Civil Engineering Reference
In-Depth Information
6.4.2.3
Impact sound. Standardized tapping machine
As mentioned in section
6.2.2,
a standard tapping machine is used to quantify the impact
sound insulation in buildings. It was also pointed out that there have been many
objections against this machine, criticism on the practical use as regards to calibration
etc., claims that its ranking of the test objects is not coinciding with a subjective ranking
of the impact sound insulation. Concerning the ranking, problematic cases arise when
used on e.g. wood joist floors. A great deal of research has be directed towards finding
alternative methods for testing impact sound insulation, on methods using other types of
sources that in a better way simulates the impact of human footfalls. Some alternative
sources are suggested and explored; some are also included in national standards (e.g.
Japan). The topic will, however, be too extensive to treat in this topic. We shall therefore
only give specifications on the standard tapping machine.
The tapping machine has five hammers, each having a mass
m
h
of 0.5 kg. The
hammers fall freely from a height
H
of 4.0 cm; each of them falls twice per second
making the tapping frequency
f
s
of the machine equal to 10 Hz. Assuming that the
impacts on the test specimen are purely elastic, this kind of source will give a force
inside a frequency band Δ
f
that may be expressed as
2
2
F
=
2
f I
⋅Δ
f
,
Δ
f
s
(6.70)
where
I
=
mv
=
m
2
gH
.
h0
h
v
0
is here the speed of the hammer at the moment of impact giving an impulse
I
. The
quantity
g
is the acceleration due to gravity. Measuring the force using one-third-octave
bands, i.e. Δ
f
≈ 0.23⋅
f
0
, where
f
0
is the centre frequency in the band, we get
2
2
F
≈⋅
0.90
f
(N ).
(6.71)
1/3octave
0
The whole of this force is not necessarily transmitted to the floor under test; the ratio of
the point impedance to the internal impedance of the source will be a determining factor.
Instead of Equation
(6.52),
we shall have to express the mechanical power input to the
floor by
⎧
⎫
⎧
⎫
1
1
2
2
WF
=⋅
Re
=⋅
F
Re
.
(6.72)
⎨
⎬
⎨
⎬
ZZ
+
Z
+
j
ω
⎩
⎭
⎩
⎭
h
h
Assuming
Z
>>
Z
h
, which will always be the case when dealing with heavy floors as
concrete etc., we are able to calculate the radiated power by inserting Equation
(6.71)
,
the equation for the force, into Equation
(6.67)
. As an example, we shall use a
homogeneous floor slab of thickness
h
. Restricting our discussion to the frequency range
above the critical frequency enables us to set σ ≈ 1 giving
1
W
=
const.
⋅
.
(6.73)
ac
3
η
The quantities contained in the constant are the material data for the floor and the
surrounding air. This implies that the radiated power will decease by the third power of
the thickness in the given frequency range or, in other words, the sound power level will
decrease by 9 dB for each doubling of the floor thickness. In addition, assuming that the
