278 Building acoustics
mentioned in the introduction, the wall elements may be mechanically coupled in
different ways. We shall not put any restrictions on the type of elements; these may be
massive heavy elements of concrete, brick etc. as well as lightweight elements such as
plasterboard, chipboard, glazing etc. There is a great demand for lightweight
constructions offering high sound insulation and we shall therefore put some emphasis
on lightweight board constructions. These have at least two layers, certainly because
single lightweight layers will never be able to fulfil the requirements e.g. imposed in
building codes for dwellings. Combinations, such as a massive heavy element and an
additional lightweight lining are practical constructions. Such combinations may achieve
a considerably higher sound reduction index than the primary heavy one.
Searching for literature on the sound insulation of double walls, one quickly
discovers that it is rather extensive, certainly on lightweight constructions. The
theoretical analysis is, however, less developed than the one for single leaf constructions,
which should not come as a surprise in view of the complexity involved. It is not only the
mechanical couplings between the leaves that is difficult to quantify, the importance of
the different, and at the same time distributed, energy loss mechanisms is difficult to
ascertain. An illustration is given in Figure 8.1, indicating how energy may be
transmitted between rooms by a lightweight double wall. A direct path coupling the two
leaves across the cavity is indicated together with the paths across structural stud
connections and along the outer boundaries.
Figure 8.1 Transmission paths for a lightweight double wall.We do not intend to give a general overview of the literature dealing with double
walls but to render an understanding of the physical variables involved by presenting a
number of idealized examples. Prediction models using infinite size elements are
appropriate also in this case. One cannot, however, avoid presenting results based on
statistical energy analysis (SEA), a method applied to these questions as early as 1970
onwards (see Chapter 7). Using SEA, suitable software may be developed for calculating
transmission factors and sound reduction indices. In practice, it may also be
advantageous to develop formulae giving rough estimates of the performance. Such
expressions, developed on an empirical basis will also be given here.
8.2.1 Double wall without mechanical connections
Assuming that there are no structural connections between the two leaves of the wall, the
energy transmission from one leaf to the other must take place by a forced excitation by