Acoustical Modeling and Auralization 219filter must have a sufficient bandwidth r to avoid
limiting the response of the impulse.
(9-7)Steady-state sound waves can be generated over
spherical (nondirectional) patterns up to frequencies of
about 30 kHz by using specially designed electrostatic
transducers. Gas nozzles can also be used to generate
continuous high-frequency spectra although issues of
linearity and perturbation of the medium must be taken
into account for receiver locations that are close to the
source.
Microphones are available with very good flatness
(±2 dB) over frequency responses extending beyond
50 kHz. The main issues associated with the use of
microphones in physical scale models are that the size
of the microphone cannot be ignored when compared to
the wavelength of the sound waves present in the
model, and that microphones become directional at high
frequencies. A typical half-inch microphone capsule
with a 20 cm housing in a 1:20 scale model is equiva-
lent to a 25 cm × 4 m obstacle in a real room and can
hardly be ignored in term of its contribution to the
measurement; furthermore its directivity can be
expected to deviate substantially (>6 dB) from the
idealized spherical pattern above 20 kHz. Using smaller
capsules (^1 e 4 in or even^1 e 8 in) can improve the omnidi-
rectivity of the microphone but it also reduces its sensi-
tivity and yields a lower SNR during the measurements.
9.2.1.5 Surface Materials and Absorption
Considerations in Physical Models
Ideally, the surface materials used in a scale physical
model should have absorption coefficients that closely
match those of real materials planned for the full-size
environment at the equivalent frequencies. For example,
if a 1:20 scale model is used to investigate sound
absorption from a surface at 1 kHz in the model (or
50 Hz in the real room) then the absorption coefficient a
of the material used in the model at 1 kHz should match
that of the planned full-size material at 50 Hz. In prac-
tice this requirement is never met since materials that
have similar absorption coefficients over an extended
range of frequencies are usually limited to hard reflec-
tors where a< 0.02 and even under these condition, the
absorption in the model will increase with frequency
and deviate substantially from the desired value. The
minimum value for the absorption coefficient of any sur-
face in a model can be found from
(9-8)where,
f is the frequency of the sound wave at which the
absorption is measured.Thus at frequencies of 100 kHz, an acoustically hard
surface like glass in a 1:20 scale model will have an
absorption coefficient of Dmin = 0.06, a value that is
clearly greater than D< 0.03 or what can be expected of
glass at the corresponding 5 kHz frequency in the
full-size space.
The difference in level between the energy of the nth
reflected wave to that of the direct wave after n reflec-
tions on surfaces with an absorption coefficient a is
given by(9-9)Considering glass wherein the model D=Dmin
= 0.06, the application of Eq. 9-9 above shows that after
two reflections the energy of the wave will have
dropped by 0.54 dB. If the reflection coefficient is now
changed to D= 0.03 then the reduction in level is
0.26 dB or a relative error of less than 0.3 dB. Even
after five reflections, the relative error due to the
discrepancies between a and amin is still less than
0.7 dB, a very small amount indeed.
On the other hand, in the case of acoustically absorp-
tive materials (D> 0.1) the issue of closely matching the
absorption coefficients in the models to those used in
the real environment becomes very important. The
application of Eq. 9-9 to absorption coefficients D in
excess of 0.6 shows that even a slight mismatch of 10%
in the absorption coefficients can result in differences of
1.5 dB after only two reflections. If the mismatch is
increased to 20% then errors in the predicted level in
excess of 10 dB can take place in the model.
Due to the difficulty in finding materials that are
suitable for use in both the scaled physical model and in
the real-size environment, different materials are used to
match the absorption coefficient in the model (at the
scaled frequencies) to that of the real-size environment
at the expected frequencies. For example, a 10 mm
layer of wool in a 1:20 scale model can be used to
model rows of seats in the actual room, or a thin layer of
polyurethane foam in a 1:10 scale model can be used to
represent a 50 mm coating of acoustical plaster in the
real space. Another physical parameter that is difficult
to account for in scale physical model is stiffness, thus
the evaluation of effects such as diaphragmatic'ffilter'ffilter^4
timpulset-----------------Dmin=1.8u 10 4– f'Level= 10 log 1 – Dn