Building Acoustics

292 Building acoustics

There is certainly a need for performing simple estimations of the sound reduction
index of double constructions on common studs. We shall therefore include the
prediction model by Sharp (1978), a commonly cited reference. The model that assumes
infinitely stiff connections, either point or line connections, again uses Equation (8.11) as
a base. We may write it in the following way

i 2.P 2 2,P 2,B 2,P

i 2,B 2,B without 2,P 2,P 2,P

10 lg 10 lg

or 10 lg 10 lg 1 10 lg 1.

R WWi W WWWW

W WW RR WW

⎛⎞

=⋅ =⋅⎜⎟⎜⎟⋅

⎝⎠+

⎛⎞ ⎛ ⎞ ⎛

=⋅⎜⎟ ⎜ ⎟−⋅ + = −⋅ +⎜

⎜⎟ ⎜ ⎟ ⎜

⎝⎠ ⎝ ⎠ ⎝W

⎞

⎟⎟

⎠

(8.19)

We have then got an expression for the sound reduction index as a difference between
the reduction index for the partition without the structural connections and a term due to
these connections. Assuming that the sound radiation caused by these connections or
bridges is dominant, i.e. W2,B >> W2,P, Sharp shows that in the frequency range f 0 < f < fd,
where Rwithout increases by 18 dB per octave the last term will increase by 12 dB per
octave. Similarly, this term will increase by 6 dB per octave where Rwithout increases by
12 dB per octave, that is to say when f > fd. Without going into detail, the resulting
reduction index will in effect have a shape as sketched in Figure 8.14. We end up with a
term 'R added to the reduction index R, the latter determined by the total mass M = m 1 +
m 2 of the partition:

()B^112

12 1

,

where 10 lg 20 lg.

RRM R

m ZZ Rn mm Z

V

=+'

⎡ + ⎤

'=− ⋅ ⋅ + ⋅⎢ ⋅ ⎥

⎣ + ⎦

(8.20)

Frequency (log-scale)

R(dB)

12 dB/oct

18 dB/oct

f 0 fd

RM

'R