302 Building acoustics
and thickness we obtain a more or less “flat” part on the curve before reaching
coincidence.
It is also important to note that even if the critical frequency is relatively high, the
radiation factor may be larger for a sandwich element as compared with a homogeneous
one. The reason is that the phase speed cB will have a value close to the speed of sound in
air over a broad frequency range. This implies that resonant transmission will be a more
important factor below coincidence than in the case of a homogeneous element.
10 20 50 100 200 500 1000 2000 5000
Frequency (Hz)100
1000
200400600800Phase speed (m/s)
50100c 0Figure 8.21 Phase speed cB of the sandwich element having bending stiffness as shown in Figure 8.20. The
speed c 0 is the phase speed in air.
How does one calculate the sound reduction index of a sandwich element having
such frequency-dependent bending stiffness? This may be accomplished by using just the
same expressions as given in Chapter 6 valid for a homogeneous single element,
however, to calculate the reduction index at each frequency by using the radiation factor
etc. appropriate for the bending stiffness in question.
An example is shown in Figure 8.22, where the reduction index is calculated for the
element discussed above, however for three different core thicknesses. We have also
assumed that the surface area is 10 m^2 and that the element has a total loss factor of 0.05.
For comparison, a curve giving the simple mass law is included. It should be obvious that
a poor design may produce quite dramatic failure in the sound insulation, added to the
fact that one is starting out with a lower reduction index than predicted by the mass law.
As opposed to the figures illustrating the bending stiffness and the phase speed, we have
not calculated the reduction index corresponding to the dashed curve, where the shear
stiffness of the 100 mm core is reduced by a factor of two. How would you expect the
reduction index to be in that case?