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The edge absorber as a ?modal brake?
Eric Kurz, Daniel Reisinger, Werner Weselak, Gerhard Graber
To cite this version:
THE EDGE ABSORBER AS A ”MODAL BRAKE”
Eric Kurz
1Daniel Reisinger
1Gerhard Graber
1Werner Weselak
1 1Signal Processing and Speech Communication Laboratory
Graz University of Technology, Austria
eric.kurz@tugraz.at, graber@tugraz.at
ABSTRACT
Nowadays, knowledge about the acoustical influence of edge absorbers (EA) on a sound field is mainly based on empirical experience. Unfortunately, there is no compu-tational model for the EA. Hence, this type of absorber is used hesitantly in the room acoustical design process. This contribution investigates the absorption behaviour of EAs systematically and proposes an approach for a com-putational model for EAs in simple room geometries. For the systematically investigations a modular EA was devel-oped and constructed. In the development process opti-mal parameters for flow resistance, perforation ratio of the absorber housing and layer thickness of the incorporated porous material could be found. Due to the modular prin-ciple of the EA flexible assembly is possible.
Different configurations of the modular EA were measured in the reverberation chamber. The acoustical behaviour of the EA was determined in several lecture halls. Equiva-lent absorption area per unit of length and lower frequency limit of the EA are dependent on the assembly depth and the respective edge of assembly. Moreover, the bandwidth for effective absorption is dependent on the EAs dimen-sions.
The modular EA was deployed in a room acoustical reno-vation and pre-post measurements were performed to con-firm the vast effect of the EA.
1. INTRODUCTION
Intelligibility of speech as well as transparency of music in a room are strongly dependent on its acoustic qualities. If speech intelligibility in a room is poor additional cogni-tive resources have to be provided by a human to process the spoken information. Therefore an adequate acoustical treatment of rooms is necessary and is often done by in-stallation of absorbent surface lining made out of fibrous or porous materials. With these absorbers the effective sound field control for frequencies above 250 Hz is given. Unfor-tunately, effective sound field control for low frequencies is a more demanding but even important task.
From psychoacoustic investigations done by Wegel [1] and Tobias [2] we know about the broadband masking effect of low frequencies, especially for frequencies above the masking frequency fM (cf. [3]). Moreover the importance
of low frequency sound field control in room acoustics and its effect on speech intelligibility and music transparency could be shown e.g. by investigations from Kuttruff [4, p. 617] and Fuchs [5–7]. 0 2 4 6 8 10 0 1 2 3 4 2kr p2 r/p2ref 0 2 4 6 8 10 0 1 2 3 4 2kr v2 r/v2ref r
Figure 1: Relative potential and kinetic Energy in front of an edge placed in a quadrant of an open 2D-space averaged over all directions of arrival [8].
In order to control the low frequency sound field it is very important to take care about the placement of absorbent material in the room and to investigate the interaction of the material with the sound field. For low frequencies the modal properties, which are mainly influenced by the rooms resonance frequencies, determine the distribution of sound pressure p and velocity v in the room. Consequently, this distribution can be used to determine optimal positions for absorbent material in a room. Moreover, from theoret-ical investigations from Waterhouse [8] follows that espe-cially in edges and corners of a room high sound pressures and velocities can be expected. Image source theory for an edge and an incoming planar sound wave from an open quarter space cause constructive interferences and an in-crease of the relative potential and kinetic energy in front of that edge (cf. figure 1).
Based on this knowledge it is reasonable that EAs, also known as bass traps, are quite popular in the room acoustic community and well-known as low frequency noise sup-pressors. The advantages of EAs are quite obvious. They provide a broadband absorption for low frequencies (ap-prox. 30 Hz to 250 Hz) and can be manufactured with a well-balanced cost-benefit ratio. In room acoustical reno-vations the subsequent assembly of EAs can often be done with minimum effort and their subtle architectural concept allows an unobtrusive integration as covering for conduc-tions and plumbings or as benches.
soft-ware like e.g. COMSOL [10] is very time-consuming, es-pecially for more complex sound fields, and therefore un-practical for the room acoustical design/planning process. Therefore the need for a suitable and computational effec-tive EA simulation software is obvious.
This paper aims to gather a more detailed understanding of the principles of modal sound field control with the help of EAs and proposes suitable acoustical parameters for a sim-ulation of EAs. The investigations presented in this paper are part of the master thesis from D. Reisinger [11]. The paper is structured in the following way: The second section presents a brief review of the basic absorption prin-ciples of EAs. Section 3 describes the developed EA that was deployed in our investigations and introduces the setup for the measurements that were performed in the reverber-ation chamber (RC) as well as in different lecture halls. To get an understanding of the acoustic behaviour of the EA results of the measurements in the RC are presented (Sec-tion 4.1). Sec(Sec-tion 4.2 describes outcomes of measurements that were performed in different lecture halls to validate the findings of Section 4.1. A discussion and a brief summa-tion of the gathered insights complete the paper.
2. THEORETICAL INVESTIGATIONS Broadly speaking, an EA can be seen as a passive absorber, that is more sensitive to sound velocity than to sound pres-sure. It is placed, like the name suggests, in edges and also corners of a room. In previous investigations by Maa [12] and Kuhl [13] it could be indicated that the deployment of porous absorbent material in room edges and corners raises the effective absorption, especially in the lower frequen-cies. A modern EA consists out of a duct construction that is filled with porous absorbent material. The height and the depth of the duct are small in comparison to its length.
2.1 Interference phenomena
The main absorption principle of the EA can be explained by looking at interference phenomena close to an acousti-cally rigid edge and the modal sound field in a room. In a first step we assume that the x-y- and x-z-plane form-ing a perfectly reflectform-ing edge (x-axis) in an infinite open quarter space. The edge is large in comparison to the wave-length λ of a sinusoidal plane sound wave of unit ampli-tude, that is incident from infinity with incident angles ϑ and ϕ (cf. fig. 2, right). For this setup an image source model can be deployed. Due to the interference of the inci-dent and the reflected wave a varying sound pressure p and particle velocity v can be expected. Both quantities vary-ing with respect to the distance from the edge and the in-cidence angle of the sound wave. It can be shown (cf. [8]) that for this model following proportionalities for the rel-ative potential energy hp2i and the relative kinetic energy hv2i are valid:
hp2i ∼ (cos b cos c)2, (1)
hv2i ∼ 1 − cos 2β cos 2b − cos 2γ cos 2c
+ cos 2α cos 2b cos 2c. (2)
Hereby the single terms are: cos α = cos ϑ,
cos β = sin ϑ sin ϕ, cos γ = sin ϑ sin ϕ,
b = ky cos β, c = kz cos γ.
Figure 2 shows the behaviour of the relative potential as well as kinetic energy of a single planar wave for kr = 1 in dependence on the incident angles ϑ and ϕ. Because of symmetry the depending surfaces for hp2i and hv2i are
plotted for 0 ≤ ϕ ≤ π/4 and π/4 ≤ ϕ ≤ π/2. The results for hp2i and hv2i are in great contrast to each other.
It is evident that hv2i ≈ 4 · hp2i for a streaking incident
angle ϑ → 0. For perpendicular sound incidence in the symmetry plane of the edge (ϑ = π/2, ϕ = π/4) hp2i < 1
and hv2i = 1. If the sound wave streaks the y- resp. x-z-plane (ϕ → 0 resp. π/2) a mean gain of hv2i = 2.45 is
achieved. However, for hp2i no additional gain is achieved
in this case. Integration over all possible incidence angles ϑ and ϕ of the half of the hemisphere is done by
hp2 ri = 1 π Z π 0 Z π/2 0 hp2i sin(ϑ)dϕdϑ (3) and hvr2i = 1 π Z π 0 Z π/2 0 hv2i sin(ϑ)dϕdϑ. (4) Inserting (1) and (2) into (3) and (4) leads to expressions
hp2 ri ∼ 1 + j0(2ky) + j0(2kz) + j0(2kr) (5) and hv2 ri ∼ 1 − j0(2ky) + 2 j1(2ky) ky − j0(2kz) + 2 j1(2kz) kz − j0(2kr) + 2 j1(2kr) kr . (6)
Whereby r2 = y2+ z2and jn(x) is the spherical bessel
function jn(x) = (−x)n 1 x d dx n sin x x . (7) 0 π/4 π/2 0 π/4 π/2 0 2 4 ϑ ϕ hp2i, hv2i x z y 0 ϑ ϕ i
Figure 2: Left: Relative potential and kinetic energy (hp2i, hv2i) of a single planar wave for kr = 1 in
We can evaluate (5) and (6) on the symmetry plane of the edge (ϕ = π/4 resp. y = z) with respect to the distance r and the frequency f of the incident sinusoidal plane waves. The results of this evaluation are shown in fig. 3 and 4. For both relative energies hp2ri and hv2ri, two distinct
ar-eas can be distinguished. The first area is dominated by constructive interferences leading to high relative energies hp2
ri ≈ 4 and hv2ri ≈ 2. For a larger r and higher
frequen-cies f this constructive interference is not given anymore. hp2
ri descends to a mean value ≈ 1 with a ripple depending
on r and f . The same is true for hv2
ri but with a little more
distinct ripple.
More detailed analysis of fig. 4 reveals a distinct increase of hvr2i that divides the two areas and reaches a maximum
of hv2
rimax ≈ 2.2. Moreover, the behaviour of hv2ri for
small r seems to be inexplicable if we assume that the sound velocity near to a acoustically rigid surface has to decrease towards zero. However, this effect is mainly valid for sound velocity components orthogonal to the acousti-cally rigid surface. Neglecting the acoustic boundary layer at the rigid surface, the streaking components of v do not
20 200 2000 0 0.25 0.5 0.75 1 1 2 3 4 f in Hz r in m hp2 ri
Figure 3: Mean potential energy hp2
ri along the
symme-try plane of the edge (ϕ = π/4) in dependence on the distance r and the frequency f of the incident sinusoidal plane waves. 20 200 2000 0 0.25 0.5 0.75 1 1 2 f in Hz r in m hv2 ri fhv2 rimax = c 6.28·r fhv002 ri fhv0 2 ri
Figure 4: Mean kinetic energy hv2
ri along the
symme-try plane of the edge (ϕ = π/4) in dependence on the distance r and the frequency f of the incident sinusoidal plane waves.
—: Fitted function for the frequency dependent behaviour of the maximum mean kinetic energy hv2rimax.
- - -: Distance-dependent lower and upper critical frequen-cies fhv0 2
riand f
00 hv2
ri.
have to decrease. Therefore, they are dominating the be-haviour of hv2
ri. Also the flat and frequency-independent
behaviour of hv2
ri for the first area can be explained with
this knowledge.
If we assume that hvr2imaxmarks the edge of the area with
hv2
ri ≈ 2 a cut-off frequency fhv2
rimax in dependence on r
can be defined. A fitting with the hv2
rimax data and with
a model similar to the λ4-rule was performed to find pa-rameter ψmax(8). Moreover distance-dependent upper and
lower critical frequencies (fhv002 riand f 0 hv2 ri) can be defined (9,10). fhv2 rimax= c ψmax· r = c 6.28 · r (8) fhv002 ri= fhv2rimin= c ψmin· r = c 1.32 · r (9) fhv0 2 ri= c (2 · ψmax− ψmin) · r = c 11.24 · r (10) The results from this theoretical contemplation lead to the impression that the conduction of the sound field due to the acoustic rigid edge is responsible for a gain of sound pres-sure and sound velocity that runs in parallel to the edge. Especially in the frequency range fhv0 2
ri < f < f
00 hv2
ri a
high sound velocity can be expected. 2.2 Modal sound field
In a next step we assume a low frequency excitation in a room that leads to a modal sound field. This modal sound field and therefore the distribution of sound pressure and velocity maxima is mainly determined by the rooms ge-ometry. Particularly this effect is present in the edges of a room, were two boundary surfaces guiding the standing waves that take shape parallel to the edge (cf. fig. 5). The additional gain for potential and kinetic energy from sec. 2.1 for the standing waves parallel to a rooms edge resulting in a further amplification of sound pressure and velocity along this edge. Empirical studies show that there can be a gain of up to 20 dB for specific frequencies. The conjunction of this two principles could be an explana-tion for the high absorpexplana-tion efficiency of porous material in room edges. pmax vmax pmax vmax pmax
3. METHODS 3.1 Development of the edge absorber
The aim of the EA development was to realize a light-weight modular and flexible EA system that is simple in construction and cost-efficient. It should have high broad-band absorption in low and low-mid frequencies and low absorption in high-mid and high frequencies.
At first, a housing for the EA was designed. Afterwards, measurements with the impedance tube according to mea-surement standard ¨ONORM EN ISO 10534-2 [15] were performed to find an optimal combination of absorbent porous material and a suitable covering.
3.2 Modular housing system
Figure 6: Model of the developed housing system module for the EA.
For our investigations a modular housing system for the EA was developed (see fig. 6). With this system a high mounting flexibility of the EA is achieved. The EA can be modified in length, amount of filling and covering. In total 9 modules with 1000 mm length and 14 modules with 1500 mm length were manufactured. All the modules have a quadratic cross section with an depth dimension of bEA = 400 mm and can be connected to each other via
a plugging system. The modular housing system allows measurements of different configurations of the EA (see sec. 3.5) as well as an effortless assembly, transport and storage. As depicted in fig. 6 one of the covering plates is perforated so that the sound wave can enter the absorber. An optimal hole ratio of σ = 20 % was found to have best suitability for the EA (cf. sec. 3.3). The non-perforated covering plate ensures a better guiding of the sound waves inside the EA.
With r = √2 · bEA and the equations 8, 9 and 10 the
frequency for an expected absorption maximum as well as upper and lower frequencies for effective absorption can be computed. The values are: fhv2
rimax = 97 Hz, f00 hv2 ri= 458 Hz and f 0 hv2 ri= 54 Hz. 3.3 Materials
In total 170 measurements of different material layer con-figurations were performed with respect to the modular housing system (see sec. 3.2).
50 63 125 250 500 1k 2k 0.4 0.6 0.8 1 f in Hz α(f ) LP20b AB385 L0
Figure 7: Absorption coefficient α(f ) for the layer con-figuration: perforated plate with hole ratio σ = 20% and plate thickness dp = 0.015 m, hole covering Molino,
ab-sorbent porous material with flow resistance Ξ ≥ 5 kP a·sm2
and layer thickness da = 0.385 m.
Based on the results from the measurements with the impedance tube the EA consists out of an absorbent porous material with Ξ ≥ 5kP a·sm2 that is covered completely with
Molino. The perforated plate for housing has a hole ratio of σ = 20% and the housing is filled completely with the absorbent porous material. The resulting absorption be-haviour is depicted in fig. 7.
Of course, the absorption coefficient α(f ) for the EA deter-mined with the impedance tube only can be a first approx-imation to its acoustical behaviour in a real sound field, especially when it is mounted in the edge of a room. Also, the paris formular [16, p. 479] seems not suitable to con-vert an incidence angular dependent α to an α for diffuse sound incidence. Consequently measurements in the RC have to be carried out (cf. sec. 3.5).
3.4 Setup
For measurement of room impulse responses (RIR) in the RC (sec. 3.5) as well as in the lecture halls (sec. 3.6) fol-lowing loudspeaker setup was used:
• Norsonic Dodecahedron Loudspeaker Nor276 with Power Amplifier Nor280
• 4 x Lambda Labs CX-1A High Power 2-way coaxial monitor with a low cut at 140 Hz
• Lambda Labs MF-15A High Power Subbass with a high cut at 140 Hz
All the speakers were used simultaneously. The coax-ial monitors together with the subwoofer extended the measurement frequency range to high as well as to low frequencies. A sine sweep from 1 Hz to 24 kHz with fS = 48 kHz and a length of 20 s was used as excitation
signal.
The measurement microphone setup consisted out of 6 G.R.A.S. 46AE 1/2” CCP freefield microphones connected to a PAK MKII measurement system from M¨uller-BBM.
3.5 Reverberation chamber
20 50 100 150 200 fG,RC
63 Hz 80 Hz 100 Hz 125 Hz 160 Hz
f in Hz
Figure 8: Distribution of axial (•) and tangential (•) modes and fG,RC of the RC of TU Graz. Vertical dotted lines
mark the boundaries of the respective 1/3-octave band. With its dimensions of 8.35 m x 5.99 m x 4.9 m (L x W x H), it has a floor area of Af = 50.02 m2, a volume of
V = 245.1 m3and a critical frequency [18, p. 344]
fG,RC=
1000
3
√
V = 159.8 Hz. (11) Measurements of frequency bands above fG,RC can be
performed without big influences of room modes. Be-low fG,RC the sound field is dominated by modal
ef-fects. When looking on the modal distribution of the RC (cf. fig. 8) strong influence of single modes on the sound field can be expected for f < 100 Hz. Moreover, there are mode clusterings at 70 Hz, 83 Hz, 105 Hz and 150 Hz for which a high absorption with an EA can be expected. 3.6 Lecture halls
To verify the findings from measurements in the RC an additional measurement series in lecture halls according to tab. 1 was performed. Floor plans of the lecture halls are depicted in fig. 13 and 15.
lecture hall Afin m2 V in m3
2a 66 243
FSI 1 128 550 FSI 2 62 257
i14 76 265
Table 1: Investigated lecture halls with depending floor areas and room volumes. Lecture hall 2a is located in Bundesrealgymnasium Keplerstrasse Graz. All the other lecture halls are located on campus Inffeldgasse of Graz University of Technology.
4. RESULTS 4.1 Reverberation chamber
The investigations in the RC included the influence of the EA on the sound field when positioned in x-, y- and z-edges and combinations of edge positioning as well as po-sitioned on the floor and wall.
To become a better assessment of the absorption efficiency of the EA an equivalent absorption area per unit length of the edge absorber is defined with:
Ae,l= S · α lEA = Ae lEA (12) Hereby, the variables are defined in the following way:
• S ... area of the EA facing the sound field • α ... absorption coefficient
• Ae ... equivalent absorption area
• lEA ... total length of the EA
To investigate the effect of an appropriate positioning of the EA comparative measurements for floor/wall position-ing and edge positionposition-ing were conducted. The correspond-ing positioncorrespond-ing situations of the EA for the x-, y- and z-edges in the RC are depicted in fig. 9. For reasons of com-parability the positioning of the EA in z-direction was done in two edges on the same wall of the RC. The resulting EA lengths/surfaces are 7.5 m/6.32 m2, 5.5 m/4.72 m2and 7 m/5,92 m2for x-, y- and z-direction.
Fig. 10 shows the equivalent absorption area per unit length Ae,lfor positioning of the EA in the three edge directions
of the RC (cf. fig. 9). It is obvious that the maximum Ae,l for every EA positioning is reached for different
fre-quencies (80 Hz, 125 Hz and 200 Hz). However, the main contribution to the absorption for the respective EA posi-tioning is in the frequency range for effective absorption. For frequencies above fhv002
rithe absorption of the EA
con-figurations resembles to each other.
(a) (b) (c)
Figure 9: Different EA positioning along the x-, y- and z-edges (a, b and c) of the RC (black elements) as well as the corresponding EA positioning on the floor (a and b) and on the wall (c) for comparative measurements (grey elements). 31.5 63 125 250 500 1k 2k 4k 8k 0 0.5 1 1.5 2 frequency band in Hz Ae,lin m2per unit length
x-edge y-edge z-edges
Figure 10: Equivalent absorption area per unit length Ae,l
in 1/3-octave bands for EA postioning in x-, y- and z-edges of the RC according to fig. 9. Vertical dotted lines fhv0 2 riand f 00 hv2 ri
Moreover, to become a better understanding of the effect of positioning of the EA in the rooms edges same ab-sorber configurations were measured for floor/wall posi-tioning (cf. fig. 9 grey elements). Afterwards the resulting equivalent absorption area per unit length for the floor/wall positioning ˆAe,l is used to compute the difference ∆Ae,l
between edge and surface positioning of the EA (13). With this procedure the relative gain of Ae,l by positioning the
EA in the rooms edges can be shown.
∆Ae,l= Ae,l− ˆAe,l (13)
Results of the procedure are plotted in fig. 11. Obviously the highest ∆Ae,lfor the respective EA positioning can be
found in the expected bandwidth for effective absorption again. The frequency for the maximum gain in Ae,lis
de-pendent on the direction of positioning of the EA but the frequencies match with those from fig. 10. Although, there is a less distinct absorption maximum for the z-edges in comparison to the x-edge positioning of the EA (cf. fig 10) the relative gain to the respective surface positioning is striking.
Further configurations of the EA, including a positioning in x- , y- and z-edges simultaneously, positioning with dif-ferent numbers of EA towers in the z-edges as well as a belt-like positioning with and without EA towers in the z-edges, were measured. Further detailed presentation of the results would go beyond the scope of this paper. How-ever, the median absorption coefficient ˜α with respective interquartil range (IQR) can be plotted for all these mea-surements (cf. fig. 12). For fhv0 2
ri< f < f
00 hv2
rithe expected
effective absorption (α ≥ 1) can be mostly confirmed. The big IQR for α between 63 and 100 Hz illustrates that the resulting absorption is highly dependent on the position-ing of the EA. Less positionposition-ing dependent variations of α are present for f > fhv002
ri, where the absorption is mainly
determined by the acoustical behaviour of the porous ab-sorbent material itself.
31.5 63 125 250 500 1k 2k 4k 8k 0
0.5 1
frequency band in Hz ∆Ae,lin m2per unit length
x-edge y-edge z-edges
Figure 11: Difference of the equivalent absorption area per unit length ∆Ae,lbetween edge and surface positioning of
the EA. Vertical dotted lines f0 hv2 riand f 00 hv2 ri mark the expected bandwidth for effective absorption of the EA (cf. sec. 3.2). 31.5 63 125 250 500 1k 2k 4k 8k 0 1 2 frequency band [Hz] α ˜ α IQR
Figure 12: Median values of the absorption coefficient ˜α for measurements with different EA configurations and de-pending interquartil range (IQR) in 1/3-octave bands. Ver-tical dotted linesf0
hv2 riand f 00 hv2 ri
mark the bandwidth for effective absorption of the EA (cf. sec. 3.2).
4.2 Lecture halls
Several EA configurations were investigated in every lec-ture hall from tab. 1. For reasons of compactness, figure 13 and 15 only show these EA configurations with most effec-tive absorption. The depending reverberation times T20for
the lecture halls with and without these EA configurations are plotted in fig. 14 and 16. Again, the results indicate that for low frequencies
fhv0 2 ri< f < f 00 hv2 ri , where a modal sound field is present, an excellent absorption can be pro-vided with the EA. Room modes, independent of their fre-quency, are damped efficiently. If the mode distribution is very dense in a certain 1/3-octave band a reduction of the reverberation time T20in this band is achieved. On
aver-age reverberation time T20can be reduced about 47% for
all lecture halls (∆T20= 0.83 s) in the expected bandwidth
for efficient absorption. Highest reductions of T20can be
achieved for lecture hall 2a in the 100 Hz band (75% resp. ∆T20= 1.34 s) and for lecture hall FSI1 in the 80 Hz band
(48% resp. ∆T20 = 1.52 s). For frequencies f > 1 kHz
the effect of the EA on T20is marginal.
(a) tables blackboard (b) tables blackboard (c)
31.5 63 125 250 500 1k 2k 4k 8k 0 1 2 3 frequency band in Hz T20
Figure 14: Initial (- - -) and resulting T20(—) for lecture
halls 2a (- - -, —), FSI1 (- - -,—) and i14 (- - -,—) in 1/3-octave bands. Vertical dotted linesf0
hv2 riand f 00 hv2 ri mark the bandwidth for effective absorption of the EA (cf. sec. 3.2).
tables blackboard
Figure 15: Floor plan of the lecture hall FSI2 with most effective EA configuration. 31.5 63 125 250 500 1k 2k 4k 8k 0 1 2 frequency band in Hz T20
Figure 16: Initial (- - -) and resulting T20(—) for lecture
hall FSI2. Horizontal dotted lines are marking the mini-mal and maximini-mal values for T20for use case “speech”
ac-cording to ¨ONORM B 8115-3 [19]. Vertical dotted lines fhv0 2 riand f 00 hv2 ri
mark the bandwidth for effective ab-sorption of the EA (cf. sec. 3.2).
A striking reduction of T20for 1/3-octave bands from 63 to
200 Hz can be observed for lecture hall FSI2 with a mean difference ∆T20 = 1.13 s. Through insertion of this EA
configuration in the FSI2 the requirements for the reverber-ation time according to ¨ONORM B 8115-3 can be achieved for all 1/3-octave bands. The mean reverberation time is T20= 0.75 s with a standard deviation of σT20 = 0.08 s.
5. DISCUSSION
Findings from the measurements in the RC are able to con-firm the investigations from sec. 2.1 and 2.2. The mode clusterings in the 1/3-octave band from 63 to 160 Hz are dominating the sound field below the critical frequency fG,RC (cf. fig. 8). Even this mode clusterings are located
in the expected bandwidth for effective absorption of the EA, fhv0 2
ri < f < f
00 hv2
ri, and can be dampened. Of course,
dampening efficiency is also highly dependent on the as-sembly situation of the EA but axial as well as tangen-tial modes in the expected bandwidth for effective absorp-tion that occur in the respective rooms edge are strongly weakened independent from their frequency. Below the lower frequency for effective absorption fhv0 2
riinfluence of
the EA on the modal sound is strongly reduced (fig. 12). Above fhv002
rihigh kinetic and potential energy in the rooms
edge can not be expected any more and the absorption be-haviour of the EA is mainly determined by the porous ma-terial itself (fig. 12). fhv0 2
ri, f 00 hv2 ri as well as fhv 2 rimax are
dependent on the assembly depth of the EA. For the devel-oped EA fhv2
rimax is located in the 80 Hz 1/3-octave band
and modes occuring in this 1/3-octave band can be dimin-ished drastically if there is appropriate positioning of the EA (fig. 10 and 12). This result reinforces the assumption that absorption of the EA for low frequencies is dominated mainly by reducing the tangential component of the parti-cle velocity of the sound field in a rooms edge.
For simulation of the EAs absorbent characteristics in sim-ple room geometries weights for every 1/3-octave wM(f )
dependent on the distribution of the room modes could be applied. This weights in connection with the ratio between covered and uncovered edges by the EA in every dimen-sion wl = lxi,EA/lxi and the absorption coefficient α(f )
6. CONCLUSION
Through the systematic investigation of the absorption characteristics of the EA it could be substantiated that an improvement of room acoustics and in particular broad-band room mode suppressionvia application of EA is pos-sible. With the automatically increased absorption of more distinct room modes the EA acts like a broad band “modal brake”.
From theoretical investigations it could be figured out that the interaction of a raise of sound pressure and velocity in a rooms edge and the distribution of this two acoustic properties in a modal sound field could be the reason for a high absorption efficiency of the EA. Hereby, an expected absorption maximum fhv2
rimaxand bandwidth for effective
absorptionfhv0 2 ri, f 00 hv2 ri
could be derived from the inter-ference pattern of the sound velocity in a rooms edge. The computed values for fhv2
rimax, f 0 hv2 riand f 00 hv2 ricould be
confirmed by measurements in the RC and lecture halls. However, the absorption maximum of an EA is not only determined via its depth dimension but also via the posi-tioning of the EA in a specific room geometry and the re-sulting interaction with the modal sound field. In general, the rooms longest edge, containing lowest frequency room modes, is the preferred mounting position of an EA and broadband absorption can be achieved by mounting the EA along at least one edge of every room dimension.
In practice, knowledge about the exact mode structure of a room is not necessary because a sufficient interaction of the EA with the modal sound field is reached by position-ing in the rooms edges. A specific tunposition-ing of the EA is not needed because of its broadband characteristics for the bandwidth with effective absorption. Furthermore, a high ratio between covered and uncovered edges by the EA im-proves absorption.
For further development of a simulation tool for EAs in simple room geometries a first approach could contain knowledge about the distribution of room mode frequen-cies. Computed weights wM(f ) for the density of room
modes in 1/3-octave bands together with absorption coef-ficients α(f ) for the EA and wl, the ratio between edge
length covered and uncovered by the EA in every room dimension, seem to be reasonable parameters for a simula-tion of an EAs acoustical characteristics.
7. REFERENCES
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