Building Acoustics

320 Building acoustics

calculate the time function of the force F and thereafter compare this with the
corresponding force without the covering.
The solution to the differential equation based on this model will depend on the
damping of the system, i.e. the damping being less than critical or overdamped, which
means we get an oscillation or just a positive pulse. The former case is assumed not to
happen as the tapping machine has a mechanism for catching the hammers before they
bounce back again after impact. It is, however, interesting to calculate the improvement
assuming that the pulse becomes oscillatory.
Examples on calculated pulse forms are shown in Figure 8.36, using a covering of
stiffness s equal to 3.2⋅ 105 N/m, giving a resonance frequency f 0 of approximately 130
Hz with a hammer mass of 0.5 kg. One of these pulse forms is slightly overdamped (≈ 20
%), while the other is less than critically damped (≈ 60 %). Critical damping is obtained
when the damping coefficient c is equal to π mf 0.

63 125 250 500 1000 2000 4000

Frequency (Hz)

0

10

20

30

40

50

60

70

80

Improvement

'

L

(dB)n

Carpet squares

Vinyl covering

Figure 8.37 Impact sound improvement of two types of floor covering. Measured data from Homb et al. (1983).
Predicted improvement with a linear model: stiffness of carpet squares 3.2⋅ 106 N/m, vinyl covering 5.2⋅ 106 N/m.
Thin solid curves – overdamped case. Dashed curves – less than critically damped.

The reduction in the transmitted impact sound may now be determined by
calculating the ratio of the Fourier transforms representing the actual force pulse and the
corresponding one obtained without the covering. Figure 8.37 gives two examples of
measured improvement data, one specimen being soft carpet squares and the other a
vinyl covering with a felt backing. In the former case, we have assumed that the covering