Building Acoustics

334 Building acoustics

The sound pressure p is the pressure in the assumed reverberant field outside the duct,
and W is the power transmitted into the duct having a cross-sectional area S. The
rationale behind the number two in the denominator is that when the power is transported
in the duct, one-half of it goes each way. Using the reciprocity relation (see section
6.6.1), assuming a point source being placed in a room outside the duct, thereafter inside
the duct, one may show that there is a direct connection between these sound reduction
indexes. Neglecting a possible attenuation of the wave in the axial direction over a duct
length L, we get

22

in out

duct duct 2

0

10 lg ,

Sf

RR

cUL

⎡π ⎤

=+⎢ ⎥

⎣ ⎦

(9.9)

where f as usual is the frequency, and U is the outside perimeter of the duct.
There remains the problem of finding an expression for one of these reduction
indexes. As mentioned above, this is not an easy task and it will be outside the scope of
this book to provide a complete prediction model. We shall, however, give a couple of
examples on measured and predicted results of the reduction index of ducts having
rectangular and circular cross sections, respectively, both examples being taken from the
paper by Cummings (2001).

50 100 200 500 1000 2000 5000

Frequency (Hz)

10

20

30

40

50

Sound reduction index

(dB)

3 dB/octave

Figure 9.8 Sound reduction index for break-out. Duct with dimensions 457 x 229 mm and wall thickness 0.64
mm. Solid curve – predicted. Points – measured data in one-third-octave bands. Reproduced from Cummings
(2001).

Figure 9.8 shows sound reduction index for break-out of a galvanized steel duct of
cross section 457 x 229 mm and wall thickness of 0.64 mm. Measured results are as
usual given in one-third-octave bands, showing a very good fit to predicted results using
a wave solution, taking account of the coupling between the acoustic wave field inside