Sound transmission in buildings. Flanking transmission. 335
the duct and the structural wave field in the duct walls. It should be noted that the
reduction index increases only by approximately 3 dB per octave, as opposed to the 6 dB
dependency of common single partitions in the mass controlled frequency range. The
duct walls certainly are mass-controlled in the low and middle frequency range but the
difference is attributed to the radiation factor of the duct, as it is a line-source of finite
length.
Ducts with a circular cross section have in general a much higher reduction index
than ducts with rectangular cross section. Figure 9.9 shows measured and predicted
results applying to a “long-seam” circular duct of 1.22 mm galvanized steel having a
diameter of 356 mm. Measured results are again given in one-third-octave bands and two
different predictions are given. As pointed out above, not only the shape of the duct will
be important but also details in its shape, and the duct in question had a single axial seam
making the duct a little flat on both sides of it. The dashed curve applies to an ideal
circular duct transporting a plane wave. The duct may then only move as a monopole
source, making the walls subjected only to membrane stress, which results in a very high
impedance for the internal plane wave and thereby a high reduction index.
50 100 200 500 1000 2000 5000
Frequency (Hz)10
20
30
40
50
60
70
80
90
100
Sound reduction index(dB)Figure 9.9 Sound reduction index for break-out. “Long-seam” circular duct, galvanized steel of wall thickness
1.22 mm and diameter 356 mm. Dashed curve – predicted for duct of ideal shape. Solid curve – predicted from
“distorted” circular duct model. Points – measurement results in one-third-octave bands. Reproduced from
Cummings (2001).
In the predicted result given by the solid curve, allowance has been made for a non-
ideal circular shape, a shape which probably applies to all duct used in building practice,
e.g. ducts with spiral seams. The internal acoustic wave then excites other vibration
modes in the duct walls in addition to the pure membrane mode, resulting in an increase
in the radiated sound and thereby a substantially lower reduction index.
In this case as well, plane wave propagation in the duct is assumed thereby giving a
discrepancy between measured and predicted results when higher order modes may
propagate. This effect may clearly be seen in the frequency range around 1000 Hz. In