Correlation of Sound Absorption Test Methods

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Technical Note (National Research Council of Canada. Division of Building Research), 1960-05-01

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Correlation of Sound Absorption Test Methods Northwood, T. D.; Balachandran, C. G.

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•

w·

ｾ NATIONAL RESEARCH COUNCIL OF CANADA

•

No .

DIVISION OF BUILDING RESEARCH

e

309

'fEClHIN

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NOTlE

NOT FOR PUBLICATION FOR INTERNAL USE

APPROVED BY

PREPARED BY ToD. Northwood CHECKED BY

and CoG. Balachandran NBH

May 1960

PREPARED FOR

. SUBJECT

ASTM Committee C-20 on Acoustical Materials

Correlation of Sound Absorption Test Methods

The purpose of this note is to review the present state of knowledge regarding the sound absorption of acoustical materials and to

discuss a program for evaluating absorption test methods. The note will

discuss in particular the significance of the reverberation room measure-ments of sound absorption and their relationship to other measuremeasure-ments

such as acoustic impedance.

It was originally envisaged that the project might include a

consideration of the performance of typical rooms. Certainly one should

keep in mind that the ultimate application of absorption test results is in room acoustics, but the design of ordinary rooms introduces so many special problems that the present program will be confined to a study of

test methods. Let it suffice to say that the most useful quantity in the

acoustical design of rooms is the random-incidence absorption coefficient. The objective of Committee C-20 should be to determine how reliable values of this quantity can be obtained.

2

-Impedance Tube Measurements and the Random Incidence Absorption It is a straightforward matter to measure the normal-incidence acoustical impedance of a small sample of material.

In principle, if the material is "locally reacting", one may then

calculate the random-incidence coefficient for the material.

There are two reasons why this is not a ｳ｡ｴｩｳｦ｡｣ｾｲｹ general

method for evaluating acoustical materials: (1) many materials

are not locally reacting. For example most suspended ceiling

systems consisting of a perforated surface backed by the

absorptive air space would not meet this requirement; (2) the behaviour of many materials depends on the way individual panels of material are mounted, and the small specimens that can be tested in an impedance tube do not demonstrate these effects.

The first difficulty might be overcome by developing

methods for measuring the impedance at selected angles. Such

methods have been tried experimentally but generally they are applicable only to small samples, whereas departures from the locally-reacting state occur most often when large structures are involved(e.g. suspended ceilings, and systems in which the

absorption mechanisms involve diaphragm vibration). The problem

might be overcome by making measurements on a large panel in a

free field. The largest panel that can readily be dealt with in

most free-field rooms would, however, be small enough that

diffraction effects would introduce a complication. It is

therefore doubted that either technique would be useful as a general practice.

For materials that are locally reacting however, it should be possible to make correlations between tube and

3

-reverberation room results. This possibility is explored in a

later section.

Reverberation Room Correlations

During the period

1951-1953,

a round robin program of

,

measurements was carried out under the auspices of A.S.T.M. C-20. Samples of three different types of acoustical material were

carefully prepared and circulated to seven reverberation room

establishments in North America. The results of this program

will not be discussed in detail but a few general comments may

be made. The seven laboratories carried out their tests by

using nominally the same method, although at this time no standard

document existed. As a result there were many important

varia-tions in technique: two laboratories used sample areas smaller

than the customary 12 square feet; several laboratories made an empirical area correction; and at least one laboratory failed to

mask the edges of the samples. It had been anticipated that

the major disagreement would be at the, lower frequencies, but

this was not the case. Agreement was fair at the lower

frequen-cies, but there were large and inexplicable variations at the higher frequencies.

Two of the participants, Riverbank Acoustical

Laboratories and N.R.C. Canada, represented, on the average, the extremes of the observations, and a careful examination was therefore made of the techniques used at these establishments. After a few minor changes an additional series of

intercompari-,

sons were made between these establishments and close agreement

was found. (It is believed that the major discrepancy originally

was due to the fact that the edges of the sample were not masked

4

-has not yet been proceeded with. Further experimental work

with the same samples has since been done by N.R.C. Canada, in connection with the commissioning of a new reverberation room. Close agreement was obtained between these tests and the earlier

comparison. Thus, it appears that Riverbank and N.R.Co obtain

good agreement in sound absorption measurements. This, of course,

dQes not guarantee that the ｱｵ｡ｾｴｩｴｹ being measured is the

"random-incidence sound absorption coefficient".

Beginning in 1959 the I.S.O. Technical Committee 43 sponsored a new round robin series in which a large number of

European laboratories participated. As in the case of the

A.S.T.M. round robin, the results demonstrated forcibly that variations in technique that had been considered unimportant

were in fact very important. It was decided to hold a second

round robin with more careful control of two of the principal variables: the size of sample, and the diffusing system used in

the room. Tests were made on three sample areas: 4m2, 8m2, and

12m2, and under at least three diffusion conditions. In general

the results varied in erratic fashion under minimum diffusion

conditions, but settled down considerably as the maximum diffusion

condition was approached. The recommended diffusion system

consisted of a large number of flat plates, totalling an area equal to the floor area of the rooID, suspended randomly in spaceo This system greatly reduced the spread in results at high

;'fre-quencies. There still appeared however to be a variation with

volume of test chamber and it was surmised that it was more difficult to obtain the reqUired diffusion condition in a small

room"especially with a large sample. A group of laboratories

with small rooms were ruled out on this basis. The five remaining

5

-as will be shown later, the average of the results obtained by the five laboratories is probably very close to the "true" sound absorption coefficient.

At N.R.C. Canada, one of the five remaining partici-pants, an additional series of experiments was carried out in

a search for the cause of the remaining spread in results. These

experiments, which will be discussed more fully later, indicated that alterations in sample position and in the exact arrangement of the "randomly" spaced diffusing panels produced significant

changes in the results. (See Figures

3, 7

and 10). Hence it

appears that these matters require further study before a

specification for satisfactory test conditions can be set do\vn. Effect of Sample DimenSions on Measured Absorption

One of the complications of the absorption measurement is the fact that the absorption of a patch of material depends

on its dimensions. If a patch of material is placed on (or set

in) an otherwise highly reflecting surface, the material near the edge of the patch absorbs more than its quota of energy, with the result that the average coefficient for the patch is

increased over the value for infinite area. Thus, strictly

speaking, in the reverberation chamber we measure the absorption

of a particular sized patch of material. The term "absorption

coefficient" implies a quantity which is dependent on the material only and not the dimensions of the sample under consideration, but it is customary to assume that this quantity refers to a patch whose dimensions are large enough that diffraction effects are negligible.

6

-evidence of the area effect since Chrisler's measurements in

1934. Unfortunately, the uncertainties associated with

rever-beration room measurements are such that it has been difficult

to obtain a reliable quantitative relation. Several attempts

have also been made to calculate the diffraction effect. It is

proposed to discuss in particular ｴｨｾ calculations made at

N.R.C. a year or two ago. (Reference 1).

Figure 1 shows·the calculated random incidence

absorption coefficient as a function of sample dimensions, and the real part of the admittance, and also the available infor-mation regarding the effects of the imaginary component of

admittance. The oblique straight line to the left of the figure

is the limiting value of the absorption coefficient for a very

small area. At this limit the coefficient is independent of

the imaginary component of admittance. The upper family of

curves shown between this limiting value and the infinite area value ((l/kn)= 0) are for materials whose imaginary coefficient

is zero. In addition, at the bottom of the figure are plotted

another family of curves for infinite area, showing the effect

of an imaginary component. At present nothing is known about

the effect of the imaginary part for patches of intermediate

size. Also it should be remarked that these curves are based

on a rather small number of calculated points. It is planned

this summer to re-calculate the diffraction effect for additional

values of admittance and (l/ka), and possibly also to determine

the effect of an imaginary component for a few cases. In the meantime, these curves have been used to calculate the random-incidence absorption of the I.S.O. round

robin material for the areas tested. Some of these results are

(1) Northwood, T.D., M.T. Grisaru, and M.A. Medcof. Absorption of

sound by a strip of absorptive material in a diffuse sound field. Journal, Acoustical Soc. of America., Vol. 31, No.5, May 1959,

,

7

-shown in Figures 2 to la, which will be discussed in detail

latero Actually, two calculations have been madeo First the

upper set of curves of Figure 1 were used to determine absorption

coefficient with the imaginary part neglected o This is the upper

dashed curve on Figures 2 to lao The lower dashed curve was

obtained by subtracting from the upper one the infinite-area

correction due to the imaginary part. Provisionally, until

further diffraction calculations are made, it is assumed that the true value will be between these two calculated values (i.e. it is assumed that for finite areas the imaginary component has an effect somewhere between the small-area and infinite-area value) •

Reverberation Theories

In reverberation room measurements and in acoustical design, the Sabine reverberation formula is almost universally

used. The view is usually held that the Norris-Eyring formula

is the correct one but that the Sabine formula is an adequate approximation, considering the other uncertainties of room

acousticso In a recent paper however, RoW. Young takes the

view that the Norris-Eyring formula is applicable only for a

room in which the boundaries have uniform acoustical properties._,

In the reverberation room, which represents a drastic departure from this condition, it is usually assumed that each surface

material absorbs in proportion to the product of its area and

its absorption coefficient (apart from diffraction effects)o Young argues that this is an unwarranted assumption and suggests

that the geometric ｭ･ｾｮ assumed in the Millington-Sette formula

is just as probable. He goes on to point out that the Sabine

formula is similar to the Millington-Sette formula except that

...

8

-The theory is offered that the various devices used in a reverberation room to achieve a diffuse sound field might

alternatively be regarded as devices to ensure a continuous

redistribution of energy among the various components of the sound

field. This in turn should ensure that each part of the boundary

receives and absorbs its fair share of the total energy. ThuS,

while we have been struggling to achieve a ltdiffuse sound field", we have perhaps inadvertently provided a situation in which the arithmetic averaging procedure is legitimate.

The reasons for using the Sabine equation are still cogent, but it will be shown that absorption data calculated by the Norris-Eyring formula agree better with other evidence than the Sabine results.

Experimental Results

The attached figures present in summary the results of the second I.SoOo round robin in which tests were carried out by five laboratories on batches of the same material, Silliano

(This material is similar to Fiberglas Type P F commonly used

in North America) 0 It is expected that detailed information

about these tests will be published shortly by Professor Kosten,

but in the meantime details will be given for only our own

_.

_.

establishment, NoR.C. Canada. It may be taken that the effects

observed at NoRoC. typify those found generally.

The IoS.Oo results are considered particularly valuable (as compared, for example, to the AoSoToMo round robin,) because the experimental conditions were more uniform than in any

previous interc omparison0 In particular the effect of diffusing

9

-maximum diffusion has resulted in a series of measurements that

can be compared with impedance tube measurements. The effect of

diffusion is illustrated in Figure

7.

It will be noted that the

standard rotating vane system at NoR.C. Canada produced results substantially lower at high frequencies than those obtained with

a diffusion system consisting of a multitude of plates distributed

through space. Our tentative conclusion is that our standard

condition is inadequate, although no change will be made for standard tests until the matter is considered by other testing

laboratories in North Americao Since our results agreed with

Riverbank ｰｲ･ｶｩｯｦｩｳｬｹｾ it is surmised that a similar effect will

be observed at Riverbank0

In Figures

4, 5

and 8, the individual and average

results obtained in the five IoSoOo laboratories are plotted,

together with the two calculations referred to previously. It

will be seen that there is fair agreement between the average

reverberation room measurements and the calculated values o The

former are slightly higher than the calculations at the upper_,

frequencies, but this discrepancy would largely disappear if the Norris-EYring reverberation formula were used instead of the

Sabine formula. The difference is shown in Figures 2, 6 and 9,

in which the N.R.C. results gre calculated by both formulae.

The spread in individual results seen in Figures

4,

5 and 8 may be compared with the spread observed at N.R.C. for

several variations within the prescribed maximum-diffusion

condition of test (See Figures 3, Ｗｾ and 10). These included

two sample positions and three arrangements of the diffusing

plates. Sample Position 1 was near one corner of the room

10

-was in the middle of the room. In diffusing conditions a and c

the panels were kept about 2m above the floor (and above the

sample); in condition b they approached within ｾｭ of the floor.

The results reported to I.S.O. were for sample Position 1, diffusion condition a.

Further correlations are planned, with studies of

different diffusion arrangements and with other types of absorbing

material. One additional result is shown in Fig.

II.

The

material used for this test was one of the A.S.T.M. round robin

materials, a perforated sugar cane fibre tile,

It"

().2 cm) thick.

Comments

Measurements have been presented of sound absorption

coefficients obtained under carefully controlled conditions in

five reverberation rooms. These have been compared with

cal-culations based on impedance tube measurements and the available information regarding the diffraction effect associated with a

small sample. The average of the five sets of results is found

to agree closely with the calculated values.

Although the average of the five establishments provides good agreement with calculations, there are still large

devia-tions among the individual laboratories. From auxiliary

measure-ments made at NoR.C. ,Canada, it appears probable that these

fluctuations are related to the diffusing system. It is

necessary therefore to determine the cause of these deviations and to find a method of prescribing the diffusion condition so that true values will be obtained.

,

11

-It follows that conditions at the edges of a sample are also of importance, since the calculations used above are based on the assumption that the face of the sample is in the same plane as the surrounding surface (which is assumed to be perfectly

reflecting). Huntley has suggested that if the sample were

suspended in space the area effect would be an inverse one, as

compared with the effect obtained when the sample is against a

reflecting surface. It is probable that this condition would

be amenable to calculation. But many samples that are commonly

tested in the laboratory constitute an intermediate condition

which certainly could not be calculated. Typical

suspended-ceiling systems, for example, stand 30 em or more above the

mounting surface. It would be of interest to carry out

diffrac-tion studies with a material such as Sillan (on a rigid backing)

at various levels from the floor. These would at least provide

experimental evidence regarding the dependence of the diffrac-tion effect on this variable.

IneVitably, the area effect calculation will be rather uncertain for many types df mateTials, either because of the effect mentioned aoove or because the material is not locally

reacting. The calculations will probably give results that are

satisfactory for field use but not very satisfying to the

testing laboratory, since the objective is to ｭ｡ｾ･ a precision

measurement. It is suggested therefore that wherever possible

the sample area should be a standard value and that the published

results should be the values for this standard area. The

infinite-area calculations might also be made and ,reported, but it should be made clear that this is an approximation.

\,

12

-should be avoided, especially when referring to measurements

made on

a

small sample since, strictly speaking, one cannot

simply multiply an area by a coefficient to obtain total

absorptiono Moreover, ｴｾ･ｲ･ is the usual problem of explaining

values greater than unity.

An

alternative, suggested by

R.K. Cqok, is to quote the "absorption cro'ss-section" of the

standard sample. Eventually, however, something equivalent to

a coefficient is required, and the arguments against continuing to use the term seem academic.

In North America the accepted standard area is 9 feet

by 8 feet {2.74m by 2.44m)o In the I.S.O. a standard area is

just being decided upon, and a size approximately the same as a North American value could be adopted with no inconvenience

to European laboratories. For example, a sample 2m by 3 m would

have a value of

(l/ka)

very close to the North American value.

A slightly better correspondence could be obtained with a slight modification of one area or the other, without seriously

impairing; continuity in the North American results.

i

Apart from this there are two other factors to consider

in settling on a standard area. First, the larger the area,

the less important the diffraction correction; but the variation is so gradual that this is not an important consideration.

Second, the larger the area, the larger ｴｾ･ room necessary to

make a reliable measurement. The I.S.O. round robin indicated

provisionally that a number of European laboratories are "too

smalltr

, under present test conditions. It is possible that

further diffusion studies might permit a lowering of the

mini-mum admissible room volume, but one of ｾｨ･ limiting factors will

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