Civil Engineering Reference
In-Depth Information
4
π
λ
r
4
π
rf
0
M
(circular path)
≈
=
.
(4.62)
eq
c
0
The quantities
r
and
f
0
are the path radius and the centre frequency in the actual
frequency band, respectively. A microphone path corresponding to three discrete
microphone positions at 100 Hz should, therefore, have a radius of approximately 0.8
metres.
Accurate estimates of the measurement accuracy at frequencies below
f
S
are
difficult to attain, but there are guidelines in measurement standards to improve the
accuracy (see below). As seen from Equation
(4.52)
, the number of modes excited is
vital, and exciting the room by band-limited noise will certainly excite most modes inside
the frequency band. However, we have seen that a source cannot excite a mode having a
node at the source position. This is one reason for the requirements in standards to use
several source positions, which is particularly important when measuring at low
frequencies. It should not come as a surprise that some laboratories are, using not only a
moving microphone but also a moving source.
Eventually, at sufficiently low frequencies, the number of modes will be too small
to realistically speak of a space averaged value of the squared pressure. The exception is
when the frequency gets so low that there will only be a homogeneous pressure field in
the room, i.e. when going below the first eigenmode for the room.
Guidelines and help on these questions are given in national and/or international
standards. These give guidance and requirements as to the choice of measuring positions
and source positioning; the number of these depending i.a. on frequency and room
volume, the distance of microphone positions from the source and from the room
boundaries etc. Information is also given on the measurement uncertainty of the
procedure or method. Concerning the latter, one will find the concepts of
repeatability
and
reproducibility
standard deviation. The former implies the standard deviation
obtained when repeating a given procedure within a short time interval and under
identical conditions (same laboratory, same operator, same measuring equipment).
Otherwise, when these conditions are unequal, we have reproducibility conditions. The
standard deviation of reproducibility therefore includes the standard deviation of
repeatability. Data for reproducibility are usually established by round robin experiments
by a number of participating laboratories.
To conclude, one will find the necessary instructions in the relevant standards to
perform most measurement tasks. The purpose of dealing in some detail with the basis
for these measurements are twofold: to give some understanding of the formulations,
found in these standards, at the same time give some assistance when presented with a
measurement task not covered by any standard.
4.6
GEOMETRICAL MODELS
A number of computer software programs, of which many are commercially available,
are developed to predict sound propagation in large rooms, e.g. concert halls or large
factory spaces. We shall not present any overview of the various programs or deal with
specific published work where these programs are used but limit ourselves to give an
outline of the principles behind the models. The majority of prediction models used for
large rooms are based on geometrical acoustics, partly combined with statistical concepts
to include scattering effects. Judged by the concepts found in the literature dealing with
these prediction models, there may be some confusion as to the number of basic methods
used. In effect, there are only two basic methods, the
ray-tracing method
and the
image-
