Building Acoustics

288 Building acoustics

32

00 0

point 32

c

22

00 0

line

c

8

,

2

,

cu

W

f

cu

W

f

U

π

U

π

=⋅

=⋅





A

(8.17)

where u 0 is velocity in the point or on the line, and ℓ is the length of the line. The
radiation factor for these two cases may then be expressed as

2

0

B, point 32

c

0

B, line

c

8 11

(^21)
and.
c
S f
c
Sf

V

π

V

π

= ⋅⋅

=⋅⋅

A

(8.18)

In the normal case using a set n of studs distributed evenly over the surface area S, where
we shall apply the last expression, the centre-to-centre distance between the studs will be
S/(n⋅ ℓ).
If we look at the expression for the sound reduction index, Equation (8.16), and
initially assume that the ratio between the velocity of the primary wall and the velocity of
the bridges are frequency independent, the improvement will increase by 12 dB per
octave until it reaches a maximum, a plateau. This maximum will be determined by the
critical frequency of the lining and the degree of mechanical contact between the wall
and the lining. It should be noted that the improvement will go to zero towards the
critical frequency. The lining will then became just as good a radiator as the primary wall
and no improvement, except for the one caused by a small increase in mass, is to be
expected. A sketch showing the improvement in principle is presented in Figure 8.9.

f 0 fc

'Rmax

'R 12 dB/octave

Figure 8.9 Sound reduction improvement caused by an additional lining.

The maximum improvement offered by a lining connected to the primary wall by
studs is shown in Figure 8.10. It should be noted that the data assume infinitely stiff
connections between the primary construction and the lining. For the case of a lining
detached from the primary wall, i.e. having contact along the edges only, one may in
practice set the c-c distance to be equal to the smallest lining dimension.