330 Building acoustics
Mechel’s Equation (9.4), which gives nearly identical results as predicted by Wilson and
Soroka (1965).
Using sealing tape only, we get a mass-spring-mass resonance of a frequency
which may also be easily calculated. We may also notice the effect of this resonance
even if the aperture is filled with mineral wool. To calculate the propagation coefficient
and complex impedance for the mineral wool a model by Mechel is used (see section
5.5.2). Calculating the reduction index for the case denoted “empty”, we have introduced
a small energy loss by setting the flow resistivity to 5 Pa⋅s/m^2 , i.e. to 1/1000 of the one
used above.
Calculation of the transmission factor for a slit shaped aperture becomes much
more complicated than for a cylindrical aperture. There will be a dependency of the
azimuth angle as well, in addition to an angle dependency of the impedances on both
sides of the aperture. Calculating for a diffuse field incidence implies a complicated
numerical integration. We shall therefore confine ourselves showing predicted results for
normal incidence only, where we may use the same equations applicable for apertures,
but where we have to exchange the radiation impedance for a circular piston with the
proper one for an infinitely long and narrow slit. An analytical formula is available,
expressed by Hankel and Struve functions (see e.g. Abramowitz and Stegun (1970)), but
we shall not give it here. It should be noted, however, that the radiation impedance of a
piston, of any shape (square, triangle etc.) and sitting in a baffle, may be calculated from
the Fourier transform of the impulse response of the piston, i.e. the response when driven
by a Dirac pulse (see Lindemann (1974)).
A
A
Section A - A
a) b) c)
Figure 9.5 Test wall of dimensions 2250 mm x 1240 mm (2.8 m^2 ) for measuring the sound reduction index of a
slit of depth 180 mm. a) Open slit; b) Slit containing 100 mm mineral wool; c) Slit with mineral wool and tape
on one side.
We shall compare predicted and measured results for a slit, where the latter was a
laboratory set-up to test the acoustic performance of different sealing methods, according
to Alvestad and Cappelen (1982). In a test wall of surface area of 2.8 m^2 a slit was made
across the aperture width of the wall, 1240 mm. The slit was formed by two steel UNP
beams placed against one another, making a slit of adjustable width (see Figure 9.5).
In the experiments, a large number of combinations of mineral wool and sealing
were tested on slit widths in the range 5 to 20 mm. We shall show some results for a slit
width of 20 mm. When comparing with the predictions, we have in addition to the