Sound transmission in buildings. Flanking transmission. 333
the ratio of the radiated sound power from the terminal in the receiving room to the
sound power entering the terminal in the source room. The attenuation includes a number
of different sound energy losses; losses at branches and bends, energy reflected at
terminal outlets, by silencers inserted in the duct etc. Prediction tools for all types of such
losses are available in the literature (see e.g. ASHRAE (1999)).
Assuming that the area S of the partition is much larger than the area St of the
terminal unit (grill, diffuser), we may use Equation (9.3) to calculate the necessary
attenuation D. We may e.g. demand that the sound reduction index R (or R') of the
partition should not be reduced by more than ΔR when the duct system is connected. This
implies that
t 1010
t10 lg 1 10 or10 lg 10 1.RDRS
R
S
S
DR
S
−Δ⎡⎤
Δ≈ ⋅ + ⋅⎢⎥
⎢⎥⎣⎦
⎡⎤⎛⎞
≈−⋅⎢⎥⎜⎟−
⎢⎥⎜⎟
⎣⎦⎝⎠
(9.6)
Example Having a partition of area 10 m^2 and sound reduction index 40 dB and
demanding ΔR < 1 dB, we need at least an attenuation D of 19 dB when there is a
terminal unit of area (10 x 20) cm^2.
In principle, we should be able to handle the situation depicted in Figure 9.7 b), in
the same way allocating a sound reduction index and an area to the duct walls. The
problem is that reduction indexes of duct walls are difficult to predict with satisfactory
accuracy, as they are dependent not only on the general shape but on details in the
structure. Ducts with rectangular cross section have the lowest reduction indexes,
whereas cylindrical ducts with an ideal circular cross section may exhibit very high
reduction indexes, in particular at low frequencies. This is, however, only part of the
aperture story. Details in the shape of cylindrical ducts, e.g. flanges, may dramatically
decrease the reduction index. This may be explained, in the break-out case, by higher
order vibration modes in the duct walls excited by the internal sound field, thereby
increasing the radiated sound power.
Several definitions are in use concerning sound reduction indexes of duct walls.
According to Cummings (2001), the most popular definition in the case of break-out is
i
out i
duct
r
r10 lg ,W
S
R
W
S
⎡ ⎤
⎢ ⎥
=⋅⎢ ⎥
⎢ ⎥
⎣ ⎦
(9.7)
where Wi and Wr are the sound power inside the duct and the radiated power,
respectively. The quantity Si is the cross sectional area of the duct and Sr is the area of the
sound radiating duct wall. Correspondingly, one may define a similar sound reduction
index for sound transmission into the duct as
2
in 00
duct4
10 lg.
2p
c
R
W
Sρ