Sound absorption by conical absorbers and glasswool layer combination

Applied Acousth's 22 (1987) 91-101

Sound Absorption by Conical Absorbers and Glasswool Layer Combination V. M o h a n a n , O. Sharma and A. F. Chhapgar National Physical Laboratory, New Delhi--ll0012 (India) (Received 21 July 1986; revised version accepted 15 December 1986)

SUMMA R Y

The,]'act that the a&fition of a cone to a porous ahsorbent can increase the range of i t s ahsorption characteristics prompted the authors to itwestigate the possihilit.t' ¢~fu.~'brga cone anti a certahl la)'er of glasswool as a suhstitute Jbr the traditumal wedge structure for treatment #t anechoic" chambers. Although the combination can )'iehl hwreased ahsorpthm in the hnt'- anti mediumfrequent)' ranges, the drop in absorption at h(gh.frequencies limits its use as an hh'al substitute.for wedge structure. Yet the comhhuttion can giz'e un(/brm high ahsorpthm for most noise and ret'erherathm control applicathms.

INTRODUCTION During measurements made on different types of sound absorbing materials in a reverberation chamber, one sample (Fig. 1), made of a jute board base with a jute sheet cone at the centre, showed higher absorption at low frequencies as compared to plain sheet materials, t While plain sheet materials gave low to medium absorption at frequencies below 500 Hz and high absorption above 1000Hz, the sample with cone gave fairly high absorption even in the 400-800 Hz range. When mounted with a 100 mm air gap, the absorption values were high down to 250 Hz (Fig. 2). The results were similar to those of the pyramidal absorbers discussed by Bruel 2 and of the suspended absorbers described by Knudsen and Harris) Bruel has ascribed the increased absorption of the pyramidal absorbers to the larger exposed surface area provided by the shape, while Knudsen and 91 Applied Acoustic'.~"0003-682X/87/$03.50 :(" Elsevier Applied Science Publishers Ltd, England,

1987. Printed in Great Britain

V. Mohanan. O. Sharma. A. F. Chhapgar

92

Fig. I. J u t e b o a r d o f size 0-61 x 0"61 x 0 ' 0 1 2 m w i t h an a t t a c h e d jute sheet c o n e (height h = 0"2 m. r a d i u s r = 0"2 m a n d thickness o f the sheet t = 0.003 m) at the centre.

Harris attribute the higher absorption of suspended absorbers to diffraction effects ofsound waves by the absorber, causing the waves to impinge on both sides of the sample. However, experiments with the cone inverted showed that increased surface area is not the main factor in increasing the absorption.t Moreover, measurements on the cone alone in a normal wave impedance tube'* and in it reverberation chamber -~showed a resonance-type curve centered around 4(X)Hz. it appeared, therefore, that the increase in Ioo

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Sound absorption by cones and glasswool combinatwn

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absorption at lower frequencies was due to some resonance phenomenon effected by air enclosed in the cone. Hence an experimental investigation was undertaken to study the resonance behaviour in cones. 6 In this paper we report the salient features o f the results, along with an empirical interpretation in probing the possibility o f using these cones in place o f conventional wedges for treatment in anechoic rooms and in other noise and reverberation control applications.

EXPERIMENTAL In the first phase o f the work, cones o f different materials and sizes were examined for their sound absorption properties in a normal wave impedance tube'* in the frequency range 50-400 Hz. Using different materials (jute sheet, aluminium sheet, chart paper, cardboard etc.), cones o f base radius r = 0"2 m and height h = 0.2 m were made locally. These were tested in an impedance tube, the cut-off frequency of which was a r o u n d 400 Hz. The absorption curves, shown in Fig. 3, show that, for all materials, there is a resonance peak at about 400 Hz. Since, due to limitations o f the normal wave impedance tube having a cut-off frequency around 400 Hz, some of the curves in Fig. 3 appear incomplete, further measurements on these materials in a reverberation chamber showed a similar resonance peak a r o u n d 400 Hz. Hence it could be inferred that these cones behaved in a more-or-less similar fashion, although their resonance frequencies were slightly different. Therefore, in the subsequent evaluation, cones made o f one material--chart paper in the present studies--were used. In the first stage o f the experiment, cones were made of different heights (h = 0.2, 0-5 and I-0 m} but of same base radius (r = 0.2 m). The resonance curves, shown in Fig. 4, indicated that the frequency of m a x i m u m absorption shifted to the low-frequency side as the heights o f the cones increased. Thus, for the same base radius, the resonance frequency is related to the height o f the cone. in the second stage o f evaluation, the heights o f the cones were fixed at h = 0-2 m while the base radii were varied as r = 0"05, 0-1 and 0.2 m. The absorption curves, shown in Fig. 5, clearly indicated that the resonance curve width broadened with larger diameter. Next, the volumes o f the cones were kept constant ( V = 0.008 m 3) and the sizes were altered as: (l) h = r = 0 . 2 m ; (2) h=0"33, r = 0 . 1 5 m ; and (3) h = 0-75, r = 0-1 m. It was also observed from the absorption curves, shown in Fig. 6, that the resonance frequency depended on the height o f the cones, and the width o f the resonance curves depended on the base radius, a result similar to that deduced above from Figs 4 and 5.

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in the next stage of the experiment, absorbers of various shapes (conical, rectangular and square) were studied for their relative sound absorption properties. The absorbers were made of chart paper and were of the same volume ( V = 0-008 m3). The absorption curves, shown in Fig. 7, clearly demonstrated the superior performance of the conical absorbers compared to other shapes. in the second phase of evaluation on conical absorbers, chart paper cones of different heights (h = 0-2, 0"5, 0"75 and I'0m) and same base radius (r = 0-2 m) were tested in combination with glasswool layers of varying thicknesses in the same impedance tube in the frequency range 50--400 Hz. The density of the glasswooi layers used was around 2 0 k g m -3. The absorption characteristics corresponding to the various combinations are shown in Fig. 8. The results clearly show that the addition of a glasswool layer beneath the cones broadens the resonance curves.

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DISCUSSION The results of the experimental investigations described in the previous section clearly demonstrated the following points, which were of importance from a design point of view. (I)

For cones of the same size, the resonance curves did not depend critically on the material of the cones, and the different cones behaved in a more-or-less similar fashion.

98

V. Mohanan, O. Sharma, A. F. Chhapgar

(2)

For cones made of the same material (chart paper in the present studies) the frequency of m a x i m u m sound absorption decreased with the height o f the cone and the width o f the resonance curve broadened with increasing radius o f the cone.

According to Wood. ~ the frequency o f vibration, f,. of a column o f air enclosed in a hollow cone closed at the base as well as at the vertex is given by .f, = nc/21

where c = velocity of sound in air, / = slant length of the cone, and n is a series of non-harmonic values given by the intersection of the curves y = x and v = tan x. The first value of n after 0 is 1-43. Hence the fundamental frequency of vibration for the enclosed air in the cone is given by .1'= 1.43C/21 This relation is plotted in Fig. 9. According to Parkin and Humphreys, 8 the frequency of maximum absorption of a panel is given by f= 60/~ where m = surface weight of panel in kg m - -', and d = depth of air gap in metres. Although the cone is strictly not a panel in the conventional sense, it can be treated its one with a varying air gap. Since the volume of air in a cone is t th~,t of a cylinder, the value o f m in the case of a cone can be taken its t m, giving the relationship shown in Fig. 9.

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Sound absorption by cones and glasswool combination

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It is also well known that, in the case of wedges in an anechoic chamber, the cut-off frequency occurs at a value of length of wedge structure 1 = 2/4, where 2 = the wavelength of sound at the cut-off frequency. This relationship is also plotted in Fig. 9. From the results of absorption characteristics due to cones given in Fig. 4 and also plotted in Fig. 9, it is seen that the cones behave similarly to wedges of the same height. This result, as well as the improvement in absorption as shown in Fig. 8, allows the possibilities of using hollow cones with porous sheet absorbers in anechoic chambers, or for enhancing the absorption of such porous sheets at lower frequencies. Therefore, measurements were conducted in a reverberation chamber with cones made of chart paper in combination with glasswool sheets, as per the relevant specification. ~ The results are shown in Fig. 10. Although the combination showed an

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improvement over absorption due to cones alone in the low- to mediumfrequency range, there is a drop in absorption in the high-frequency region when compared to that of glasswool alone. The drop in absorption at high frequencies can be explained along the following lines. If a sample has to qualify as a wedge for treatment in an anechoic chamber, the pressure reflection coefficient of the sample should not be more than 10% in the frequency range of interest, i.e. from the cut-off frequency to very high frequencies. '~ Further, the sample should present a gradually increasing impedance to the incident sound wave, so that the

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FREOUENCY (Hz) --Fig. I I. Variation in sound absorption characteristics in a reverberation room of chart paper cones in combination ~ith a glasswool layer, as the area of exposed glasswool surface changes duc to a reduction in the number of cones. passage from air to the material should be without sudden change in impedance. It may be argucd that, in the case of the cones plus ghtsswool combination, this condition may not be fulfilled completely in the highfrequency rcgion where the absorption is mainly caused by the porous material. As the cones cover an appreciable area ofglasswool surtace, the net absorption drops in the high-frequency region, where the effect of resonance absorption in the cone is not substantial. Further, it had been observed that the drop in absorption at high frcquencies can be reduced by reducing the number o f cones, so that more ghtsswool area becomes exposed to direct sound energy, as shown in Fig. 11. However, the reduction in the number of cones should not affect the lowfrequency performance of the sample. Hence it can be inferred from the above absorption char:tcteristics that the covered area o f the porous absorbent should not be more than 20--30% of the total exposed sample area, in order to get increased absorption throughout.

CONCLUSIONS Although one can use these conical absorbers in certain cases where wedges are used, they cannot replace the wedges altogether. As is evident from Fig. 8, the case of. say, 50 mm glasswool plus the cone almost resembles the wedge structure, but the reflection coefficient for most o f the combinations is more

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than 10% except in the vicinity o f resonance. This fact is also evident from the results o f Fig. 10, in which the high-frequency absorption has been reduced as less glasswool surface is exposed to the direct sound field. As we reduce the n u m b e r o f cones, more glasswool surface is exposed to direct sound. However, there is a slight drop in the low-frequency absorption o f the sample also. It is thus inferred that the cones should not cover more than 20--30% of the glasswool surface to get uniform high absorption. Therefore, the cones plus glasswool combination cannot be an ideal substitute for wedges for treatment in anechoic chambers. However, the combination can be used for general noise and reverberation control applications, especially at lower frequencies, to a high degree o f satisfaction.

REFERENCES I. V. Mohanan, O. Sharma and A. F. Chhapgar, Absorption characteristics of jute boards with an attached cone at the centre, J. At'oust. Soc. hldia, l0 (1982), 136-8. 2. P.V. Bruel, Smmdinsuhttion atulroom acoustics, Chapman & Hall, London, 195 I, p. 121. 3. V.O. Knudsen and C. M. I-larris, Acousth'alth's(t, nhlg in architecture, John Wiley, New York, 1950, p. 129. 4. ASTM Standard, hHpt'danct, and ahsorptimt ol'acousth'al materials h.v hnpedance tube mcthocL ASTM 1981 Standard C-384-77, p. 146. 5. Indian Standard Specification, Method q/'measuremtmt of ahsorpthm coe[ficient ha a recerherathm room. IS: 8225-1976. 6. V. Mohanan, O. Sharma and A. F. Chhapgar, An experimental investigation into the augmented absorption characteristics of conical sound absorbers, J. ,4coust. Soc. hulia, 12 (1984), 14~18. 7. A. B. Wood, A textbook ofsountL Orient Longmans, New Delhi, 1960, p. 182. 8. P. H. Parkin and H. R. Humphreys, Acoustics, noise and buildings, Fabcr and Faber, London, 1958. p. 59. 9. M. Pancholy, A. F. Chhapgar and S. C. Bansal, Sound absorption ofindigenous wedge shaped structures, J. Acoust. Soc. hulia, 5 11977), 63-80.