240 Building acoustics
measured and calculated results compares very well. The standard EN 12354–2 gives an
alternative expression for the normalized impact sound pressure level, which is
(^) ns
ref
155 30lg 10lg 10log 10lg (dB).
f
LmT
f
=− + + +σ (6.76)
However, using this equation we will obtain the same results as shown in the figure. The
quantities TS and fref are the structural reverberation time given by Equation (6.59) and a
reference frequency of 1000 Hz, respectively.
In Figure 6.20, we have also included a result measured on a thicker concrete slab
of the hollow core type. A vertical section of such a slab is shown in the sketch in the
same figure. These kinds of element exist in different thicknesses, also having hollows of
different shapes. Statically considered they are equivalent to the massive slabs but, as
seen from the figure, the curve shape of the impact level is quite different. To our
knowledge, a similar model for the impact sound pressure level, as given for the massive
slab, is not known.
6.5 Airborne sound transmission. Sound reduction index for single walls
To calculate airborne sound transmission we are presented with a more complicated
problem than with impact sound. We are again forced to calculate the bending wave field
induced by the excitation and thereafter find the resulting radiated power due to this
field. In this case, however, the vibration pattern of the structure is more complex having
two components:
- A forced vibration field; imparted to the wall due to the external sound field.
This is also called the non-resonant field. - A resonant field; a vibration field due to the natural modes excited by
reflections from the boundaries.
The radiated sound power may now be expressed as
WcSuac00 ff rr=⋅+⋅ρσσ{ ^22 u}, (6.77)
where the indices f and r indicate “forced” and “resonant”, respectively. An exact
theoretical treatment of this case will be rather involved, partly due to these two different
mechanisms, partly due to a complicated dependency of the angle of sound incidence.
We shall choose to give an overview of the physical background for these phenomena,
followed by a calculation procedure covering the case of most interest, the airborne
sound transmission by a diffuse field.
By analogy with the treatment of impact sound, it is useful to start considering a
single wall or floor modelled as an infinitely large thin plate excited by a single plane
wave. Such a simplification may be justified by the fact that several of these predicted
results also apply for plates of finite dimensions. The reasoning behind this fact will be
treated in section 6.5.2.