Sound absorption measurement method using ensemble averaging technique:A robust method for surface impedance including in-situ applications
Toru OTSURU(1) , Reiji TOMIKU(2) , Siwat LAWANWADEEKUL(3) , Daiki MATSUOKA(3) , Ryota YOSHIMOTO(3)(1) Oita University, Japan, otsuru@oita-u.ac.jp(2) Oita University, Japan(3) Graduate School of Oita University, Japan

Abstract
Sound absorption characteristics of materials are of importance for controlling the quality of sound fields aswell as of materials. In the authors’ previous papers, we proposed the concept and measurement method forsurface normal impedance and sound absorption coefficient at random incidence condition, namely, ensemble
averaged surface normal impedance and sound absorption coefficient. We named the measurement method as
EA method, for short. We also showed the theoretical validation using boundary element method and experimental confirmations on the effectiveness of EA method in successive several papers. In this paper, outline of
EA method is summarized, first. Then, reproducibility of the results are examined on measurements conductedboth in a reverberation room as well as in five in-situ sound fields. All the measurements were conducted by EA
method with a pressure-velocity sensor (Microflown PU-sensor) which was calibrated on-site using an acoustic
tube. The results reveal that robust absorption coefficient values with the uncertainties less than 0.03 ∼ 0.04
were obtained regardless of sound fields.
Keywords: Sound Absorption Coefficient, Surface Impedance, Ensemble Averaging, Measurement

1 INTRODUCTION
Since the early days of architectural acoustics established by W. C. Sabine, sound absorption characteristics ofmaterials play crucial roles for predicting as well as controlling sound fields in built environments. To measure
the values, various methods have been proposed; and some of them were standardized internationally. Not asmall number of people, however, frequently encounter difficulties at their practical measurement stages formaterials’ sound absorption characteristics. Sometimes, the difficulty depends on the material’s property itself:
i.e. mounting issues are pesky enough for certain materials to measure sound absorption characteristics properlyin the tube method, an expensive reverberation room is indispensable for the reverberation room method, resultsof the reverberation room method depend on the room’s characteristics, standard area size required for thereverberation room method might cost a lot for certain materials under development, and so on.
The ensemble averaging technique was proposed to overcome such difficulties. First, Takahashi et al. [1]proposed an in-situ measurement method utilizing the transfer function method with two-microphone, namely
EApp method, for short. Then, Otsuru et al. [2] presented an improved method utilizing a pressure-velocity
sensor (PU-sensor, Microflown), EApu method; and they also revealed, using boundary element method, thatthe ensemble averaging efficiently cancels the disturbing interference effects caused by the specimen’s edge
diffractions. Comparisons of measurement results between EA method and tube method were presented by Nazliet al. [3] along with detailed discussions on the effects of sample size and receiver-to-sample distance. They
also examined the reproducibility and applicability of EApu method method with round robin tests conducted atfour reverberation rooms and three ordinary environments: a classroom, lobby and corridor.
On the other hand, Asniawaty et al.[5, 6] reported a humidity effect on measurement values by EApu method.
Then, Sakamoto et al. [7] proposed a refined on-site calibration method; and, with the method, EApu ’s reproducibility in three reverberation rooms located at different cities were presented.
In this paper, EApu method outline is summarized, first; and detailed information required for practical applica-

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Figure 1. Measurement setup of the EA method. At the sensor position, EApu method sets PU-sensor; andEApp method sets two-microphone. Sensor is located d m above the specimen surface.

Figure 2. Specimen size and receiving points.
tions is exhibited. Then, to show EApu method’s applicability, results of EApu method measurement conductedat sound fields including in-situ conditions, when on-site calibration is performed, are demonstrated.

2 EA METHOD OUTLINE
Standard setup for EA method is illustrated in figure 1. At the sensor position, EApu method sets PU-sensor;
and EApp method utilizes two-microphone. In this paper, EApu method is focused on because of the theoretical
simplicity based on their geometrical allignment.
2.1 Geometrical configurations
Theoretically, the less is the distance d between PU-sensor and specimen surface, the better the values ofabsorption characteristics become, which was supported by BEM simulation presented in literature [3]. While,in a practical measurement, certain distance is inevitable because of physical sensor-sizes as well as roughnessof specimens’ surfaces. Based on many trial-and-error measurements using PU-sensor (Microflown, PU regular),the authors have employed d = 0.01 m since the studies focused on the measurement within the frequency range
from 200 Hz to 1500 Hz [4]. Considering that the PU-sensor sensor diameter is half-inch, the distance is asafer compromise. However, when a precise measurement in higher frequency range is to be conducted, some
improvements be required.
Sample specimen’s size effect is also discussed in one of our former papers [3] and, when EA method is
conducted, specimens made of the same material with the dimensions larger than 0.5 m × 0.5 m result almost
identical sound absorption characteristics: ensemble averaged surface normal impedance Zn,EA and absorption
coefficient αEA . In case non-uniform materials are to be measured in rather high frequency regions, selectionof proper receiving points shall be an important issue. The issue, however, will be discussed in another paper,and hereinafter, PU-sensor is located at three points on a specimen to average(figure 2). A measurement on a
specimen with the same setting at one of the three points is repeated three times to examine repeatability, i.e.
the total number of a single measurement equals nine.

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2.2 Sound source
EA method at early stage [1] utilized environmental pseudo-random noise as sound source for measurement;
and, in case it is insufficient, loudspeakers radiating incoherent pseudo-random noises were employed. In suchmeasurements, two-microphone of IEC 61672 class 1 quality was employed and signal to noise ratios (SNR) at
measurements were considerably satisfactory.
On the other hand, it is known that SNR of particle velocity sensor in rather lower frequency region is less satisfactory comparing to those of microphones for precise measurements. Then, up to until now, in EApu methodmeasurements conducted in-situ, we have employed four to eight portable loudspeakers to radiate incoherent
pink noises which were moved around randomly by human-hands at the speed about 0.8 ∼ 1.0 m/s on an ideal
sphere with the radius about 1.5 m away from the specimen’s center receiving point. At the measurements
conducted in reverberation rooms, four to six loudspeakers and one or two sub-woofers were set on the floor
which radiate incoherent pink noises, as well [7].
2.3 Signal processing [2]As is illustrated in figure 1, sound pressure P and particle velocity Un normal to specimen surface are respectively measured by PU-sensor through a Hanning window with a time length of 0.64 s ∼ 1.00 s on a
2-channel fast Fourier Transform (FFT) instrument. Then, ensemble averaged surface normal impedance Zn,EA
and corresponding absorption coefficient αEA are defined and calculated by the following equations:
Zn,EA =

αEA = 1 −P,
Un

Zn,EA − 1 2.
Zn,EA + 1

(1)
(2)

On the FFT, Zn,EA is measurable as the transfer function HU,P between Un and P with linear averaging 150
times in the time domain; and ensemble averaging is, thus, performed automatically.
2.4 On-site PU-sensor calibration
Generally speaking, sensor calibration is essential for a precise measurement. In EApp method, the authors
employ the "changing sensor position" method. While, in EApu method, we recommend on-site calibration
using an acoustic tube, the details of which is discussed in literature[7]. A brief summary is given, below.
When an in-situ measurement of some kinds for sound absorption is conducted, environmental conditions, e.g.
atmospheric temperature and humidity, frequently fluctuate. To avoid contamination of the atmospheric fluctuations from measured results by PU-sensor, on-site calibration is preferable[5, 6, 7]. Figure 3 illustrates an
overview of an acoustic tube for PU-sensor calibration. The acuostic tube with the dimensions of D = L − X =0.05 m is designed to cover the frequency range from 100 Hz to 3000 Hz, or, from 125 Hz to 2500 Hz in 1/3
octave band[7]. Whenever a measurement is conducted by EApu method, it is desirable to perform a calibration
using such an acoustic tube. The authors’ former studies[5, 6] have revealed that relative humidity difference
within 8% is acceptable between relative humidities at a sound absorption measurement and at a PU-sensor
calibration.
Although wind speed is another important issue on environmental conditions, it will be discussed near future.
All the measurements in this study are conducted when wind speed is slow enough to neglect the effect. Fromthe view point of wind speed, closed tube is advantageous in eliminating the effect. Influence of environmental
noise is easy to eliminate, too.

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Figure 3. Acoustic tube for PU-sensor calibration. End walls are openable for the purpose of ventilation.[7]Table 1. Abbreviations and dimensions of measured specimens.
Material
Glass-wool (32 kg/m3 )Needle felt

Abbrev.
GW
NF

Dimensions [m×m×m]
0.5 × 0.5 × 0.05
0.5 × 0.5 × 0.01

3 MEASUREMENT SETUPS FOR REPRODUCIBILITY EXAMINATION
3.1 FFT setting
Following above mentioned configurations and procedure, EApu method measurements were conducted using
2ch-FFT (B& K, Pulse) and PU-sensor (Microflown, PU regular). The time length of Hanning window was set
to 0.64 s to shorten measurement time especially for in-situ measurement.
3.2 Specimens and on-site PU-sensor calibration
Sound absorption characteristics, Zn,EA and αEA , of two specimens listed in table 1 were measured. The two
specimens were brought to each sound field to measure their absorption characteristics in-situ. As mentioned
above, each measurement of a specimen was conducted at three receiving points (figure 2) on the specimen
surface and the measurement was repeated three times on different days to investigate the repeatability.
Here, on-site PU-sensor calibration using the acoustic tube was performed just before/after a series of measurement in a day at one of the following sound field. At every on-site PU-sensor calibration, both end walls wereopened for ventilation to make atmospheric conditions similar to each other between in and out of the acoustic
tube.
3.3 Sound fields
Measurements were conducted in five in-situ sound fields and in Oita university reverberation room. Detailsof the sound fields are listed in table 2. As to show an example overview, photographies of Caf are shownin figure 4. All the in-situ measurements were performed at ordinary furniture conditions with desks, tables,
chairs, and so on. Only extraordinary impulsive noise like door-bangs were eliminated manually but ordinary
environmental noise like air-conditioner noise existed during the measurements.
3.4 Sound source systems at measurements
As mentioned in section 2.2, all measurements conducted in Oita university reverberation room employed thesound source system consists of both a sub-woofer (YAMAHA, NS-SW700) and six full-range loudspeakers(Fostex, FE-103En mounted in wooden box) located on the floor. While, the other measurements conductedin-situ employed a system that consists of six portable loudspeakers (JBL, Micro wireless) moved by humanhand. Incoherent pink noises were emitted from the loudspeakers as well as from the sub-woofer. Figure 5
shows frequency characteristics of Leq,20s measured by sound level meter during the three-day EApu method1353

Table 2. Sound fields used for the measurements.
Abbrev.
RR
Caf
Cr
Tr
R-E
RC

Name
Oita univ. reverberation room
Cafeteria
Corridor in a building
Terrace (semi-outdoor)
Room for environmental simulation
Reinforced concrete house

Volume [m3 ]
168
2389
177
70
34

Interior surface materials (ceiling, walls, floor)
Concrete, Concrete, Concrete
Wood, Wood & Glass, Stone
Gypsum board, Mortar, Vinyl tile-, - & Glass, Brick-tile
Rock wool board, Wall cloth & Glass, Tile-Carpet
Concrete, Concrete, Concrete

Figure 4. Snapshots of sound field at Oita university cafeteria "Caf" where in-situ EApu method measurements
were conducted. (Left): overview, (Right): scenery at EApu method measurement of GW.
measurements at the specimen’s center point in Caf. Microphone position of the sound level meter is set close
to the location of sensor of PU-sensor.

4 RESULTS AND DISCUSSION
4.1 Comparison between six sound fields
Figure 6 shows sound absorption characteristics measured by EApu method at the six sound fields. Both Zn,EA
and αEA are averaged over nine-time repetitions; and mean values of them are compared between sound fields.
As for GW, agreements of Zn,EA values between sound fields are excellent in the frequency region from 500

Figure 5. Frequency characteristics of Leq,20s measured by sound level meter during the three-day (1st, 2nd and3rd) EApu method measurements. Microphone of the sound level meter was placed at the specimen’s center
point close to PU-sensor. The measurements were conducted in the sound fields Caf (Left) and Cr (Right).

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Figure 6. Sound absorption characteristics of GW (left column) and NF (right column) measured by EApu
method at six sound fields (RR, Caf, Cr, Tr, R-E, RC). Mean values over nine-times repetition in each soundfield are plotted. (upper row): surface normal impedance; and (lower row): absorption coefficient.
Hz to 3000 Hz. Although, in the lower frequency region below 500 Hz, certain discrepancies caused by zig-zag
shape fluctuations are observable, overall tendencies agree well each other.
Likewise, agreements of αEA values between six sound fields are excellent in the frequency region from 500
Hz to 3000 Hz; and similar tendencies to those of ZEA values are observable.
On the other hand, as for NF, agreements of both Zn,EA and αEA values are rather worse comparing to those of
GW; and Zn,EA values in the frequency region below 500 Hz show certain large deviations.
Here, it is noteworthy that both Zn,EA and αEA values measured in R-E show distinct differences from thosemeasured in the other five sound fields. The differences are considered to be caused by flooring materials
behind NF listed in table 2. In R-E, floor material is tile carpet; while, in the other five rooms, floor materials
are concrete, stone, vinyl tile, brick tile, and concrete. Thus, higher absorption coefficient obtained in R-E isconsidered to result from the absorptive tile carpet behind NF. The effect is not obvious for GW because of thespecimen’s higher absorption.
4.2 Reproducibility examination
To examine the reproducibility of measurements by EApu method over sound field difference, 1/3 octave bandvalues of αEA and their standard deviation σ values are plotted in figure 7. As for both GW and NF, agreementsof 1/3 octave band mean values of αEA between six sound fields are excellent in all the frequency region from100 Hz to 3000 Hz except those of NF measured in R-F. The reason why the exception occurs is resulted fromthe existence of the absorptive tile carpet behind the specimen, as stated above.
Due to the disagreement caused by the measurement of NF in R-E, standard deviation σ values of NF become

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Figure 7. Comparisons of 1/3 octave band mean values of αEA of GW and NF between six sound fields (RR,
Caf, Cr, Tr, R-E, RC). Standard deviation σ values are plotted together with right axis.
larger than 0.03 in the frequency region from 1000 Hz to 2000 Hz. Nonetheless, the other σ values stayaround or less than 0.02, which shows the reproducibility of EApu method applied to sound fields including
in-situ. Note that, though all the in-situ measurements at five sound fields were conducted with six portable
loudspeakers moved around by human-hands, αEA values were obtained with such small deviations.
Thus, EApu method following above mentioned configurations and procedure results robust results with σ ≤0.03 ∼ 0.04 regardless of sound field difference provided on-site PU-sensor calibration is performed.

5 CONCLUSIONSAs a measurement method for sound absorption characteristics of materials, EA method is robust and advantageous in: (1) short measurement time about 1 min (for 150 times linear averaging in time domain on FFT); (2)in-situ measurements give almost similar results to those measured in a reverberation room; (3) reproducibility on sound field difference is as exhibited above: standard deviation σ ≤ 0.03 ∼ 0.04 for 1/3 octave bandmean values of αEA ; and (4) edge effect of material is insignificant: i.e. flexible for specimens in shapes andsizes (larger than 0.5 m × 0.5 m area is recommended). A disadvantage might be that PU-sensor calibration
takes some additional time. Meanwhile, material’s non-uniformity issue is needed to be discussed and various
applications including the issue are undertaken, as well.

ACKNOWLEDGEMENTS
The paper is based on Ms. S. Yamauchi’s master thesis. The authors would like to thank to her and Mr. S.
Tajima for his continuous support as a technical staff of Oita University. This work was partly supported by
JSPS, Grant-in Aid for Scientific Research (B) 16H044565, 2016-18 and (B) 19H02298, 2019-21

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