ACOUSTIC PROPERTIES OF
MATERIALS
SESSIONS
Variational formulation of the radiation impedance of
absorbing patches in finite rooms
D. Holmberg, P. Hammer and E. Nilsson
Department of Engineering Acoustics, Lund University, LTH, P.O.Box 118, SE221 00 Lund, Sweden
The effect of splitting absorbers into different patches in order to improve their sound absorbing performance is investigated. A
numerical evaluation of the impact an alteration of radiation impedance, Zr , has on the statistical absorption coefficient, αstat , is made
by means of variational analysis. Implications of an alternative definition of αstat is analysed in connection with the ordinary definition
and their application in room acoustics.
INTRODUCTION
The shape of absorbers and their interaction has been
of interest for researchers for a long time. An important
drawback is that most approaches assume infinite structures. Arbitrary shapes of structures can be handled with
a variational technique developed by Morse in e.g. [1].
The radiation impedance for various (periodic) patterns
of absorbing patches is treated by the authors [2]. In this
paper radiation impedance is calculated in order to obtain
the corresponding statistical absorption coefficient. The
resulting formulations are valid under the assumption that
the driving field is sufficiently homogeneous over the various surfaces.
FORMULATION OF THE PROBLEM
It is has been claimed that, in order to increase the
sound absorption, a group of sound absorbers should not
be placed together but preferably be scattered out when
mounted in a room. The only parameter that is changed,
and relevant for the sound absorption, is the radiation
impedance. A variational formulation of the radiation
impedance Zr for periodic patterns of absorbing patches
is [2]:
ik
Zr =
∑
∑ S i, j
Z
S0
Z
e−ikR eikx,y x,y
dS0 dS
2πR
S
(1)
where the summation is over each subarea S, the integration is over both interacting areas and R is the distance between the interacting points. This formulation is a more
general formulation of Zr because of its angle dependence
(cf. figure 1). If only the angles θ = 0 and ϕ = 0 is considered, the general formulation is identical to a Zr with
no angle dependence.
Accordingly, the ordinary statistical absorption coefficient, αstat , is (cf. figure 1)
αstat (θ, ϕ) = 4 · Re(Zr ) ·
Z π/2
0
sin(θ)
dθdϕ
|ZA + Zr |2
(2)
FIGURE 1. Orientation of the angles characterising an incident
sound wave.
Furthermore, setting the absorber impedance to ZA = Zr∗
will thus give maximum absorption. In order to prevent
the absorption coefficient from exceeding unity, Thomasson [3] suggested a correction factor, K, which compensates for the increase of available power at low frequencies
Z
Z
1 π/2 2π sin(θ)
K=
dθdϕ
(3)
π 0
0 Re(Zr )
This defines an alternative statistical absorption coefficient [3]
αstat
α0stat =
(4)
K
NUMERICAL EVALUATION
In order to evaluate the influence of radiation
impedance, the absorption is calculated for the cases of
four identical square absorbing patches placed together
and apart respectively (cf. figure 2). The impedance
of the patches was chosen as ZA = ρc, the characteristic
impedance of air. This choice made it possible to make a
direct comparison to the radiation impedance of a plane
piston mounted in an infinite baffle. In the case of one
large patch, case A, the radiation impedance for perpendicular incidence is almost indistinguishable. When the
patches were spaced apart, case B, there were fluctuations
that can be explained in terms of aliasing (cf. [2]). The
difference in radiation impedance, Zr , shows when the
SESSIONS
FIGURE 2. The left figure, case A, shows the four absorbing
patches placed together and, therefore, acting as one large patch.
The right figure, case B, shows them spaced two side-lengths
apart.
statistical absorption coefficient, αstat , is calculated. As
expected, αstat is to some extent higher in case B, when
the patches are separated. At high frequencies (or small
dimensions) the effect is less because Zr → ρc, the characteristic impedance of air, in both cases. Similarly, at
low frequencies Zr → 0 in both cases.
FIGURE 4. The statistical absorption coefficient compensated
for available power, αstat , for the two configurations shown in
figure 2. The slashed line shows αstat for case A and the dotted
line shows αstat for case B. This coefficient never exceeds unity,
but should reach unity for high frequencies when ZA = ρc. A
better resolution when integrating over ϕ would give a closer
match.
CONCLUSIONS
FIGURE 3. The statistical absorption coefficient, αstat , for the
two configurations shown in figure 2. The slashed line shows
αstat for case A and the dotted line shows αstat for case B.
If Thomasson’s alternative statistical absorption coefficient, α0stat , is utilised, the result is the opposite. In the
region where αstat is higher in case B, α0stat is higher in
case A. This is important of two reasons. The use of α0stat
implies a characteristic behaviour for an absorber when
the available power is constant, whereas αstat gives the
performance in a diffuse field, e. g. near the conditions in
a reverberation room. The contributions from various angles show a great variety in some cases. Therefore, it may
be a better approach to weigh the contributions from various angles in order to characterise a room. In the case of
α0stat it is better to utilise the angle-dependent absorption
coefficient, which comes from the definition of Zr . The
other aspect is that the absorption is a characteristic for
the system. Furthermore, the fact that α0stat never exceeds
unity does not implicate that it is a material characteristic.
The change in radiation impedance when separating absorbing patches, accounts for the improvement of
sound absorption characteristics. Therefore, caution must
be exercised when conclusions are drawn from the statistical absorption coefficient, αstat , in the usual form
0 , i.e. compensated for available
and formulated as αstat
power. The usual form gives the performance of an applied absorber, whereas in the latter case α0stat never exceeds unity. α0stat is on the other hand not a characteristic
of the absorber, because absorption is a characteristic of
the system.
The differences in the statistical absorption coefficient
for periodic structures can be explained in terms of aliasing. However, deviations from a perfect diffuse field may
in practical application account for bigger differences.
Therefore, care must be taken when integrating over the
incident angles.
REFERENCES
1. P. Morse and H. Feshbach, Methods in Theoretical Physics,
McGraw-Hill, New York, 1954, Volume II.
2. D. Holmberg, P. Hammer and E. Nilsson, "Variational Solutions of Absorbing Structures with Various Patterns", in
Proc. Internoise 99, edited by J. Cuschieri et al.,Noise Control Foundation, pp. 621-626 (1999).
3. S. I. Thomasson, Acustica, 44, pp. 265-273 (1980).
SESSIONS
Optimising the Parameters Influencing the Acoustic
Properties of Plane Space Absorbers
G. A. Barnesa and C. G. Donb
a
Acoustical Design Pty Ltd, Blackburn, 3130, Victoria, Australia
Dept. of Physics and Materials Engineering, Monash University, Clayton, 3165, Australia
b
Often theatres, public buildings and working areas require additional absorbing material to improve their acoustic performance. A
lightweight broad band panel space absorber was formed from a fabric membrane pulled taut over a high density polyester
blanket supported by a perforated metal backing. By hanging the panel on different length spacers a variety of air gaps can be
created between the wall and the perforated metal sheet. A panel consisting of a 25mm thick absorbing blanket with a nominal
density of 48 kg/m3, spaced 25mm from a hard supporting surface gave a NRC rating of 0.87 when measured in a reverberation
chamber. The panel had a front surface area of 10m2 and the measurements were taken when the perimeter was not closed so
sound can pass sideways into the air cavity. This report considers ways to improve the low and mid-band frequency performance
of the panel by adjustment of the cavity depth, varying the thickness and density of the acoustic insulation, and by inserting a
septum into the cavity.
INTRODUCTION
Reflective walls often require to be treated with
additional absorbing material, which needs to occupy a
minimum of space, be readily mounted and have an
attractive surface finish. To this end, lightweight panels
have been designed which consist of a perforated metal
sheet, with a typical surface area of 2 m2, folded at the
edges to form a tray 25mm deep. Unlike most
conventional systems where the tray is filled with
absorber and the metal forms the face of the absorber
[1], in these panels the absorbing material is placed on
the outer surface, away from the wall. The air gap
between the perforated sheet and the wall can easily be
varied by using longer or shorter holding brackets
supporting the tray. As indicated in Fig.1, an
appropriate fabric then covers the absorbing blanket.
Hard Backing
(Wall or floor)
Air gap
Fabric
placed together on the hard concrete floor of a 200m3
reverberation room. A swept boom microphone was
used to measure the reverberation time at 10 positions
in the room for two different loud speaker positions
and the 20 measurements were subjected to a least
square fit. Sampling was at 0.25s intervals if T was
greater than 4s, and 0.10s for smaller values.
To test the reproducibility of the results,
measurements were taken on two different panel
configurations. One used 5 large panels while the other
was formed from 10 smaller panels. In both cases they
rested on the hard floor with a 25mm air gap between
the metal and the floor. Overall the agreement was
satisfactory, the results overlapping except for small
deviations above 1 kHz.
As many acoustic problems require increased
absorption at lower frequencies, an investigation was
undertaken to optimize the panel performance in this
region. For comparison purposes, all changes were
made to the 5 panel set, designated as the reference set.
Optimizing Parameters
Absorber
Perforated metal
FIGURE 1. Schematic of panel
A reference panel was constructed using a 25mm
thick layer of polyester with a nominal density of 48
kg/m3. The steel sheet was 0.6mm thick with an array
of circular holes giving 11% open area. A number of
such panels, with a total surface area about 10m2, were
Raising the panels above the floor on timber battens
increased the effective thickness of the air gap. No
attempt was made to enclose the sides of the panels. A
dip in the absorption coefficient becomes more
pronounced and shifts to a lower frequency as the gap
width increases, as is shown in Fig.2. This seems to
occur around a wavelength corresponding to twice the
air gap width. Improved absorption occurs at lower
frequencies, although the change becomes marginal
once the gap width exceeds about 110mm.
SESSIONS
ratio, averaged from the 25mm and 50mm type 1 data,
at different frequencies. It is apparent that below about
250 Hz the back surface has little effect, as these
wavelengths do not penetrate around the edge of the
panels. By contrast, above 250Hz the back surface is a
significant absorber.
Absorption Coefficient
1.40
1.20
1.00
0.80
0.60
130mm airgap
0.40
115mm airgap
Table 1. Effect of back surface as an absorber
Freq.(Hz) 125
250
500
1000 2000
Sx/Sp
0.94 1.07
1.37
1.44
1.35
70mm airgap
0.20
25mm airgap
0.00
100
160
250
400
630
1000
1600
2500
4000
Frequency (Hz)
FIGURE 2. Effect of changing thickness of air gap behind
perforated metal sheet
The use of absorbent blankets with different
thickness and density is shown in Fig.3. A less dense
blanket of the same thickness has reduced high
frequency characteristics while the more expensive
option of doubling the thickness of absorber produces a
significant improvement, especially at lower
frequencies.
The effect of insertion of a septum is demonstrated in
Fig.4. In this case the septum was formed by placing a
3mm thick sheet of plywood 70mm from the hard
backing with the metal panel a further 60mm away.
Thus the septum was essentially near the centre of a
130mm air gap. The 1.8m x 1.2m plywood sheet was
supported only around its edges, so the centre area was
free to vibrate. At frequencies above 300Hz the system
acts like a single 60mm air gap. A significant
improvement at the lower frequencies is achieved by
the insertion of the septum compared to the empty
130mm air gap.
1.40
1.40
1.20
1.00
0.80
0.60
25mm thick absorber, type 1
0.40
50mm thick absorber, type 1
0.20
0.00
100
25mm absorber, type 2
160
250
400
630
1000
1600
2500
4000
Frequency (Hz)
FIGURE 3. Use of different absorbing blankets. Density of
type 1 is 48kg m-3, type 2 is 18kg m-3.
This improvement is achieved by the panel
apparently having a exceeding unity above 500 Hz.
The 50mm blanket has the greater absorption
especially at lower frequencies, however, it may not be
immediately obvious why a increases so markedly.
Sabine’s formula allows the determination of the
effective absorption coefficient, a, of a material with
surface area Sp placed in a reverberation chamber.
When calculating the above results Sp was taken to be
the top face area of the panels. In practice, however,
some of the sound is absorbed by the surface facing the
floor. If the absorption coefficient of just the acoustic
blanket is ao, then the effective absorbing area of the
panels, Sx, can be found from aSp = aoSx. The ratio
Sx/Sp is a measure of the effectiveness of the back
surface as an absorber, being unity or less when the
latter plays no part in the absorption. Table 1 lists this
Absorption Coefficient
Absorption Coefficient
1.60
1.20
1.00
0.80
130mm air gap with septum
inserted
0.60
130mm air gap
0.40
70mm air gap
0.20
0.00
100
160
250
400
630
1000
1600
2500
4000
Frequency (Hz)
FIGURE 4. Effect of insertion of a septum
CONCLUSION
A panel with absorber on top of the perforated metal
sheet can cause the effective absorption coefficient to
exceed unity by a significant factor and permits the air
gap thickness to be easily adjusted. Insertion of a
septum produced essentially the same low frequency
results as using a thick, more expensive, acoustic
blanket. At higher frequencies the system behaved like
a single reduced depth air space.
ACHNOWLEDGEMENT
The authors wish to thank Mr. P Dale for his
assistance when using the Royal Melbourne Institute of
Technology reverberation room.
REFERENCE
1. Davern, W.A. Applied Acoustics, 10, 85-112 (1977).
SESSIONS
Strip Absorbers
J.P. Parkinsona J.R. Pearsea M.D. Latimerb
a
Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand
b
D.G. Latimer and Associates Ltd, P O Box 12-032, Christchurch, New Zealand
An experimental study has been carried out on the use of alternating strips of materials to produce wideband absorbers. The
absorption of a film faced foam was successfully combined with the absorption of a plain foam by combining the two materials
in strips. Excess absorption (more than the average of the constituent strips' absorption) was found in each case. The strip
absorber comprised of foam and film faced foam had greater wideband absorption than a similar absorber with the materials
layered parallel to the backing surface (film sandwiched between two layers of foam) at 24 mm total thickness but not at 48
mm thickness.
INTRODUCTION
Figures 1 and 2 show the absorption of periodically
arranged foam and film faced foam compared to the
absorption of the foam by itself and the film faced
foam by itself. The strip absorber combined the
results in a quasi-average fashion.
1.2
1.0
0.8
0.6
0.4
0.2
4000
2500
1600
1000
630
400
250
0.0
160
A Bruel and Kjaer 2260 sound analyser was used to
measure reverberation times in a reverberation room
(volume 217 m3) with and without the test specimen
present. A total of 12 reverberation decays were
measured at a variety of microphone positions and
loud-speaker
locations
for
each
absorber.
Repeatability tests indicated that the absorption
coefficients had an uncertainty of ± 1.5% in the
frequency range from 250 to 5000 Hz.
RESULTS
100
MEASUREMENTS
The foam used was a combustion modified partially
reticulated polyurethane foam of the polyether type
(CMSG). It typically has 36-38 cells / 25mm and a
bulk density of 43 kg/m3. The film used was
Mylar™, a thin (100 mm) metallised polyester film
with a surface density of 140 g/m2. Test specimens
comprised four sheets of 1.2 x 2.4 m absorber.
Absorption coefficient
Multilayer acoustic absorbers have historically been
developed with the aim of attaining high wideband
absorption.
A rigid porous layer in combination with a thin
porous sheet was modelled by Ingard [1]. It was
found that adding a thin porous cover screen gave a
significant increase in low frequency absorption.
Takahashi [2] studied the phenomenon of excess
sound absorption of periodically arranged flat
surfaces. Excess sound absorption (more than the
average of each material’s absorption) occurred in all
cases of periodically arranged surfaces.
The work described here was based on the idea of
excess sound absorption as described by Takahashi
[2]. The aim was to experimentally determine
whether the phenomenon of excess absorption applies
to impervious film faced foams, the objective being to
combine the relatively high absorption in low
frequencies of the film faced foam with the high
frequency absorption of plain foam. Comparisons are
made with the same thickness of foam but with the
film sandwiched between the foam layers as in a
traditional multilayered absorber.
Frequency (Hz)
FIGURE 1. Strip absorber of 24 mm total thickness; [·]
alternating 150 mm wide strips of foam and film faced
foam, [c] film faced foam, [o] plain foam.
SESSIONS
1.2
1.0
1.0
Absorption coefficient
0.8
0.6
0.4
0.2
0.8
0.6
0.4
0.2
0.0
Frequency (Hz)
4000
2500
1600
1000
630
Frequency (Hz)
The absorption of the strip absorber in figure 1 is
shown in figure 3, together with the average of the
absorption of the constituent strips.
The strip
absorber shows excess absorption in all frequency
bands above the 400 Hz band. The 48mm thick strip
absorber showed a similar trend..
FIGURE 4. Absorption of strip absorber compared to film
sandwiched between two layers of foam at total thickness of
24 mm; [·] alternating 150 mm wide strips of foam and film
faced foam, [c] film sandwiched between two layers of 12
mm thick foam.
1.2
Absorption coefficient
FIGURE 2. Strip absorber of 48 mm total thickness; [·]
alternating 150 mm wide strips of foam and film faced
foam, [c] film faced foam, [o] plain foam.
1.2
1.0
1.0
0.8
0.6
0.4
0.2
0.8
4000
2500
1600
630
400
250
1000
0.4
160
0.0
0.6
100
Absorption coefficient
400
250
100
4000
2500
1600
1000
630
400
250
160
100
0.0
160
Absorption coefficient
1.2
Frequency (Hz)
0.2
4000
2500
1600
1000
630
400
250
160
100
0.0
Frequency (Hz)
FIGURE 3. Excess absorption at 24 mm thickness shown
for [·] strip absorber comprised of alternating 150 mm wide
strips of foam and film faced foam compared to [´¾´] the
average of the film faced absorber and the plain foam
absorber.
The absorption of the strip absorber of figure 1 is
compared to the absorption of a film sandwiched
between two layers of foam in the traditional method
of layering the materials in figure 4. Both absorbers
have the same total thickness. The strip absorber has
greater absorption than the sandwiched film absorber
in most of the frequency bands.
A similar
comparison is given in figure 5 but for a total
thickness of 48 mm. The alternating strip technique is
less effective at this thickness. The strip absorber's
performance is clearly impaired in the higher
frequency bands when compared to the layered
system.
FIGURE 5. Absorption of strip absorber compared to film
sandwiched between two layers of foam at total thickness of
48 mm; [·] alternating 150 mm wide strips of foam and film
faced foam, [c] film sandwiched between two layers of 24
mm thick foam.
CONCLUSIONS
Alternating strips of equal width effectively
combined the absorption of the constituent strips for
each system. Excess absorption was also found for
each case. The strip absorber had greater wideband
absorption than a layered absorber at 24 mm thickness
but not at 48 mm thickness. The modelling method of
Takahashi will be used to optimise the absorption of
these materials for different strip widths, periods and
materials.
REFERENCES
1.
Ingard, U., Notes on sound absorption technology. Noise
Control Foundation. 1994.
2.
Takahashi, D., Excess sound absorption due to periodically
arranged absorptive materials, Journal of the Acoustical
Society of America, v86, 1990:2215-2222.
SESSIONS
An Innovative Sound Absorption System which Fulfils the
Highest of Acoustic and Aesthetic Requirements
H.D. Sulzer
Dipl. lng., BASWA AG, Baldegg Sound and Heat Absorption Company,
Marmorweg 10, 6283 Baldegg, Switzerland
®
The newly developed BASWA -phon absorptive system, which is seamless and looks like plaster, closes a gap in the field of
absorptive solutions and opens up new design possibilities for builders and architects. The absorptive coefficients measured are
excellent, especially in the low frequency range, due to resonance of the microporous membrane formed by the absorptive plaster
after drying. The loss of room height is minimal, since the total thickness of the system is maximum 6 cm. Seamless surfaces of
up to 500 m2 have been installed without any problems.
INTRODUCTION
The multiple reverberation of sound waves in rooms
often creates an undesirable acoustical field, in which
music can become distorted and the human voice can
become barely audible.
Reverberation occurs
· in medium- and large-sized rooms,
· in rooms whose boundary surfaces are hard and reflecting,
· in domes and vaults, which are particularly sensitive,
as they tend to focus reverberation on the underlying
floors.
The usual measure to decrease reverberation consists
of the treatment of a part of the boundary surfaces with
an absorptive porous layer made of juxtaposed elements. Many absorptive systems are available on the
market. They are not greatly favored by building owners, users or architects, however, as they are not
aesthetically pleasing and are difficult to integrate into
new and existing buildings. They also imply a sensitive
reduction of room height and important additional
costs.
The method presented here is suitable in most cases
and adaptable to any specific surroundings. Usually
only the room’s ceiling is subject to treatment. Walls
and vaults can also be made absorptive, however. It has
to be emphasized that a room’s acoustics can also be
corrected after construction has been completed and
high reverberation has been established, as is the case
in many historical or multi-purpose buildings.
POROUS COATING MATERIALS
A porous coating compound called BASWA-phon
has been developed, which possesses very good acoustic qualities when applied on propriatory mineral wool
panels leading to air-flow resistance of 100-160 Rayls.
The seamless absorptive plaster, applied on site, is
made of white granules of similar size and offers a
smooth but microporous surface after drying, allowing
the sound to penetrate the underlying fibrous absorptive panels, which have been previously glued to the
surface to be treated.
When the compound dries, a 5 mm thick membrane
is formed. Its natural color is white (RAL 9002), but
coloring the compound is possible, on the condition
that the pigment component does not exceed approximately 1%. Coloring is done in the factory.
THE ACOUSTIC ABSORPTION
SPECTRUM
The BASWA-phon coating’s formulation is calibrated in such a way that after it has dried, an extensive
system of micro-pores is created in the 5 mm coat that
has been applied. Sound absorption takes place in the
pores and in the fibrous underlying mat on account of
friction between vibrating air molecules, with the result
that sound energy is converted into heat and dissipated.
This is the usual physical process which takes place in
almost all sound absorption materials available on the
market. The random distribution of the micro-pores
and the coating’s three-dimensional porousness, however, increases the effect when compared to standard
methods.
In addition, by coating glass fiber mats with the material, a favorable combination of two sound absorbing
materials, and thus an enlarged absorbing spectrum, is
created. The dried and now hard 5 mm BASWA membrane simultaneously vibrates on the elastic fiber mat
with a main vibrational spectrum in the low frequencies. This effect complements the friction absorption in
the low frequency range. Thus a balanced-out total
absorption spectrum between 125 and 4000 Hertz is
created. The system has ‘wide-band’ absorption quali-
SESSIONS
even after the intense application and smoothing procedure, so that its acoustic effectiveness is largely
independent of the site handling procedure.
Degree of sound absorption as
Degree of sound absorption as
ties, a fact which is always praised again by acousticians (Figures 1 and 2).
The BASWA coating’s porousness remains intact
Frequency f
FIGURE 1. Sound absorption capacity of a 5 mm BASWAphon coat on 60 mm mineral fiber boards, with the system’s
distance from the ceiling = 0 mm.
FROM THE MATERIAL TO THE
SYSTEM
As has already been mentioned, the coating compound is applied seamlessly to fiber mats, which in
turn are stuck to the raw ceiling. Thanks to the coating’s full compatibility with 3 - 6 cm thick glass fiber
mats architects, acousticians and building owners now
have a new, fair-price solution to the problem of room
acoustics. It is increasingly accepted and used, particularly in representative rooms such as entrance halls,
bank service till halls, conference rooms, exhibition
centers as well as in schools, hospitals, restaurants,
residences, gyms and multi-purpose halls. The new
system is particularly appreciated in the preservation of
monuments, as the absorptive surfaces can be accommodated within existing stucco profiles without any
problems. The material is independent of the size and
texture of the ceiling (vaults, for example). Elements
such as lights and fire alarms can be integrated without
any problems.
MATERIAL AND PROCESSING
Frequency f
FIGURE 2. Sound absorption capacity of a 5 mm BASWAphon coat on 60 mm mineral fiber boards, with the system’s
distance from the ceiling = 250 mm.
white coating seamlessly in two operations. The material itself is supplied as a wet ready-to-use compound
in plastic buckets. Layers of BASWA-phon are applied
and have to dry during 24 to 48-hour periods (the compound has to dry completely), until a thickness of
approximately 5 mm is reached. As the compound
behaves like plaster during processing and is applied
by plasterers, it can be adapted to any shape, such as
arches, vaults or walls.
CLEANING, RENOVATION
Of course you have the possibility of cleaning smoke
stains and fat, for example, off dirty surfaces, using a
special solution developed by the producer.
CONCLUSIONS
With BASWA-phon, architects and acousticians have
a material available for the correction of a room’s
acoustics which is aesthetic in appearance and flexible
in use.
The glass fiber mats have to be glued to the raw
ceiling first, or to unperforated plaster boards in suspended ceiling systems. Following this, the joints between the mats are closed with a special seam fill. The
final step involves sanding the base and applying the
SESSIONS
Absorption for the Control of Reverberation by Using
Perforated Gypsum and Wood Boards
J. Ramis, J. Alba ,J.M. Bravo and J.Redondo.
Departamento de Física Aplicada, Escuela Politécnica Superior de Gandia, 46730 Grao de Gandia, Spain
For the acoustics conditioning of auditoriums is very important the control of reverberation. In this work results from
measurements of absorption coefficient for perforated gypsum and wood boards carried out in the reverberation chamber of
EPS Gandia are presented. This device could be applied for the control of reverberation in the range of medium to low
frequencies. We analyse the influence of different kinds of porous sheets in the air cushion and the influence of others factors
that are significant influence in the results. The results are interesting from point of view of architect that it is interested in
room boundaries with the same appearance but with different acoustical properties.
INTRODUCTION
The absorption for the control of reverberation is very
important speaking rooms acoustics. Porous material
are very effective sound absorbers . Their absorption
coefficients decrease at low and medium frequencies.
However, most porous sound absorptive sheets do not
present suitable surfaces for rooms. Perforate plates
were originally introduced as acoustically transparent
covering that could be easily cleaned and painted.
Figure 1b show typical configurations.
is produced for the resonant frequency). For
configuration 1b (perforated plates), the maximum of
absorption is presented for :
f 0 = 5480
where , P is the percentage of perforation defined by:
P=
Sa
Sb
L’ = L + 1.6a
wall
air
absorbent
board
air
wall
absorbent
FIGURE
ERRORE.
L'ARGOMENTO
PARAMETRO È SCONOSCIUTO..
Typical
configurations. a) without perforation b) With
perforation
For the first configuration (figure 1-a), the resonance
frequency can be estimated by the equation
600
f0 =
md
(2)
(3)
Sa being the perforated surface and Sb the surface of
plate, and L’ is the effective length
Perforate plate
board
P
L' d
(1)
where m is the surface density (in Kg/m2) and d the d
la distance to wall (in cm). (The maximum absorption
(4)
Where L is the thickness panel and a is the radius
perforation.
Only if the percentage of perforation is large enough
the plate will be acoustically transparent. In this case,
the absorption coefficient of the system and that of the
absorbent material would be roughly the same.
DETERMINATION OF ABSORPTION
COEFFICIENT IN REVERBERATION
ROOM
The procedure followed for the determination
absorption coefficient is described in [2]. From
measurements reverberation time with and without
material sample can be obtain the absorption
coefficient of device. Limitations and uncertainly for
this method are discussed in [1] and [3].
SESSIONS
MEASUREMENTS
0,900
0,800
We have characterized configurations with air cushion
of 2.5, 5, 10 y 15 cm, totally and partially filled of
rockwool of 40, 70 y 90 Kg/m3 density. With the
plenum partially filled, the rockwool was placed either
next to the wall, or next to the plate.
0,700
0,600
0,500
0,400
0,300
0,200
0,100
0,000
Next, we show some results. Figure 2 show the
variation of absorption coefficient for different widths
plenum. In figure 3 we present the effect if number of
holes is incremented. Figure 4 describes the effect of
the increment of the diameter of the holes. The
consequence of introducing an absorbent material in
plenum is shown in figure 5. Figure 6 corresponds to a
wood a panel with different absorbent material in the
plenum.
100
10 0 0
FIGURE 5. Variation of the absorption coefficient
with the frequency. Continuous line: with material
absorbent. Dotted line: without rockwool of 70 Kg/m3.
0,80
0,70
0,60
0,50
0,40
0,900
0,30
0,800
0,20
0,700
0,10
0,600
0,00
100
0,500
1000
10000
0,400
0,300
0,200
0,100
0,000
100
1000
FIGURE 2. Variation of the absorption coefficient
with the frequency for two air cushions. Continuos
line: 5cm. Dashed line: 2.5 cm.
CONCLUSIONS
For perforation percentages less than 10 % and more
of 50%, the application of equation (2) in not
satisfactory. In this range, the increment in the number
of holes or their diameter produces a increment of the
frequency of resonance. If the air cushion is enlarged
the maximum of absorption is presented for a larger
frequency.
0,400
0,350
0,300
0,250
0,200
0,150
0,100
0,050
0,000
10
FIGURE 6. The same as fig.5. Continuous line:
Plenum Wide. Dashed line: 40 Kg/m3 .Dotted line:
Rockwool 70 Kg/m3.
100
1000
FIGURE 3. Variation of absorption coefficient with
the number of holes. Continuos line: 150 holes.
Dashed lines: 75 holes.
The introduction of absorbent material produces a
decrease of the resonant frequency and an increase the
bandwidth.
When the air cushion is partially filled with absorbent
material, it is more efficient than when it is placed next
to the plate.The more permeable is the fabric the more
is the increase in absorption coefficient after
introduction of the absorbent material
0,900
0,800
0,700
0,600
0,500
0,400
0,300
0,200
0,100
0,000
100
1000
FIGURE 4. Variation of absorption coefficient with
holes diameter. Continuos line: D=13 mm. Dotted
lines: D=10 mm.
REFERENCES
1. E. Cremer et Al., Principles and Applications of Room
Acoustics, London: Applied Science Publishers (1982).
2.
ISO 354, Measurements of the absorptioncoefficient in
a reverberation room (and UNE 74-041).
3.
3.Alba, J. et AL, Incertidumbre en la técnica de medida
de la absorción en cámara reverberante.. Tecniacústica
99. Ávila (Spain).
SESSIONS