326 Building acoustics
transmission via a suspended ceiling common to two neighbouring rooms, i.e. the
partition wall does not seal off the cavity above the ceiling. This certainly may result in
some flanking transmission along the suspended ceiling panel, but the airborne sound
transmission in the cavity between the basic ceiling and the suspended panel is normally
more important.
We shall treat a number of these transmission paths before presenting a model
where the flanking transmission is included. We shall start with a simple calculation of
the sound transmission index of a partition made up of a combination of different parts,
e.g. a wall including a window or door. We may use this result to exemplify the effect of
non-intentional weaknesses of a partition such as badly sealed cable ducts or direct
building defects such as cracks (slits) or apertures in the construction. Furthermore,
sound transmission by way of common ventilation ducts will be looked at and, as an
introduction to the theme of calculating the apparent sound reduction index, we shall
treat the subject of sound transmission by way of a suspended ceiling.
9.2 Sound reduction index combining multiple surfaces
When calculating the sound reduction index of a partition consisting of an assembly of
two or more parts or surfaces, one normally assumes no interaction between the different
parts; each part vibrates independently driven by the incident sound pressure. This is
certainly a simplification but it may be justified by giving a rough and reasonable
estimate. The total transmission factor τtotal of a number n of partial surfaces Sn having
transmission factor τn will be given by
(^) total^11 2 2^1
12 0
,
n
ii
nn i
nS
SS S
SS S S
τ
ττ τ
τ =+ +⋅⋅⋅⋅+
=
+ +⋅⋅⋅⋅+
=
∑
(9.1)
where S 0 is the total area. Expressed by the corresponding sound reduction indices, we
find
(^) total^0
10
1
10 lg.
10
n Ri
i
i
S
R
S
−=⎡ ⎤
⎢ ⎥
⎢ ⎥
=⋅⎢ ⎥
⎢ ⋅ ⎥
⎢ ⎥
⎣ ⎦
∑
(9.2)
An example showing the use of this expression is given in Figure 9.1, where there are
just two components (n = 2) giving a diagram useful for dimensioning a partition
containing a door or window. It should be noted that R 0 is the sound reduction index
belonging to the total area S 0 , i.e. the index before the smaller part of area S 1 with
reduction index R 1 is inserted. The explicit expression, certainly assuming S 1 ≤ S 0 , is
01(^1110)
0total
00
10 lg 1 10.
RR
SS
RR
SS