Building Acoustics

Multilayer elements 281

(^0)
12

1

,

2

s s

f

π mm

=+ (8.5)

where m 1 and m 2 are the mass per unit area of the two leaves and where s is the stiffness
per unit area represented by the cavity. As evident from the expression, this resonance
corresponds to a symmetrical movement of two masses connected by a spring. Assuming
that the spring stiffness is solely determined by the air in the cavity, it will have a value
in the range between U 0 c 02 /d and P 0 /(V⋅d). Here the quantities d, P 0 and V are the distance
between the leaves, the barometric pressure and the porosity of the porous material,
respectively.
In the latter expression we have assumed that the sound propagation takes place
isothermally, whereas the former will apply for an empty (air-filled) cavity. In practice, it
is not very important which one to use as the difference is given by the factor γ⋅V, where
γ is the adiabatic constant. The latter is approximately equal to 1.4 for air and the
porosity is normally above 0.9, which leaves us with a difference in the range of 10–15
%. For a rough estimate one normally finds expressions that applies to an air-filled
cavity, such as

0 01 2() 12

0

12 12

60.

2

c mm mm

f

mm d mm d

U

π

+ +

=≈

⋅ ⋅⋅⋅

(8.6)

63 125 250 500 1000 2000 4000

Frequency (Hz)

0

10

20

30

40

50

60

70

80

Sound

reduction index (dB)

Cavity filled

Predicted, f < fd

Predicted, f > fd

Cavity empty

Figure 8.4 Sound reduction index of a double wall, 13 mm plasterboards mounted on separate studs, 150 mm
cavity depth. Measured data from Homb et al. (1983). Predicted data from model by Sharp (1978).