Building Acoustics

280 Building acoustics

type (see Figure 8.3). These calculations are performed using a transfer matrix model
described in Chapter 5 (section 5.7.1.1). The wall impedance of each board, see Chapter
6, section 6.5.1.2, is given by

(^) ()
2
4
w
c
j1 1jsin
f
Zm
f
ω ηM.

⎡ ⎛⎞ ⎤

=−⋅+⎢ ⎜⎟ ⎥

⎢⎣ ⎝⎠ ⎥⎦

(8.4)

The model of Mechel (1976) is used to describe the porous absorber in the same way as
when calculating the transmission through the absorber alone; see Chapter 6 (section
6.5.4). The flow resistivity of the porous layer is varied in steps to simulate various
degrees of cavity damping, starting from a value of 10 kPa⋅s/m^2 , which corresponds to
the value found for common products of mineral wool.

Figure 8.3 Sound reduction index of an unbounded double wall. Diffuse field incidence. Two 9 mm
plasterboards, 7.2 kg/m^2 with critical frequency 2250 Hz. 50 mm cavity with porous material. Parameter is the
flow resistivity: curve 1 having r = 10 kPa.s/m^2 and for each curve 2–4 the resistivity is reduced by a factor of
five. Lower dashed curve – reduction index for a single board.

50 100 200 500 1000 2000 5000

Frequency (Hz)

0

10

20

30

40

50

60

70

80

Sound

reduction index (dB)

9 50 9

18 dB/oct.

1

2

3

4

Figure 8.3 exhibits some typical features found for the sound reduction index of
double walls with no structural connections between the leaves. At low frequencies,
where the distance between the leaves is much smaller than the wavelength, the leaves
will be strongly coupled by the acoustic stiffness of the air in the cavity, this in spite of
the presence of the porous absorber. If the vibrations of the leaves are mass controlled,
the wall will behave like a single leaf, having a mass equal to the sum of the masses of
the leaves; compare with the dashed curve giving the reduction index of each leaf.
The acoustic coupling across the cavity will give a double wall resonance, resulting
in a minimum value of R at a frequency expressed as