Building Acoustics

338 Building acoustics

plasterboard and there is no absorber in the plenum. The height h of the plenum is 0.43
metre. In addition to the measured results and the results according to the model theory
predicted results are given using the aforementioned one-dimensional model. The latter
model is outlined in the following section.

Figure 9.11 Sound reduction index Rcl of a suspended ceiling of 9.5 mm plasterboard without plenum absorber.
Measured results and predicted results according to a modal theory, reproduced from Mechel (1995). Predicted
results by a one-dimensional model by Mechel (1980). See Equation (9.20) (ε =2).

63 125 250 500 1000 2000 4000

Frequency (Hz)

0

10

20

30

40

50

60

70

80

Sound

reduction index (dB)

Measured

Modal analysis

1 - dim. model

Looking at the results predicted by the modal theory these exhibit quite large
excursions, presumably due to single frequency calculations, two for each one-third-
octave band. Averaging over a larger number of single frequencies for each band would
probably make the curve smoother. Apart from giving systematic lower results, the one-
dimensional model is also quite good in this case.

9.2.3.2 One-dimensional model

In the model by Mechel (1980) we envisage that the ceiling in the sending room, having
length LS, is divided into elements of area ΔLS ⋅ b where b is the width of the room. Since
the model is one-dimensional this width is certainly of no importance. The transmission
through these elements is assumed to be uncorrelated, and the power transmitted into the
plenum on the sending side is determined by the transmission factor of the ceiling, made
up of the transmission factor τS,pl of the ceilings plates and the transmission factor τS,a of