Sound absorption provided by an impervious membrane/cavity/activatedcarbon arrangement
Veronica MARIN(1) , Jorge P. ARENAS(2)(1) Institute of Acoustics, Univ. Austral of Chile, PO Box 567, Valdivia 5090000, Chile, vmarinbley@gmail.com(2) Institute of Acoustics, Univ. Austral of Chile, PO Box 567, Valdivia 5090000, Chile, jparenas@uach.cl

Abstract
A tensioned impervious membrane at the entrance of an air cavity which is backed by a reﬂecting end provides
high and narrow sound absorption peaks at certain frequencies. In the absence of ﬂexural bending, the soundabsorption is mainly due to the vibration energy dissipation in the membrane. The frequencies at which maxima
of sound absorption occur are dependent on the membrane resonances and the geometry of the cavity. Inclusionof a porous material inside the air cavity broadens the sound absorption curve at low frequencies making theabsorber more efﬁcient. It has been shown that, due to adsorbing and desorbing physical mechanisms, granulated
activated carbon exhibits unusually very good low-frequency sound absorption properties. This article presents
some experimental and theoretical results of a circular tensioned membrane clamped in a cylindrical cavity thatis closed with a reﬂecting backing. The effects on the normal-incidence sound absorption coefﬁcient of adding
a porous layer of activated carbon inside the cavity are reported. The use of an activated carbon layer showed
better performance in the low frequency range than traditional ﬁberglass with the same thickness.
Keywords: Sound absorption, Membrane, Activated carbon

1

INTRODUCTION

Sound absorption can be achieved by different ways. Membrane sound absorbers are typically used to absorb
low-frequency noise. Basically, they consist in a vibrating element such as a ﬂexible panel, plate, or tensioned
membrane which is fastened over its entire perimeter in front of an air cavity that ends in a rigid wall. The
vibrating element is forced by an incident sound wave. The cavity can be either partly or completely ﬁlled witha porous material. The case of a tensioned clamped membrane is simpler than that of a plate [1], since we do
not have to deal with the plate’s bending stiffness and thus the speed of transverse vibration waves does notdepend on frequency. Therefore, the sound energy dissipation of an impervious tensioned membrane will bemainly dependent of its mechanical damping which is usually given in terms of a loss factor.
The use of vibrating membranes in acoustics has been studied for many years. Ingard [2] reported the resultsof absorption and transmission of a circular membrane inside a tube which had sound absorbing material at its
end. The velocity distribution of the system was derived by using equivalent circuits. Other authors [3, 4] havestudied the sound absorption produced by a single membrane placed in front of a rigid wall which resulted in a
mass-spring system. Kiyama et al. [5] presented the results of double-leaf membranes and describe the effects
of a double-mass-spring resonance. The effect of placing sound absorption material inside the air cavity wasinvestigated by Bosmans et al. [6].
It seems that Song and Bolton [7] were the ﬁrst to consider the membrane tension on the sound absorption
characteristics of a membrane backed by an air cavity. They developed a theoretical model capable of explaining
the effect of membrane tension and the energy dissipated by the motion of the membrane itself. Later, theyextended their theory to the case of permeable membranes [8] and to other types of membrane-based soundabsorbers [9]. More recently, the sound absorption characteristics of thin microperforated membranes backed
by an air cavity have been investigated by considering the spatially varying acoustic impedance due to themembrane perforations [10]. They found good agreement between theoretical and experimental results.
On the other hand, inclusion of a porous material inside the air cavity broadens the sound absorption curve2967

at low frequencies making the absorber more efﬁcient. Usually porous materials placed inside the cavity havebeen either cellular or ﬁbrous, such as foams, ﬁberglass and rockwool. The use of ﬁne granular material is lesscommon and may require the use of an impervious membrane. In particular, activated carbon has received muchattention as an absorbing material due to its unusually very good low-frequency sound absorption properties. It
has been shown that these properties are due to adsorbing and desorbing physical mechanisms [11].
A ﬁrst stage in manufacturing activated carbon is to carbonize a raw material which can be coconut husk
or coal, which is subjected to an inert atmosphere with temperatures between 700 and 1000 ◦ C. Later, thecarbonized material is activated with oxidizing gases such as carbon dioxide or water vapor, at temperatures
between 800 and 900 ◦ C. The combination of carbonization and activation creates a range of porosities that goesfrom nanometric pores to micrometric pores inside the grains. This range of porosities produces an increase inits surface area and determines the sorption characteristics of this material [11]. Activated carbon has also beenused in ﬁltering and puriﬁcation applications, among others.
In this article, we present the sound absorption performance of a system composed of a thin tensioned impervious circular membrane backed by an air cavity which is partially ﬁlled by activated carbon.

2

THEORYThe sound absorption of a combination of a circular membrane and an air cavity backed by a rigid termination
which is partially ﬁlled with a porous material can be determined by using the impedance translation theorem[12]. For this, the governing equation of a thin tensioned clamped membrane of radius a which is forced by aperiodic force f (r, θ ,t) acting uniformly on the membrane is [13]T ∇2W (r, θ ,t) + f (r, θ ,t) = ρs

∂ 2W (r, θ ,t)
,
∂t 2

(1)

where W (r, θ ,t) is the transverse displacement of the membrane and ρs is the membrane’s mass per unit area.
(1 + jη), where T0 is the memThe effect of membrane damping is included by the complex tension T = T0√
brane’s tension (N/m), η is the damping loss factor of the membrane and j = −1. The velocity amplitude forharmonic excitation can be expressed as u = jωW .
Since the membrane is excited by the action of a uniformly distributed pressure (a plane sound wave) only
axisymmetric modes need to be considered. The membrane average surface impedance is determined as theratio between the sound pressure and the spatially averaged velocity on the surface of the membrane u which
is given by 
 2π  a
1
2π a
1u(r)dS = 2
u(r)rdrdθ = 2
u(r)rdr.
(2)
u =
S
πa 0
πa 0
0
S
A simpliﬁed expression of such membrane spatially averaged surface impedance is [10]−1
2 J1 (km a)−1
Zm = − jωρ,(3)
km a J0 (km a)where J0 and J1 are Bessel’s functions, ρ is the air density, and km = ω ρs /T .
The total impedance Z of the absorber shown in Figure 1 is determined by including the effect of the air
cavity and the inﬁll porous material using the impedance translation theorem [12]. An identical methodology isapplied in [1], but here D is the cavity depth and d p is the thickness of the inﬁll porous material. Thus, thenormal-incidence sound absorption coefﬁcient is obtained as α = 1− | R |2 , where R is the complex reﬂection
coefﬁcient obtained from the total surface impedance of the absorber R = (Z − Z0 )/(Z + Z0 ), where Z0 is thecharacteristic impedance of the air.
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Membrane

௦

௣

(a)

(b)

Figure 1. Schematics of the sound absorber. (a) empty; (b) partially ﬁlled with a porous material

3

EXPERIMENTAL METHOD

A series of experiments were performed for assesing the sound absorption properties of the absorber. A rigid
vertical impedance tube of inner diameter 100 mm was adapted to implement a circular membrane absorberat one end and a loudspeaker at the opposite end (see Figure 2). The standardized two-microphone techniquedescribed in ISO 10534:2001 Part 2 was used to measure the normal-incidence sound absorption coefﬁcient of
the absorber. The loudspeaker was driven with white noise signal that varied from 0 to 2 kHz. The signals
were generated and processed by a two-channel real-time fast Fourier transform analyzer, which was connected
to a computer for data analysis.

Figure 2. Experimental setup for measuring the normal-incidence sound absorption coefﬁcient of the membraneabsorber
Because of the random characteristics of the noise signal, a total of 200 averages were taken for each measurement. The transfer functions were measured between the signals of two 1/4-inch microphones at increments of
1 Hz. In light of the diameter of the standing wave tube and the center-to-center spacing between two micro-

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phones (100 mm), the measurements according to the ISO standard were assumed valid in the frequency range
200 to 1500 Hz. Care was taken to ensure a good sealing of all the elements of the experimental setup.
The absorber was made of milled stainless steel cylinders that perfectly ﬁtted the impedance tube inner diameter.
Two kinds of porous materials were used in the experiments: 1) a ﬁberglass sample of thickness 20 mm andﬂow resistivity of 12848.2 Ns/m4 and 2) granular activated carbon kindly supplied by Salford Research andDevelopment, UK. The activated carbon was compacted inside the air cavity. The elastic membranes weremade of silicone with a thickness of 0.623 mm, constant η = 0.005, surface densities between 0.237 and 0.265
kg/m2 , and subjected to different tension values. The acoustic characteristics of both the ﬁberglass and theactivated carbon were measured independently in the impedance tube before being used as inﬁll materials in
the absorber.

4

RESULTS AND DISCUSSION

Figure 3 shows the results for two absorbers without absorbing material in the air cavity. It can be observedthat this kind of absorber exhibits narrow maxima of sound absorption coefﬁcient. It is noted that the frequencyof these maxima are close to the natural frequencies of the membrane and located at frequencies at which
the surface reactance becomes zero. We observe that there are a good correlation between the theoretical andexperimental results. In addition, these ﬁndings agree well with those reported in the literature [7].
1

0.8

Measured
Theory

(a)

0.6

0.4

0.2

0
200

400

600

Frequency, Hz

800

1000 1200

1600

Sound absorption coefficientSound absorption coefficient

1

0.8

Measured
Theory

(b)

0.6

0.4

0.2

0
200

400

600

800

1000 1200

1600

Frequancy, Hz

Figure 3. Sound absorption coefﬁcient for a membrane absorber without porous material in its cavity. (a)D = 100 mm, T = 76.53 N/m2 , ρs = 0.265 kg/m2 ; (b) D = 40 mm, T = 81.04 N/m2 , ρs = 0.237 kg/m2
In Figure 4 we can observe the effect of introducing a 20 mm thick porous material in the cavity. Figure 4ashows the effect of ﬁberglass in the cavity where the sound absorption values are increased for frequencies
below 600 Hz. The measured sound absorption coefﬁcient (blue line) has a ﬁrst maximum around 250 Hz,
which increases its sound absorption value by about 0.1. In addition, a second broad maximum in soundabsorption appears, which is not present in the empty absorber (gray line). The correlation between thesemeasured values (blue line) and those calculated (red line) below 300 Hz is less accurate compared to what isobserved in Figure 3, where the theoretical values overestimate the measured ones. Above 300 Hz there is little
difference between the measured and estimated results.
Figure 4b shows the corresponding results using activated carbon in the cavity. We see that, for this case, there
is a better agreement between theoretical and measured values, observing three maxima of sound absorption that
increase the bandwidth in comparison to the empty absorber. By comparing Figures 4a and 4b, it is veriﬁedthat the sample of activated carbon exhibits better sound absorption than the ﬁberglass sample, increasing thevalue of the sound absorption coefﬁcient for the ﬁrst two maxima by 0.4 approximately. It is noted that over600 Hz, the sound absorption behaves quite similar independently of the type of porous material in the cavity.

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1
Measured empty
Measured FG 20mm
Theory FG 20mm

0.8Sound absorption coefficientSound absorption coefficient

1

(a)

0.6

0.4

0.2

0
200

400

600

800

1000 1200

Measured empty
Measured AC 20mm
Theory AC 20mm

0.8

(b)

0.6

0.4

0.2

0
200

1600

400

600

800

1000 1200

1600

Frequency, Hz

Frequency, Hz

Figure 4. Sound absorption coefﬁcient for a membrane absorber (D = 100 mm, T = 76.53 N/m2 , ρs = 0.265
kg/m2 ) partially ﬁlled with a porous material of thickness d p = 20 mm in its cavity. (a) ﬁberglass (FG); (b)activated carbon (AC)The effect of ﬁlling the cavity with porous material on the sound absorption coefﬁcient and on the total surface
impedance is observed in more detail in Figure 5. Figure 5b shows the experimental results of the real andimaginary part of the total surface impedance of the absorber as a function of frequency. It can be seen how
the total surface resistance increases by the presence of both materials, which is much higher for the activatedcarbon than for the ﬁberglass of the same thickness.

0.8

empty
FG 20 mm
AC 20 mm

(a)

0.6

0.4

0.2

0
200

400

600

Frequency, Hz

800

1000 1200

1600

3000

Surface impedance, Ns/m 4

Sound absorption coefficient

1

2000

(b)

1000
0
Re(Zs) empty
Im(Zs) empty
Re(Zs) FG 20 mm
Im(Zs) FG 20 mm
Re(Zs) AC 20 mm
Im(Zs) AC 20 mm

-1000
-2000
-3000
200

300

400

500

600

700

800 900 1000

Frequency, Hz

Figure 5. Experimental results for a membrane absorber (D = 40 mm, T = 81.04 N/m2 , ρs = 0.237 kg/m2 )partially ﬁlled with either ﬁberglass (FG) or activated carbon (AC) of thickness d p = 20 mm in its cavity. (a)sound absorption coefﬁcient; (b) real and imaginary parts of its surface impedance
Figure 6 shows the results of the sound absorption coefﬁcient for another absorber (D = 40 mm, T = 55.2 N/m2 ,ρs = 0.265 kg/m2 ) with d p = 20 mm of porous material within the air cavity, i.e., ﬁberglass (Figure 6a) andactivated carbon (Figure 6b). It is observed that the sound absorption maxima are broadened between 300 and
800 Hz for both materials. It is also observed that a 20 mm thick activated carbon provided better improvementof the sound absorption than ﬁberglass. By comparing the sound absorption measured values for the absorber
reported in Figure 4 with that of Figure 6, it can be noticed that the same samples of porous material (20 mmof ﬁberglass and activated carbon) increase differently the total sound absorption. For the absorber in Figure 6
the porous material ﬁlls 50% of the air cavity and the sound absorption becomes more effective, reaching about
100% sound absorption with 20 mm of activated carbon. In the case of the absorber in Figure 4, these porous
materials only ﬁlled 20% of the cavity, reaching a maximum of about 80% in sound absorption with the same

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sample of activated carbon. When comparing the results of Figures 4 and 6, it can be said that the agreement
between the measurements and predictions of sound absorption of the absorber with porous material within its
air cavity is satisfactory. A common observation is that for both absorbers, the frequency range for which anincrease in sound absorption is achieved is limited, and outside this range of frequencies the sound absorption
maxima remain with a narrow bandwidth.
1

0.8

Measured
Theory

(a)

0.6

0.4

0.2

0
200

400

600

Frequency, Hz

800

1000 1200

1600

Sound absorption coefficientSound absorption coefficient

1

0.8

Measured
Theory

(b)

0.6

0.4

0.2

0
200

400

600

800

1000 1200

1600

Frequency, Hz

Figure 6. Sound absorption coefﬁcient for a membrane absorber (D = 40 mm, T = 55.2 N/m2 , ρs = 0.265
kg/m2 ) partially ﬁlled with a porous material of thickness d p = 20 mm in its cavity. (a) ﬁberglass (FG); (b)activated carbon (AC)It is interesting to note that, although the 20 mm thick ﬁberglass and the 20 mm thick activated carbon do
not exhibit a large sound absorption coefﬁcient at very low frequencies, both increase the sound absorption
performance of the membrane absorber at frequencies below 1000 Hz. A similar result was reported by Venegas[11] for two Helmholtz resonators ﬁlled with activated carbon. In this case, an increase of approximately
three times the maximum in sound absorption was observed. The device did not improve the sound absorption
properties at high frequencies. Using a microperforated membrane with 1% of perforation rate also did notreport improvement when compared with the empty resonator. These observations also agree with the ﬁndings
reported in this article.

5

CONCLUSIONSIn this article an absorber made of a tensioned impervious membrane at the entrance of an air cavity which
is backed by a reﬂecting end has been presented. It was observed that this absorber provides high and narrowsound absorption peaks at certain frequencies that are related to the natural frequencies of the membrane. Thesesound absorption values are mainly due to the vibration energy dissipation in the membrane. Inclusion of aporous material inside the air cavity increases and broadens the sound absorption curve at low frequencies
making the absorber more efﬁcient. It was observed that the use of activated carbon as an inﬁll porous material
reported better performance in the low frequency range than traditional ﬁberglass of the same thickness. It
was also observed that the improvement in sound absorption is also related to the amount of volume of the
air cavity that is ﬁlled by the material. Although quite simple, theoretical estimations of the sound absorption
coefﬁcient by using the average surface membrane impedance and the impedance translation theorem, show
good agreement with the experimental results.

ACKNOWLEDGEMENTS
The authors would like to gratefully acknowledge the support of CONICYT–FONDECYT under Grant 1171110.
In addition, the authors sincerely thank to Dr. Rodolfo Venegas and Salford Research and Development for their2972

valuable support during this research.

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[5] Kiyama, M.; Sakagami, K.; Tanikawa, M.; Morimoto, M. A basic study on acoustic properties of doubleleaf membranes, Applied Acoustics, 54(3), 1998, 239–254.
[6] Bosmans, I.; Lauriks, W.; Lombaert, G.; Memans, J.; Vermeir, G. Sound absorption of stretched ceilingwith an impervious synthetic membrane, Journal of the Acoustical Society of America, 106(1), 1999, 233–
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