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Sound absorption coefficients and acoustical design
Northwood, T. D.; Balachandran, C. G.
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1.41
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2NATIONAL
RESEARCH
COUNCIL
A P ~ A L Y Z E D
C A N A D ADIVISION O F BUILDING RESEARCH
SOUND ABSORPTION COEFFICIENTS AND
ACOUSTICAL DESIGN
BY
T. D. NORTHWOOD AND C. G. BALACHANDRAN
R E P R I N T E D F R O M
P R O C E E D I N G S O F T H E T H I R D I N T E R N A T I O N A L C O N G R E S S O N A C O U S T I C S V O L . 2. 1961. P. 847 - 849.
R E S E A R C H P A P E R NO. 141
OF T H E
DIVISION O F BUILDING RESEARCH
OTTAWA
DECEMBER 1961
This publication i s being d i s t r i b u t e d by the Division of Building R e s e a r c h of the National R e s e a r c h Council. I t should not be reproduced in'whole o r in p a r t , without p e r m i s
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Reprinted from Prweedlngs 3rd Inremartonal
Congress on Acousl~cs
tdlror: L . Crcmer Prtnted In the Netherknds Elsevler Publlsh~ng Company. Amsterdam
Sound Absorption Coefficients and Acoustical Design*
T. D. NORTHWOOD A N D C. G. BALACHANDRAN**B l r i l d i n g P h y s i c s S e c l i o t ~ . D i v i s i o t z of B u i l r l i n g R e s e a r c l t , N a t i o t r a l R e s e a r c h C o u i i c i l , O t r a r v a ( C a n a r l a )
The acoustical design of rooms is usually based on the ordinary reverberation theory of room acoustics, in which the reverberation time is expressed in terms of the room dimensions and the sound absorption coefficients of the various boundary surfaces. The assumptions inherent in this approach are well known, and have been the cause of much speculation. This paper reports o n recent systematic studies of some of the assumptions and comments on their importance in acoustical design.
Most of the measurements have been made in a reverberation room. By definition such a room is designed t o conform closely to the requirements of the theory, and it is of interest t o determine how well it meets this objective. Moreover, since it is used t o measure what purport to be sound absorption coefficients of materials, it is important to know what these measurements signify and how they may be applied in the design of other rooms.
A crucial point in the reverberation theory is the assumption of a diffuse sound field: it is assumed that the time average of the sound level in the space remote from boundaries of a room is everywhere the same, and that at any point the average flow of energy is the same for all directions. Such a condition is difficult to achieve in a simple finite room with plane boundaries, and in a reverberation room various dif- fusing devices are employed t o improve matters. Such diffusers function by modi- fying the simple room modes and providing a continuous interchange of energy among them. If the diffusers are successful the decay of sound will be truly logarith- mic, and each portion of the boundary surface will be exposed t o sound arriving from all possible directions. Comparative studies were recently carried out o n four diffusing systems: wall irregularities, space scatterers, distributed patches of absorb- ing material, and a rotating inclined vane'. The diffuseness of the resulting sound field was tested in several ways, but perhaps the most relevant question is whether the reverberation theory is valid in the given circumstance. T o answer this question the absorption of a standard sample of material was determined in each case. If the absorption agreed closely with the known accepted values f o r the material, it was considered that the sound field was sufficiently diffuse for purposes of acoustical design. In the work reported earlier, there was little correlation between the measured sample absorption and the degree of diffusion as indicated by other criteria. The results were complicated by the fact that the diffusers inevitably added absorption to the room, and this was first thought to be the key t o the problem. More recent stu-
*
This is a contribution from the Division of Building Research, National Research Council, Ottawa, Canada, and is published with the approval of the Director of the Division.**
On leave from the Central Building Research Institute, Roorkee, India.848 T. D. NORTHWOOD A N D C. G . R A L A C H A N D R A N
dies, however, have indicated that the anomalies were due to the presence of absorb- ing bodies within two or three wavelengths of the sample position. When this con- dition was avoided, the absorption measurements were satisfactorily consistent even in the bare room except at the lowest test frecluency. is is concluded that diffusing elements are necessary for the low frequencies but that this can easily be accomplished. It follows that in ordinary rooms typical furniture and furnishihgs probably provide adequate diffusion for purposes of reverberation calculations.
The apparent importance of total absorption in the diffusion studies has led to a separate consideration of absorption effects. The reverberation theory assumes that sound waves are reflected 1iia1ly times, interacting with all boundaries, during the time required for sound to decay a significant amount. This condition is best met when the reverberation time is long. It is of interest to know how short it may be made before the theory ceases to apply. Absorption measurements wcre made with
N O R R I S - E Y R I N G F O R M U L A
1
e a V1"..
7
0 .02 . 0 4 . 0 6 .08 . I 0 . I 2 .I4ROOM ABSORPTION COEFFICIENT
IL 0 0 . 9 m 4 w 0 . 8 -1
Fig. 1 . Measured absorption of standard sample versrrs average empty room absorption coefficient (1000 CIS.).
- S A B I N E F O R M U L A
-
o-O/---
- -
+ - - 0 - - 0 0
the standard sample as the average chamber absorption coefficient was varied from 0.02 to 0.12. Typical curves of the variation in sample absorption over this range are shown in Fig. 1. Since there is still some controversy about reverberation formulae2, both Sabine and Norris-Eyring formulae have been used to calculate absorption of the standard sample, and both results are shown. It appears that the Norris-Eyring formula gives the more reliable results, and that it is still adequate up t o an average absorption coefficient of 0.12. Further tests to compare the reverberation formulae more directly will be reported later.
A n important consideration in absorption measurements is the variation in absorp- tion coefficient with dimensions of the test sample. Previous work3, 4, has shown
that the absorption coefficient of a patch of material is significantly higher than the "infinite-area" value when the dimensions are less than 3 o r 4 wavelengths. It follows that laboratory coefficients, obtained on a relatively small sample, are correct only for a patch of the specified dimensions, mounted on a n otherw~se reflecting surface. Larger o r smaller patches should have smaller or larger coefficients respectively. The
S O U N D A B S O R P ~ - I O N COEFFICIENTS A N D ACOUS-TICAL DL:SIC;N 849
proximity o f other absorbers will also reduce the absorption of the test sample, a n d this extraneous effect must be guarded against in reverberation chamber experi- ments such a s those described above, in which the absorpiion o f a standard s a m p l e is used a s a criterion.
REFERENCES
1. C. G. BALACHANDRAN, J. ACOIISI. SOC. A t u . , 3 1 (1959) 1319-1321.
2. R. W. YOUNG, J. ACOIIS~. SOC. A t l i . , 29 (1957) 912.
3. R. K. COOK, J. ACOIIS~. SOC. Am., 29 (1957) 324; also this book. p. 883.
4. T. D. NORTHWOOD, M. T. GRISARU A N D M. A. MEDCOF. J . ACOIISI. SOC. All!., 31 (1959) 595. 5. W. KUHL, this book, p. 882.
