p
0
and
A
0
are the reference values 2⋅10
-5
Pa and 10 m
2
, respectively. This is
equivalent to a radiated power
W
n
to the receiving room
p
2
2
W
=
⋅ =⋅
A
a F
.
(6.124)
n
4
ρ
00
