Building Acoustics

Multilayer elements 279

way of the cavity. As a first approximation to this case, which may well be found in
practice, we shall deal with a situation where we assume diffuse sound fields, not only in
the sending and receiving rooms but in the cavity as well. This certainly presupposes the
cavity depth is larger than the wavelength. Such a situation is depicted in Figure 8.2
where the sending and receiving rooms are separated by a double wall represented by
two single partitions having sound reduction indexes R 1 and R 2.

L 1 L 2 L 3

R 1 R 2

Figure 8.2 Rooms separated by a double wall with a large cavity.

We may express these sound reduction indexes as:

112

2

223

3

10 lg

and 10 lg ,

S

RLL

A

S

RLL

A

=−+⋅

=−+⋅

(8.1)

where S is the area of the partitions. L and A denote the sound pressure level and the total
absorption area, respectively, having indices according to the figure. The sound reduction
index Rd of the “double” wall is expressed as

(^) d13
3
10 lg ,

S

RLL

A

=−+⋅ (8.2)

which, by inserting the Equations (8.1), gives

(^) d1210 lg^2.

A

RRR

S

=++⋅ (8.3)

In spite of the assumption, having a diffuse field in the cavity, the importance of the
cavity damping is a general one. A porous absorber inside the cavity will generally
attenuate waves running parallel to the wall leaves, and we know that obliquely incident
waves are easily transmitted.
As an example we shall perform a calculation on an unbounded double wall of two
9 mm plasterboards with a 50 mm cavity filled with a porous absorber of mineral wool