210 Building acoustics
S SR
RR R1
10 lg 20 lg 10 lg 10 lg ,p SS
RLL
τ pA A⎛⎞ ⎛⎞
=⋅ = ⋅⎜⎟ ⎜⎟+⋅ = − +⋅
⎝⎠ ⎝⎠
(6.6)
where D = LS – LR is the difference in the mean sound pressure level in the sending and
receiving room. This is the expression used in a standard laboratory procedure based on
measurements of the sound pressure levels (see ISO Standard 140 Part 3).
An alternative procedure is based on determination of the transmitted power to the
receiving room by way of measuring the intensity. An important reason for applying
such a method is when the traditional method breaks down due to substantial flanking
transmission. Using this method one determines the mean transmitted intensity IR over a
surface SR that completely encloses the actual element having an area S. Instead of
Equations (6.5) and (6.6) we get
RR 2
S
(^400)
I S
p
S
cτρ⋅
=
⋅
(6.7)
and
2
S
SR
00 R R R10 lg 10 lg 10 lg 6 dB.
Ip 4 Ip SS
RLL
ρcI S S⎛⎞⎛⎞ ⎛⎞
=⋅⎜⎟⎜⎟+⋅⎜⎟≈ − +⋅⎜⎟−
⎝⎠⋅ ⎝⎠ ⎝⎠
(6.8)
The latter expression corresponds to the one to be found in ISO 15186 Part 1, having
introduced the mean sound pressure level LpS in the sending room and the mean intensity
level LIR taken over the measuring surface SR. In addition, the characteristic impedance
ρ 0 c 0 for air is set equal to 400 Pa⋅s/m.
Do we get the same results when applying these two methods? In theory, there will
be a difference due to a certain underestimating of the transmitted power by the
traditional method, resulting in a higher sound reduction index. When determining the
mean sound pressure level in the receiving room certain limits are imposed on the
distance to the room boundaries, i.e. the power is determined by measurements in the
“inner part” of the room. A modified sound reduction index RI,M will therefore be more
in accordance with R determined using Equation (6.6). This is defined as
(^) ,M 10 lg 1 b0,
8
IIcI
Sc
RRKR
Vf
⎛⎞
=+=+⋅ +⎜⎟
⎝⎠
(6.9)
where the last term is the so-called Waterhouse correction (see section 4.5.1.1). The
quantities Sb and V are the total surface and volume of the receiving room, respectively.
For the frequency f one uses the centre frequency in the actual frequency band.
6.2.1.1 Apparent sound reduction index
As opposed to the measuring situation in a laboratory, the normal situation in a building
is the existence of a large number of transmission paths for the sound energy (see Figure
6.3). As indicated in the figure, sound energy may, in addition to being directly
transmitted through the wall partition, be transmitted via flanking constructions, via
crack formations, out and in through windows, via a common ventilation duct, via cable
ducts etc.