1

Acoustic Instrumentation and Measurements April 2015, Argentina

ABSORPTION COEFFICIENT MEASUREMENT

AUGUSTO BONELLI TORO

1 NAHUEL CACAVELOS

1

1 Universidad Nacional de Tres de Febrero, Buenos Aires, Argentina.

abonellitoro@gmail.com

fnahuelc@gmail.com

Abstract - In the present work, fiberglass panel arrangement absorption is measured according to the reverberation

chamber method. The P500 with black veil and the Acoustic Panel P are combined to quantize their absorption

according to ISO 354.

1. INTRODUCTION

1.1 Reverberant Chamber

The reverberation chamber must create a diffuse

sound field; this means that the energy of the field

will be distributed at all points. To achieve this goal,

they should wear reflective surfaces and diffusers

with high reflectivity and low absorption coefficient

to disperse energy but not absorb it. [1]

Possible uses of the reverberation chamber:

Measurement of absorbent material

properties through reverberation method.

Measurements under the method of Kath

& Kuhl.

Measurements of the diffusion coefficient.

Measurements of acoustic power source in

reverberation chamber.

Transmission Loss measurements walls.

In the ISO 354 Standard, the volume of the

chamber should be at least 150 m3, but is

recommended higher than 200. The room should not

be parallelepiped.

To decrease the influence on low frequency

modal response it is recommended that there should

not be two dimensions that are integer ratio numbers.

1.2 Critical Distance

When the listener moves away from a sound

source, in non-anechoic conditions, one will

gradually leave the domain of the direct field and

enter that of the reverberant field. The point where

the two sound fields are equal is known as the critical

distance, beyond which the level of the sound will

soon tend not to reduce any farther as one move away

from the source. The result is that the critical distance

will be frequency dependent and so the effect of

moving away from the source will not be perceived

equally at all frequencies.[2,3]

The critical distance equation:

√

(1)

Where Q is the Directivity Coefficient and R is

equal to:

(2)

Si = individual surface area in the room.

αi= absorption coefficient for individual surface in

the room.

αm= mean absorption coefficient of the room.

Figure 1: Critical Distance plot.

1.3 Modal Density

In the most of cases, the distribution of the energy

and variation with frequency of a sound field in an

enclosure is difficult to determine with precision.

Average quantities are often sufficient and

procedures have been developed for determining

these quantities. In the low-frequency range, an

enclosure sound field is dominated by standing waves

at certain characteristic frequencies. Large spatial

variations in the reverberant field are observed if the

enclosure is excited with pure tone sound, and the

2

sound field in the enclosure is said to be dominated

by resonant or modal response. [4,5]

This equation defines where are placed the nodes

and the peaks of pressure at a certain frequency:

√(

)

(

)

(

)

(3)

Also, it can be estimated the number of modes at

a certain frequency:

(

)

(

)

(4)

The modal analysis becomes very complicated

and difficult to model with increasing frequency. At

high frequencies, there is an overlapping between the

peaks and the nodes, and the pressure level almost

equal in all space (field tends to be diffuse).

There is a limit on the use of the model defined by

the frequency of Schroeder:

√

(5)

1.4 Noise Criteria

The Noise Criteria (NC) is the original standard

suggested by Beranek in the 1950s.

The NC curves (extended from67Hz to 8000Hz)

are defined from sound pressure level over eight

octave band center frequencies. The measured

spectral noise level is then compared to these curves

and the NC value is obtained (the measured noise

curve will fall between some of the NC curves).

1.5 Absorption Principles

When sound propagates in small spaces, as in the

case of the pores of a given material, energy is lost.

This is mainly due to viscous boundary layer effects.

Sound dissipated via friction on the porous walls,

because it is a viscous fluid. Another important

material loss will be because of losses due to thermal

conduction from the air to the absorbent material.

This is most significant at low frequencies. It is

important to note that to be effective absorption, air

paths must be interconnected through the material, so

it is imperative a porous structure.[6] Losses due to vibrations of the material are

usually less important than the absorption coefficients

for two porous absorbers illustrating the effect of

material thickness. If it’s wanted that the porous absorbent generate a

significant absorption, it must be placed where the

particle velocity is high. Particle velocity at the

boundary of the room is zero, thus there is no sense in

placing there. A quarter of the wavelength absorbs all

the incident sound, but a tenth of the wavelength also

cause significant absorption. In turn, if the porous absorbers are used in

conjunction with resonant absorbers, passive

absorption generates a wider bandwidth of

absorption. Within rooms, porous absorbers are often finished

by cloth wrapping to protect the absorbent material

and make it look better. The cloth wrapping

potentially has little effect on the absorption obtained.

Care must be taken to ensure the high frequency

absorption is not reduced because the glue prevents

sound entering the porous material. The sound absorption coefficient of a plane

absorber or a specified array of test objects shall be

calculated with:

(6)

where is the equivalent sound absorption area of

the test specimen, in square meters and S is the area,

also in square meters.

1.6 Reverberation Chamber Method

In the most of applications, the incident sound

will be random incident in the absorptive material at

once. It’s not efficient to measure the different angles

of the absorption coefficients in free filed and then

reconstruct the samples to get a random incidence

absorption coefficient.

The random incidence absorption coefficient is

implemented for room design, but is not very useful

for those who want to validate their prediction

models.

For this method big samples are required (10-12

m2), and a specially designed room, a reverberant

chamber, to get an accurate measurement.

The method measure the reverberation time

before and after the sample is introduced. By

knowing these two values, it’s possible to get the

random absorption coefficient. It’s very necessary to

get a diffuse field.

The source is usually positioned in one of the

corners of the room, pointing to a corner, since this is

the condition in which the modes of the room

are full excited and the amount of direct sound is

reduced from the loudspeaker to the sample of test.

The reverberation time before the sample is

introduced:

(7)

Where V is the room volume, c the speed of light

α0 the average absorption coefficient of the empty

room, and S the surface area of the room.m1 is for air

absorption in the room.

The reverberation time after the sample is

introduced:

3

[ ] (8)

where Ssαs the absorption coefficient of the sample.

To get an accurate measurement, it is necessary to

have a big difference between T0 and T1.

The sample will be always affected due to edge

effects. The sound is diffracted around the axes of the

sample which causes an increase in absorption. That

is why the edges of the sample are covered to reduce

these effects. Given this fact, sometimes absorption

coefficients are higher than 1.

If it is assumed that the material is attached to a

wall, so that force to the air particles near the wall

being with almost null velocity, increasing gradually

as a we move away from the wall, but being almost

null nearby it. As the speed of the sounds is so low

within the absorbent material, the friction with the

material particles is minimal, producing a minimum

transformation in heat energetic.

1.6.1 Experimental error of the method

Taking the standard deviations of reverberation

times T0 and T1 can be calculated randomized

experimental error. Standard deviations are calculated

for a series of reverberation times obtained for all the

different source positions and microphones. If the

standard deviations of the reverberation time T0is ,

then the confidence limit of 95 percent is given by:

√ (9)

where n is the number of source and receiver parts.

The accuracy of the empty room average absorption

coefficient is given by:

|

| (10)

where the effect of inaccurate estimation of air

absorption has been assumed to be smaller than the

effect of reverberation time variation between

measurement positions.

√|

| (

[ ]

)

(11)

While a good repeatability in a laboratory can be

achieved, there are often problems of reproducibility

between different laboratories.

The method of reverberation chamber can also be

used to measure single objects.

1.6.2 Repeatability

The repeatability of the RT measurements are

calculated as shown in next equation

√

(12)

where T is the Reverberation Time measured, f is the

center frequency of the third octave band and N is the

number of measurements made for that reverberation

time.

1.7 Edge effect absorption

In cases where the absorption footprint is larger

than the area of the specimen, the sound absorption

coefficient is greater than 1.00. This is named the

edge effect or diffraction effect because it results

from wave diffraction at the edges of the specimen.

The effect increases with decreasing frequency, by

reducing the sample size by increasing the aspect

ratio, and to increase the absorption coefficient.

The absorption of a finite sample is described by

(13)

where is the absorption of an infinite sample and

is a factor as can be seen in Fig. 2:

Figure 2: factor from experimental and theoretical

studies

In the equation of the absorption of a finite

sample, the E is the relative edge length defined

by:

(14)

where is the wavelength.

4

1.8 Log Sine Sweep

The log sine sweep (LSS) consists of an

excitation signal whose frequency varies

exponentially between ω1 and ω2. The advantage of

this sine sweep is that it has longer duration of low

frequency tones than a linear sine sweep. [7, 8]

The MLS sequences depend heavily on the

assumption that the system is LTI. The technique of

sine sweep largely resolves this limitation.

There is a single excitation frequency for each

time “t”, then it is possible to apply a deconvolution

to the linear response of the system, and the response

of each distortion products. Harmonic distortion

appears temporarily pre- linear impulse response.

The equation of the LSS:

[

(

)(

(

) )] (15)

where is the lowest frequency, is the last highest

and T is the duration of the LSS.

The implementation of the linear convolution

avoids the temporal aliasing problems, even if the

time window analysis had the same length than the

sweep. In that case, information will be lost, but it the

processing won’t add spurious signals.

In practice a silence is added to the end of the

sweep, to retrieve a tail of the IR.

Since one frequency at a time is excited, the

Signal to Noise ratio (SNR) is greatly improved.

2 TEST SAMPLES

The test specimen to be used is a combination of

two different types of fiberglass wool. The objective

of this arrangement is to improve the absorption

acoustic characteristics for low frequency.

An important factor to consider when choosing

absorbent material is its thickness, as absorption

depends of it, may be higher or lower for certain

frequencies.

The maximum absorption values will being in

frequencies where the thickness is equal to λ/4 or an

odd multiple of λ/4.

2.1 Isover Acustiver P500

The Acustiver P500 is a fiberglass panel. The

panel dimensions are shown in Table 1:

Sizes

Thickness 50mm

Length 1.2m

Height 1m

Table 1: Acustiver P500 proportions

The density of this material is

.

2.2 Acustiver P VN

This is a common fiberglass panel which has the

same sizes as the P500. This panel is coated on one

side with black glass veil. This panel is a good choice

for coating an enclosure.

Figure 3: Both panels dimensions

The density of this material is

.

Figure 4: Fiberglass panels arrangements

2.3 Design of acoustic absorbent

In order to achieve the absorption of low

frequencies both materials were used in the test.

The application of the specimen is projected to be

installed in the control of a home studio. The room

has large reverberation times and small proportion.

This way, is needed to get high absorption in a wide

range of frequencies. Each proposed material has 50

mm of thickness reaching the low frequency of

theoretical high absorption over 1750 Hz. Because

this material has a high absorption coefficient, is not

needed to get maximum of velocity to get high

absorption.

In this way, it is possible to observe in a table

provided acoustic test developed by the Laboratory of

Acoustics and Lighting of the Commission for

1,20

m

1,20

m

5

Scientific Research in Buenos Aires P500 material,

that it has good conditions for absorbing frequencies

greater than 160 Hz. [9]

Figure 5: Absorption coefficient of P500

As a solution it is proposed to double the material

thickness for greater absorption frequencies below

160Hz ideally making greater absorption to 80 Hz.

Another factor taken into account was the difference

in density of each panel. In this case Acustiver P

panels they were used with black veil 35 kg / m3 on

the outside and P500 50kg / m3 against the wall ,

both 50mm thick.

This panel was designed with the objective to

obtain higher rate of absorption to vary the density of

materials. This way, the impedance of the room will

be better, helping to the incidence of the sound wave

within the material having a low density in at the

beginning of the material and increasing it as going

deeper, increasing in that way also the absorption.

3 PROCEDURE

3.1 Equipment

Tascam US1641

4 Earthworks M-50

Outline Omnidirectional Source

Sound Level Meter SVANTEK 959

Laptop

Absorbent

3.2 Characterization of the Room

The dimensions of the room for measurements are

6:5.2:3 meters giving a 93.6 m3 room volume and a

129.6 m2 of total surface. The walls of the room are

made of plasterboard and the floor of tiles.

To accomplish the characterization of the room,

the Reverberation Time of the room was obtained

with a LSS at four different points in the room with

three different positions of the source in order to get

different frequency responses of the room. Then, the

Critical Distance was estimated, according to eq. (1).

The result was:

Frequency RT (s) r (m)

100 1.99 0.57

125 2.05 0.56

160 2.69 0.49

200 2.61 0.50

250 2.79 0.48

316 2.59 0.50

400 2.53 0.50

500 2.78 0.48

630 2.64 0.49

800 2.58 0.50

1000 2.63 0.49

1250 2.63 0.49

1600 2.77 0.48

2000 2.65 0.49

2500 2.47 0.51

3200 2.32 0.53

4000 2.11 0.56

5000 2.08 0.56

Table 2: Reverberation Time and Critical Distance in

octave bands

Figure 6: Reverberation Time of the room

6

Figure 7: Critical Distance of the room

The estimation of the critical distance is an

important factor to take into account when doing a

measure in a room, because it’s the distance at which

the direct sound and the reverberant sound are equal

when dealing with a directional source. Then, the

estimation of the critical distance is a parameter that

indicates where to place the microphone during the

measure to get a good relation between the direct

sound and the reflections.

3.3 Noise Criteria

The background noise was measured in octave

bands and then compared with the NC chart. The NC

Criteria found was NC55 as shown in the Figure.

Figure 8: Noise Criteria

This measurement aims to set the sound sources

level above the noise level below.

This background noise level was found before

starting the measurement. The background noise

level after the measurement was almost the same

except for frequencies below 1 kHz. Those frequency

bands were 10 dB below than the first measurement.

3.4 Measurement

3.4.1 Signal to Noise Ratio

The measurement took place in an UNTREF

classroom used as a Reverberation Chamber for

academic purposes.

The background noise level was measured as can

be seen in the Noise Criteria. Then, the signal level in

the room was calculated to know if the Signal to

Noise Ratio (SNR) was correct.

Figure 9: Signal to Noise Ratio measured with the

sonometer

As can be seen, the Signal in low frequencies is

very low giving a negative Signal to Noise Ratio

when measuring with the sonometer. The reason is

because the LSS of 45 seconds of duration was

implemented between 80 Hz and 10 kHz. The reason

of this choice is because the frequency range to

satisfy the ISO 354 is between 100 Hz and 5 kHz.

Figure 10: Signal to noise ratio of the impulse response

When we analyze the impulse response given by the

LSS and its inverse filter, the SNR improved

appreciably, complying with the proposed regulations

3.4.2 Position of the microphones and source

Four microphones were placed in a fix position

and one omnidirectional source was placed in three

different points of the room, according to ISO 354. In

7

fig. 11 can be seen the places of each one of the

microphones and source positions.

Figure 11: Microphones (blue) and source (red)

position

3.4.3 Test Sample positioning

The sample under test was placed with three

different arrangements. At this point, it wasn’t

possible to fully meet the standard conditions due to

room dimensions.

Four pairs of fiberglass wool panels were placed in

the center of the room for the first arrangement.

Figure 12: First arrangement of the sample under test

As can be seen in the picture, the microphones and

the sample test are very close, so the solution was to

place the microphones at a greater height to respect

the standard as possible.

For the second arrangement, the four pairs were

placed in different parts of the room.

Figure 13: Second arrangement of the sample under test

For the third arrangement, two pairs of panels

together were placed in each part of the room.

Figure 14: Third arrangement of the sample under test

4 RESULTS AND DISCUSSION

4.1 Measurements uncertainties

The room employed to make the measurement

didn’t comply with the regulations of a reverberant

chamber, therefore, either the samples used didn’t

had the necessary sizes.

One of the uncertainties in this measurement is

the Standard deviation of the reverberation time T20.

Figure 15: Repeatability of the measurement

Temperature values and barometric pressure couldn’t

be determined due of a lack of proper

instrumentation. Therefore, these parameters were

not registered during the different measurements. As

a solution, the values were taken from the national

meteorological service. Therefore, the variations of

8

these parameters were not registered during the

different measurements.

4.2 Data Processing and Analysis

The data was recorded using Adobe Audition with

16 bits resolution and 44100 Hz of sample rate. All

the audio files recorded were processed with Adobe

Audition Aurora software to get the impulse response

of the signal. In order to get the Reverberation Time

data in third octave bands, a Matlab algorithm was

implemented.

The power attenuation coefficient defined by ISO

354 is not considered because climatic conditions

were not changed during the whole measurement.

The average reverberation times of the room with

and without the samples are shown in fig. 10:

Figure 16: Reverberation times of the room with and

without the samples

Then, the absorption coefficient for the three

arrangements of the test samples was calculated.

Figure 17: Absorption coefficient of the test sample.

4.3 Reverberation Time Computation

Given the large number of measurements and

subsequent analysis, MATLAB software was used

for the Reverberation Time to make the analysis and

subsequent averaging of the different measurements.

Each impulse response in time is filtered using a

FIR filter designed for specifics functions of the

program for this purpose. Thus, every third octave is

used in a manner that a filter order of 6 is obtained.

Figure 18: Octave Band Filter

Then, each of the filtered signals by third octave is

analyzed with RT calculation program with the

method of Schroeder Integral. This makes a least

square fitting averaging by analyzing the region EDT

[-5 to -35] dB.

Figure 19: Schroeder method plot

Then all the results of each measurement RT are

averaged together to each octave band , thus

obtaining the average RT .

4.4 Edge effect absorption

The edge effect absorption was calculated with

the Ten Wolde correction

Figure 20: β factor for Ten Wolde correction

9

Figure 21: Absorption coefficient with Ten Wolde

4.5 Modal density of the room

In order to evaluate the modal density of the room, it

can be performed simultaneous measurements in

different parts of the room measuring the modal

response of the room. To accomplish this task, it

should be noted the deviations in amplitude relative

to the frequency of analysis. This can be globalized

by a factor that addresses this problem and then

standardized.

This will give us the proper spatial deviation of the

enclosure.

4.6 Measuring a corner absorber

The standard implemented does not contemplate

measuring absorbent corner, so it is necessary to

specify that if it is measured conventionally in it, it

will present greater absorption surface, but will also

be more absorbent to not be located at the corner

where two reflective hard surfaces, so that the

velocity of the sound will be slightly higher.

On the other hand, the evaluation of the material

would not represent the actual absorption in situ , so

it is proposed to make other measurement besides the

one specified in the standard, one with the sample

located in the position where it will be used, and by a

calculation include positioning parameter covered by

that change .

Another possible method is to place two reflective

surfaces in the two of the faces of the sample, with

the aim of simulating the wall, although this will lead

to edge effects. These reflective surfaces should be

added in the calculation of the total surfaces of the

room.

5 CONCLUSION

It must be noticed the increase of its absorbent

qualities for low frequencies compared to P500

material. This is given mainly to the use of the

proposed compound which doubles its thickness,

reaching to cover the spectrum at low frequencies.

On the other hand, a decrease is observed in the

quality of sound absorber for high frequencies, this is

due to the implementation of the black veil cover

which spoils the porous material properties under

protect the same detachment, and moisture.

The results given are consistent with expectations

and demonstrate its usefulness for the intended use.

The acoustic treatment must be reinforced for low

frequency range where the absorption coefficient of

the material is low and may not get to decrease to a

certain range the reverberation time of the room.

Thus it is proposed to contemplate the use of reactive

absorbent as membrane resonators at frequencies

where the room presents specific problems. It is

important that the bandwidth of this absorbent is

large since the use of such absorbent is not effective

for a very narrow bandwidth

10

6 REFERENCES

[1] International Standard ISO 354, “Acoustics Measurement of sound absorption in a reverberation room”,

2003.

[2] Domingo R “Acústica Medioambiental Vol.1”. ECU. Spain.

[3]http://www.acs.psu.edu/drussell/Demos/Burns_PhD_animations/Burns_PhD_anim.html

[4] Bies D, Hansen C “Engineering Noise Control”. Spon Press. USA. 2009.

[5] Long M. “Architectural Acoustics”. Elservier Academic Press. USA. 2006

[6] Cox T., D’Antonio P. “Acoustics absorbers and diffusers”. Taylor & Francis. USA. 2009.

[7] Farina A.“Simultaneous measurement of impulse response and distortion with a swept-sine technique”.AES

Convention Paper. 2000

[8] Farina A. “Advancements in impulse response measurements by sine sweeps”. AES Convention Paper. 2007

[9]http://www.isover.com.ar/serdoc/12130726164238-

Medicion%20AbsorcionAcustiver%20P%20esp%2050%2070%20y%20100.pdf

11

Appendix A

ISO 354 Summary

Average reverberation time of the room is measured with and without the specimen. These reverb times of the

absorption area of the specimen is calculated using the Sabine equation.

Frequency range: 100 Hz – 5kHz

Room Volume

The room volume must be above 150 m3, but is recommended to be greater than 200 m

3.

When measuring in a room with a volume of 500 m3

or greater, it must be taken into account the air absorption,

because this is going to change the absorption at high frequencies

Absorption Area

The equivalent absorption area of an empty room must not be above the following values:

Frequency (Hz) 100 125 160 200 250 315 400 500 630

Equivalent sound

absorption area, m2

6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5

Frequency (Hz) 800 1000 1250 1600 2000 2500 3150 4000 5000

Equivalent sound

absorption area, m2

6.5 7 7.5 8 9.5 10.5 12 13 14

Table 1: Maximum equivalent sound absorption areas for room volume V = 200 m3

If the volume is not equal to 200 m3, the given values in the table must be multiplied by a (

)

factor.

Test Specimen

The test specimen must have an 10m2 to 12m

2. If the room volume is greater the superior limit of the sample

must be increased with the (

)

factor.

The chosen area depends on the room volume and the absorption of the specimen. If the room is bigger, the test

specimen must be greater too. For specimens with a low absorption coefficient, the upper area limit should be

chosen.

As to the proportions of the sample, the ratio L/W must be between 0.7 and 1.

It should be placed so that it is spaced from the walls at 1m distance to any wall of the room. If you are a heavy

specimen can be mounted vertically on the walls of the room and resting on the floor.

Temperature and humidity

Changes in temperature and humidity during measurement can have a significant effect on the measured

reverberation time, especially at high frequencies and at relatively low humidity.

Measurements should be performed in an empty room with the specimen under conditions of temperature and

relative humidity are almost the same and the absorption of high frequencies in the air does not vary too much. The

relative humidity should be between 30 and 90 %.

The temperature should be 15 ° C throughout the test

Microphones

Polar pattern: Omnidirectional

The measurements must be in different microphone positions where:

The microphones must be at a distance of 1.5 m.

12

The microphones must be at a distance of 2 m from the source.

The microphones must be at a distance of 1 m from any room surface and from the specimen

The reverberation time curves must not be combined

Source

Polar Pattern: Omnidirectional

It must be used positions at almost a distance of 3m

Number of measurements

The number of decay curves indepently measured must be almost 12. That is the number of microphones

positions by the number of positions of source.

The minimum number of microphone positions must be 3.

The minimum number of source positions must be 2.

13

Appendix B

Absorption Coefficient table

Frequency (Hz) A B C

100 0,31 0,11 0,27

125 0,34 0,30 0,31

160 0,85 0,79 0,78

200 0,96 1,10 0,96

250 0,90 1,14 1,07

316 0,98 1,22 1,14

400 1,15 1,35 1,28

500 1,24 1,50 1,27

630 1,16 1,41 1,19

800 1,07 1,30 1,10

1000 0,99 1,32 1,16

1250 0,88 1,09 1,04

1600 0,91 1,11 0,94

2000 0,88 0,98 0,94

2500 0,81 0,92 0,79

3200 0,77 0,94 0,81

4000 0,72 0,78 0,70

5000 0,62 0,74 0,73 Table 1:Third octave band absorption coefficient α for first

(A) second (B) and third (C) absorbent arrangements.

Frequency (Hz) A B C

100 0,31 0,11 0,27

125 0,34 0,30 0,31

160 0,85 0,79 0,78

200 0,81 0,95 0,82

250 0,55 0,78 0,71

316 0,51 0,75 0,67

400 0,63 0,83 0,76

500 0,86 1,11 0,88

630 0,88 1,12 0,91

800 0,88 1,12 0,92

1000 0,87 1,20 1,05

1250 0,88 1,09 1,04

1600 0,91 1,11 0,94

2000 0,88 0,98 0,94

2500 0,81 0,92 0,79

3200 0,77 0,94 0,81

4000 0,72 0,78 0,70

5000 0,62 0,74 0,73

Table 1: Third octave band absorption coefficient α for first (A)

second (B) and third (C) absorbent arrangements with Ten Wolde

corrections