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Active sound absorption in an air conditioning duct
Journal o f Sound and Vibration (1978) 58(3), 333-345
ACTIVE SOUND ABSORPTION IN AN AIR CONDITIONING DUCT G. CANEVET Laboratoire de Mdcanique et d'Acoustique, Centre National de la Recherche Scientifique, " 31 eheminJoseph Aiguier, 13274 Marseille Cedex 2, France (Receiced 24 Nocember 1977) Jessel's theory of active sound absorption has allowed the design and construction of practical systems. In this paper, two recent tripolar absorbers are described and a few experimental results are presented. Absorption experiments were performed successively on pure tones, narrow band noise and broadband noise, propagating in an air conditioning duct. For these three categories of noises, the attenuations achieved were respectively45 dB, 15 dB and 10 dB. I. INTRODUCTION Noise control by means ofactive absorption is an old idea but at the same time it still presents many problems in practice. Indeed, the first realizations of active absorbers go back to 1936 [1 ] and nevertheless 40 years later one still seeks a solution well suited to industrial needs. In part, one may attribute this slow development, the most significant stages of which have been summarized by Mangiante [2], to difficulties of a technological and more precisely o f an electronic nature. But in large part the slow implementation o f active sound absorption systems has been due to the poor formulation of the basic problem; this is reflected in the fact that recent practical progress has followed new developments of a theoretical nature, principally due to Swinbanks [3], whose work has been supported by the experiments of Leventhall and his group [4, 5], and to Jessel [6, 7] whose theory has led to important recent developments [2, 8, 9-13]. In this paper the latest results of experimental investigations of the absorbers deduced from Jessel's theory are presented, and thus it is a continuation of an article by Mangiante and Jessel previously published in this journal [10]. After a short qualitative review of Jessel's theory and its implications, the characteristics and performance of recent experimental models are described. After that, as a practical example, sound absorption in an air conditioning duct is studied. 2. THEORY AND EXPERIMENTAL MODEL OF AN ACTIVE ABSORBER Active sound absorption was formulated by Jessel as a reciprocal of Huygens' principle. "Given a source S (Figure 1) radiating in a space O is it possible to insert, on the trajectory of the waves, a 'barrier' of secondary sources 2: radiating out of V a field in opposition to that of S, and into V a zero field so that the resulting total field is equal to the primary one inside V and equal to zero outside ?" It is very important to point out that this approach to the problem is different from that of Swinbanks. Indeed, Jessel makes no initial assumptions regarding the nature of the secondary sources while Swinbanks, from the beginning, considered only the problem of sound absorption in a wave guide by two rings of monopolar sources. 333 0022-.460XI7810608-.0333 802.00/0 9 1978 Academic Press Inc. (London) Limited
334
G. CANEVEr Tripolor sources
9,,
Silence
/
I2 Figure 1. Schematic representation of active absorption. In particular Jessel's theoretical solution of the problem [11] has established that, for perfect absorption, the boundary Z must hold an infinite set of sources, the characteristics of which are highly dependent on the noise to be cancelled; e.g., for noise propagating as spherical waves it can be shown that the absorbing sources must be tripolar, a result which follows directly from Huygens' principle. In practice, of course, a continuous distribution of sources cannot be achieved, hence, according to Jessel's theory, rendering perfect sound absorption unobtainable. This observation highlighted the weakness of devices proposed up to now and foreshadowed the difficulties of realizing an efficient active absorber. However, the impossibility of realizing a perfect absorber arises from the condition imposed on the acoustic field exterior to _r, viz. of completecanceilation in the zone to be protected. This condition is very stringent and one could as a first attempt require not a total suppression of the noise but merely its attenuation. It seemed possible to produce such an attenuation by using an array oftripolar sources, each consisting of a monopole and a dipole in close proximity, distributed on the theoretical absorbing surface Z. This finite set of absorbing sources would thus make up an "active acoustic barrier". By fixing the number ofsources and their positions, their radiation could be calculated by discretizing Jessers integral formulas. Of course, after this simplification which makes the question more realistic one can imagine that tridimensional active absorption remains a very difficult problem, since it deals ultimately with the reconstruction of an acoustic event, but inverted. That is, the difficulty is two-fold" first it is necessary to effect a reproduction channel with pe.rfect temporal response; and secondly the set of sources forming the array must be able to reproduce the exact spatial character of the incident wave in such a way that the primary and secondary waves superimpose precisely, neutralizing each other at any point where silence is desired. Realizing that a problem of such complexity could only be solved gradually, we chose first to work on the interesting special case of the absorption of plane waves in a wave guide. The experimental realization corresponding to this problem has been previously described [8, 10]. The tripolar anti-noise source was made with three horn drivers (Figure 2(a)) which at sufficiently low frequencies excited only plane wave propagation in the duct. The absorption of a wave coming from the primary source was performed progressively in the neighbourhood of the secondary sources, assumed to be appropriately adjusted, within a zone extending from a point A to a point B. Figure 2(b) gives a few curves ofsound attenuation as a function o f t h e distance along the duct. They are results of experiments made at 300 Hz in a rectilinear duct 8 cm on each side, with perfectly reflecting walls. Of course this was only a trial device and it presented several disadvantages already reported [8]. In the first place the inefficiency of the drivers made the sources unsuitable for generation o f low frequency sound below 300 Hz say. Further, the system was non-auton-
335
ACTIVE SOUND ABSORPTION
-B
80
\
~/-\ ~
\
{~_Inc'~dent
l
A
Horn drivers (0)
(i)
60
40
/-----
20
(ii) 60 & 4O
20
80
(iii) --
9
-
-
-
-
v
.
-
60
40
20 I 0
I 5O Distance
I I00 along
the
I
150
guide (cm)
(b)
Figure 2 (a) Radiation of the absorber in the guide. (b) Sound pressure curves in an experimental guide, where attenuation is achieved by horn drivers; the measurements are made at 300 Hz; (i) along the wall near the dipole; (ii) along the axis of the guide; (iii) along the wall near the monopole.
omous in that each driver was powered by its own amplifier and tuned one at a time by hand, so that individual adjustment was necessary for each different frequency of incident sound studies. In this configurationthen, the tripole was able to absorb only a pure tone since it could not automatically track the incident wave. Thus we sought to develop an apparatus which could at the same time be efficient at low frequencies and automatically self-controlled in order to obtain a broader band of sound absorption. 3. REALIZATION OF A BROAD BAND ACOUSTIC DIPOLE Our first objective, following these preliminary experiments was to construct an acoustic doublet having a dipolar radiation pattern whatever the frequency and the level of the sound signal to be emitted. This device would then be used as the dipole component of the tripolar source.
336
G. CANEVET
\
/
/
\
r~
>->'.-(~<
r-'
3
Figure 3. Pattern of a broad band dipole.
270~ 90"
270* 90*
O" I
IBO ~
270*
B
0
*
~
-
0~
270~
Figure 4. Radiation pattern of a broad band dipole in an anechoic room, for various frequencies: (a) 100 Hz; (b) 500 Hz; (c) 700 Hz; (d) narrow band noise (Af= 100 Hz, central frequency 300 Hz). Scale: l0 dB between each circle; outer circles at 80 dB.
337
ACTIVE SOUND ABSORPTION
To reach this objective several systems have been tested and that of Figure 3 has been selected. It comprises two identical loudspeakers mounted back to back in an enclosure. The interesting possibility of this set is the close coupling of the loudspeaker diaphragms through their back radiation, if they are driven 180 ~ out of phase with one another, this having the effect of improving the acoustical symmetry of the set and equilibrating the sound level emitted by each mouth. In addition, the loudspeaker dimensions are not limited in this design so very low frequency or high power absorbers can be constructed in the same way. The dipolar properties of this source have been verified by two kinds of experiments. In the first its radiation pattern was studied in an anechoic room. The enclosure itself was put on a turntable (Briiel & Kjaer 3922). The analysis microphone (Briiel & Kjaer I0 mm) was located one meter from the enclosure axis in the plane of the mouths. The sound pressure level and phase were then recorded, the phase on the axis (zero degree on the curves) being used as a reference. The results illustrated by Figure 4, demonstrated that the source radiation was fairly symmetrical over the frequency range it was intended for. ~
Frequency
Generolor
A
analyser
~
I
Oi~ote I, r-'-x ; Q
Monitorinq microphone
.
Anechoic lerminatlon
(mineral ~001)
(a) I
I
I
O
50
70 60 50 (i)
-- 70
_.e w
60
5O
60 50 iii)
-IOO
I -50
10(2
Distance along the guide(c~) (bl
Figure 5 (a) Experimental arrangement for dipole radiation analysis in an infinite waveguide. Co) Acoustic pressure along the axis of the waveguide for various freqeuneies: (i) 500 Hz; (ii) 700 Hz; (iii) 900 Hz; the dipole is centered at x = 0.
338
G. CANEVET
Secondly the dipolar source was mounted on a hard-walled wave guide, both ends of which were blocked with mineral wool to form anechoic terminations. Under these conditions the sound pressure along the axis of the wave guide was plotted. Once more the results, some of which are shown in Figure 5(b), confirmed the dipolar behaviour of our source. It must be pointed out that the bandwidth of such a source suffers a few natural limitations at low frequencies as well as at high ones. At low frequencies two factors arise. First, one must choose the dimensions and the efficiency of the loudspeakers to give adequate, frequency response down to the lowest frequency of the noise to be reduced. Secondly, the proximity of the dipole mouths, a d d e d to the fact that their radiations are out of phase, produce as a consequence an absorption of the acoustical energy of one by the other, which considerably reduces the radiated power, especially as the frequency decreases. This problem, already pointed out by Poole and Leventhall [5], can be quantified by writingdown the equation for the radiation from two simple sources out of phase and having the same amplitude: A p(/~t) -- - -
A e -J~tr-a~ -- - -
-r-d
e -J~t'+d),
r+d
p(M) being the resulting acoustic pressure at the point M produced by the two sources, separated by the distance 2d. The radiation of each ofthe component sources is assumed to be spherical and of amplitude A. The modulus of the pressure is then deduced as
Ip(M)I' = r - d cosk(r - d) - r---~-~cos k(r + d) -,4 s i n k ( r - d ) + sink(r +d) + r-d r+d
'
or
I p ( M ) ] = A JCr---7-S~ + (r +1 d) 2
r 2 _2 d2 cos2kd.
Figure 6 gives an illustrative example where A is chosen to be unity, and with a distance o f 14 cm between the mouths, which was the exact value for one of the dipoles used experimentally. This amplitude variation can for the most part be corrected electronically by using an equalizing circuit. I
! m
4 ta.
t~
3
"'.
2 I I 500 Frequency
I IOOO (Hz)
Figure 6. Frequency response of an acoustic doublet.
339
ACTIVE SOUND ABSORPTION
90*
90*
90*
270* (i)
( ii ) {o}
2?'0~ (iii}
8of' 70 8O
t
(ii)
e= 70 ~" 6O
w 50
8 70 - I00
0 I - 50
~
t .
I I 0 50 Distance along the axis (cm)
I00
(bl
Figure 7. Radiation of a dipole when increasing frequency. (a) Free field directivity pattern (pressure and phase) for various frequencies (2 < 2d): (i) 900 Hz; (ii) 1500 Hz; (iii) 2000 Hz; 2d= 28 cm. Scale: 10 dB between each circle; outer circles at 90 dB for (i) and (iii), 80 dB for (ii). (b) Effect of the duct on the radiation of a dipole: (i) 2000 Hz; (ii) 2150 Hz; (iii) 2665 Hz; 2d= 19 cm. At high frequencies there are also two parameters which limit the performance of such a source. On the one hand, the distance separating the mouths is not infinitely small, so our source ceases to be dipolar as 2 decreases below 2d, after which the radiation pattern becomes highly variable as the frequency is progressively increased further. In addition, since our device is intended for the absorption of plane waves, it will cease to be efficient as soon as the wavelength of the signal becomes smaller than that of the first oblique propagational duct mode; and thus high frequency performance is limited by the cross-sectional dimensions of the duct; Figure 7 illustrates these limitations. Notwithstanding these qualifications it is nevertheless conceivable that such a device could be capable of significant absorption in the frequency range for which it is designed. As an example, the application of active sound absorption of noise propagating in an air conditioning duct is given below.
340
G.
CANEVET
4. EXPERIMENTS OF SOUND ABSORPTION IN AN AIR CONDITIONING DUCT A square air conditioning duct, 43 cm on each side, was constructed of sheet metal I mm thick. It was fed from an air conditioner AirWell 552 AR by a centrifugal fan. The air conditioner and fan were located outside the main laboratory in a separate unit, which was mounted on vibration isolators (see Figure 8).
_rt Analysis ~ i I '..4 microphcre I '
' /
I I i i
Ii,--,-~j I ooa,y,~,
~
/-~
Driving microphone I ~
/
L--TT ~
shifte;s
Air
r~'VCq-lc~'ooe, on~
I
H
I;
, I
W
f
" I
Figure 8. Block diagram of the experimental set-up.
During the experiments the air velocity in the duct was maintained at 6 m/s. The anti-noise source was fed by a microphone located upstream of the absorber designed to monitor the sound wave to be reduced and thus to make the system autonomous, in contrast to the configuration mentioned in section 2 and that discussed by Mazanikov and Tyutekin [14]. This driving microphone has of course been chosen to be as directional as possible in order to avoid possible feedback; specifically the experiments were conducted with a Phillips N 8500 electret microphone equipped with a windscreen. The absorbing source consisted of one monopole and one dipole (see Figure 9), the monapole being a simple loudspeaker housed in an enclosure and connected to the duct by an appropriate converging horn. Three identical loudspeakers were used to make the absorbing
r
1
Figure 9. Disposition of the absorber (monopole + dipole) on the duct.
341
ACTIVE SOUND ABSORPTION
source. They were loudspeakers of 13 cm diameter and each was capable of handling 20 watts rms of electrical power. The apparatus used to drive the loudspeakers is shown in schematic form in Figure 8. It will be seen that, starting from the microphone Me, the signal to be reproduced is first filtered. This filtering improves the stability ofthe system, already aided by the marked directionalities of the microphone M, and of the absorbing source, and it also selects the operational frequency range of the absorber. The signal is then fed to the monopole and the dipole simultaneously through two separate amplifying channels. The phase shifters incorporated in the circuit delay the signal in order to compensate for the sound wave propagation time from the microphone M, to the source, the loudspeakers' inertia also being taken into account of course.
The performance of this tripolar absorber has been tested on various kinds of noises, and the results of the experiments are described in the following sections. ABSORPTIONOF A PURE TONE First, pure tone absorption was tested. Since the noise produced by the air conditioning unit and propagated down the duct had an almost fiat pressure spectrum, no pure tone
4.1.
9. g s o
)
o
z50
5oo (a)
7'50
Iooo o Frequency (Hz)
:'50
,soo
7'50
rooo
(b)
Figure 10. Active absorption of a pure tone superimposed on the air conditioner noise. (a) Pure tone of 250 Hz, at a level orS0 dB (the 0 dB revel is arbitrary): (i) absorber o n ; (ii) alJsorber off. (b) Pure tone at 500 Hz at the same level: (i) absorber o n ; (ii) absorber off.
emerged with sufficient distinctness to adequately test the performance of the absorber in this mode. We thus introduced, near the air conditioning unit an additional noise source, a high power loudspeaker mounted in a baffle and capable of producing a pure tone of sound pressure level 40 to 50 dB higher than that of the machinery noise. Under these conditions it was verified that the anti-noise device was able to attenuate any pure tone between approximately I00 Hz and 800 Hz by about 40 dB, the frequency limits depending, let us recall, on the loudspeakers used and on the dimensions of the duct. Figures 10(a) and 10(b) illustrate these results by two examples. They represent the sound pressure spectrum of the noise received by the analysis microphone Mo (Figure 8) downstream of the absorber when the system was in operation (Figures 10(a)(i) and 10(b)(i)) and when it was switched off (Figures 10(a)(ii) and 10(b)(ii)). In these examples the pure tones superimposed on the natural noise of the air conditioner have frequencies of 250 and 500 Hz respectively. Note that these results as well as the following were obtained from a real-time analysis (Ubiquitous Spectrum Analyzer UA--500 A) of the
342
G. CANEVET
acoustic signal, the air temperature being continuously about 25~ about 6 meters per second.
and the flow velocity
4.2. ABSORPTION OF A N A R R O W B A N D NOISE Under the same conditions as before narrow band noise was added to the air conditioner noise. This narrow band noise was a signal which was produced by a random noise generator (Sine-Random generator Briiel and Kjaer type 1024), filtered by a gate before amplification, and then supplied to the primary source. The gate is a spectrometer Briiel and Kjaer type 2112, acting as a ~ octave filter. Two examples ofthe results obtained appear in the Figures 11(a) and 50~(i)
~
J
250
500
t
I
i}
,
i
250
95 0 0
,
i
750
I000
25
O
750
10OO
Frequency
{Q)
0
"
(Hz)
[b)
Figure 11. Active absorption of a narrow band noise superimposed on the air conditioner noise. (a) Narrow ban d centered at 250 Hz: (i) absorber on; (ii) absorber off. (b) Narrow band centered at 500 Hz: (i) absorber on; (ii) absorber off.
1l(b), showing the absorption of a band of noise, the first one centered at 250 Hz, the other at 500 Hz. As a general rule, for this kind of narrow band noise situated in the low-frequency range, it was found that a tripolar sound absorber could produce about 15 dB of attenuation. Thus the performance of a tripolar source formed by the juxtaposition of one monopole and one dipole is reasonable. Nevertheless it deteriorates significantly as soon as the noise bandwidth is appreciably broadened. This results from several causes, but especially from the different behaviour of the monopole and of the dipole as the frequency of the signal is varied. More precisely, the response curves of the monopole and of the dipole being necessarily different, their relative phase and level adjustment, appropriate for one frequency, ceases to be appropriate for the next one. As a consequence the set ceases to be a tripole and the active absorption conditions are no longer satisfied. For these reasons we were led to conceive another kind of source, where monopole and dipole would be integrated in the same enclosure. The model we have built is described in the following section. 4.3. BROADBAND NOISEABSORPTION;INTEGRATEDTRIPOLARSOURCE Independence o f the monopole from the dipole being a cause of imperfection, we tried to construct a compact tripolar source, driven from a single amplifying channel. In our model (Figure 12) the three loudspeakers are mounted in the same box, two forming the dipole as before, and the third connected in parallel with one of the others forming the monopole. This set radiates through the mouths D~', M and D-, the radiation of D + and 3 f being in
343
ACTIVE SOUND ABSORPTION
( Figure 12. Integrated tripolar source.
50
_~ 4o ~
30
-o
g
20
~
~0
o ~:
o
30
40
50 70
1(30
150
200
300
400 500
700
I000
FrequenCy (Hz)
Figure 13. Frequency response of the integrated tripolar source: curve a sound pressure level at one meter from D+; curve b sound pressure level at one meter from D-.
50~
'
F ~ ~
'
o
C
25
0
125
250
375
500
Frequency (Hz)
Figure 14. Low frequency spectrum of the air conditioner noise: (a) absorber off; (b) absorber on.
344
G. CANEVET
phase but out of phase with that of D-. One can imagine that the resulting radiation of the set is a cardioidal one, or at least has a marked directivity. T o assess this directivity, the sound pressure level of the source was measured as a function of frequency along the axis ofthe holes, in the plane ofthe mouths, first at one meter from D § (Figure 13, curve a), then at one meter from D - (Figure 13, curve b). This study showed the tripole radiation to be relatively directional between 70 and 300 Hz roughly. Indeed when installed on the experimental rig it was found to be able to attenuate the fan noise about 10 to 15 dB in this frequency range (note the shaded area in Figure 14). Of course these results must be improved to make the integrated tripolar source usable in practical applications. In particular, more accurate electronic control of the response o f the loudspeakers--that is, more precise servo-control--should contribute to improved performance. 5. CONCLUSION Active sound absorption seems to be, nowadays, a well posed problem, and theoretically solved. It is solved too, for the most part, experimentally, for modern technology no longer raises important obstacles to practical realizations. In fact, the actual problem lies in conceiving the sources themselves: that is, in producing the required acoustical characteristics and in elaborating their control system. Active absorption, indeed, is necessarily associated with very stringent equipment requirements, because not only must the sources be very high fidelity emitters in terms of their temporal response, but also their radiation pattern must be very well defined and suited to the particular application. Before active absorption may be applied to low frequency noise, suitable sources must be found which satisfy these requirements, the latter especially posing difficulty. It seems that up to now highly directional low frequency sources have not been developed. This is one of the most important problems remaining in active sound absorption. ACKNOWLEDGMENT The author is grateful to J. Stuart Bolton for his assistance in preparing the English version of this paper. REFERENCES I. P. LUEG 1936 U.S. Patent No. 2 043 416. Process of silencing sound oscillations. 2. G. MANGtANTE1974 Th~se de Doctorat d'Etat, Facldtd des Sciences de Marseille. Application du principe de Huygens a rabsorption acoustique active. 3. M.A. SWINBANKS1973 Journal of Sound and Vibration 27, 411--436. The active control of sound propagation in long ducts. 4. H. G. LEVENTHALL1976 Noise Control Conference, Varsovie, 33-42. Developments in active attenuators. 5. J. H. B. POOLEand H. G. LEVENTHALL1976 Journal of Sound and Vibration 49, 257-266. An experimental study of Swinbanks' method of active attenuation of sound in ducts. 6. M. JESSEL1972 Revue d'Acoustique 5, 37-42. La question des absorbeurs acoustiques actifs. 7. G. CAN~VETand M. JESSEL1971 7th bzternational Congress on Acoustics, Budapest, Paper 20 E 5. Les absorbeurs acoustiques actifs. 8. G. CAN~VETand G. MANGIANTE1974 Acustica 30, 40-48. Absorption acoustique active et antibruit fi une dimension. 9. G. MANOtAN'rE1976 Acustica 36, 287-293. Application du principe de Huygens aux absorbeurs acoustiques actifs. I. Th~orie des absorbeurs actifs. 10. M . J . M . JESSELand G. A. MANGIANrE1972 Journal of Sound and Vibration 23, 383-390. Active sound absorbers in an air duct.
ACTIVESOUNDABSORPTION
345
11. G. MANGIANTEand G. CANFVET1976 Revue du Cethedec 48, 109-137. Principe de Huygens et absorption aeoustique active. 12. G. MANGtAr,,q'E1977 Acustica 37, 175-182. Application du principe de Huygens aux absorbeurs acoustiques actifs. II. Approximation du principe de Huygens. 13. G. MANGIANTE1977 Journal of the Acoustical Society o'fAmerica 61, 1516-1523, Active sound absorption. 14. A. A. MAZ-~N~KOVand V. V. TYU'r~KIN1976 Akustische Zeitschrift 22, 729-734. Autonomous active systems for the suppression of sound fields in a single-mode waveguides.
ACTIVE SOUND ABSORPTION IN AN AIR CONDITIONING DUCT G. CANEVET Laboratoire de Mdcanique et d'Acoustique, Centre National de la Recherche Scientifique, " 31 eheminJoseph Aiguier, 13274 Marseille Cedex 2, France (Receiced 24 Nocember 1977) Jessel's theory of active sound absorption has allowed the design and construction of practical systems. In this paper, two recent tripolar absorbers are described and a few experimental results are presented. Absorption experiments were performed successively on pure tones, narrow band noise and broadband noise, propagating in an air conditioning duct. For these three categories of noises, the attenuations achieved were respectively45 dB, 15 dB and 10 dB. I. INTRODUCTION Noise control by means ofactive absorption is an old idea but at the same time it still presents many problems in practice. Indeed, the first realizations of active absorbers go back to 1936 [1 ] and nevertheless 40 years later one still seeks a solution well suited to industrial needs. In part, one may attribute this slow development, the most significant stages of which have been summarized by Mangiante [2], to difficulties of a technological and more precisely o f an electronic nature. But in large part the slow implementation o f active sound absorption systems has been due to the poor formulation of the basic problem; this is reflected in the fact that recent practical progress has followed new developments of a theoretical nature, principally due to Swinbanks [3], whose work has been supported by the experiments of Leventhall and his group [4, 5], and to Jessel [6, 7] whose theory has led to important recent developments [2, 8, 9-13]. In this paper the latest results of experimental investigations of the absorbers deduced from Jessel's theory are presented, and thus it is a continuation of an article by Mangiante and Jessel previously published in this journal [10]. After a short qualitative review of Jessel's theory and its implications, the characteristics and performance of recent experimental models are described. After that, as a practical example, sound absorption in an air conditioning duct is studied. 2. THEORY AND EXPERIMENTAL MODEL OF AN ACTIVE ABSORBER Active sound absorption was formulated by Jessel as a reciprocal of Huygens' principle. "Given a source S (Figure 1) radiating in a space O is it possible to insert, on the trajectory of the waves, a 'barrier' of secondary sources 2: radiating out of V a field in opposition to that of S, and into V a zero field so that the resulting total field is equal to the primary one inside V and equal to zero outside ?" It is very important to point out that this approach to the problem is different from that of Swinbanks. Indeed, Jessel makes no initial assumptions regarding the nature of the secondary sources while Swinbanks, from the beginning, considered only the problem of sound absorption in a wave guide by two rings of monopolar sources. 333 0022-.460XI7810608-.0333 802.00/0 9 1978 Academic Press Inc. (London) Limited
334
G. CANEVEr Tripolor sources
9,,
Silence
/
I2 Figure 1. Schematic representation of active absorption. In particular Jessel's theoretical solution of the problem [11] has established that, for perfect absorption, the boundary Z must hold an infinite set of sources, the characteristics of which are highly dependent on the noise to be cancelled; e.g., for noise propagating as spherical waves it can be shown that the absorbing sources must be tripolar, a result which follows directly from Huygens' principle. In practice, of course, a continuous distribution of sources cannot be achieved, hence, according to Jessel's theory, rendering perfect sound absorption unobtainable. This observation highlighted the weakness of devices proposed up to now and foreshadowed the difficulties of realizing an efficient active absorber. However, the impossibility of realizing a perfect absorber arises from the condition imposed on the acoustic field exterior to _r, viz. of completecanceilation in the zone to be protected. This condition is very stringent and one could as a first attempt require not a total suppression of the noise but merely its attenuation. It seemed possible to produce such an attenuation by using an array oftripolar sources, each consisting of a monopole and a dipole in close proximity, distributed on the theoretical absorbing surface Z. This finite set of absorbing sources would thus make up an "active acoustic barrier". By fixing the number ofsources and their positions, their radiation could be calculated by discretizing Jessers integral formulas. Of course, after this simplification which makes the question more realistic one can imagine that tridimensional active absorption remains a very difficult problem, since it deals ultimately with the reconstruction of an acoustic event, but inverted. That is, the difficulty is two-fold" first it is necessary to effect a reproduction channel with pe.rfect temporal response; and secondly the set of sources forming the array must be able to reproduce the exact spatial character of the incident wave in such a way that the primary and secondary waves superimpose precisely, neutralizing each other at any point where silence is desired. Realizing that a problem of such complexity could only be solved gradually, we chose first to work on the interesting special case of the absorption of plane waves in a wave guide. The experimental realization corresponding to this problem has been previously described [8, 10]. The tripolar anti-noise source was made with three horn drivers (Figure 2(a)) which at sufficiently low frequencies excited only plane wave propagation in the duct. The absorption of a wave coming from the primary source was performed progressively in the neighbourhood of the secondary sources, assumed to be appropriately adjusted, within a zone extending from a point A to a point B. Figure 2(b) gives a few curves ofsound attenuation as a function o f t h e distance along the duct. They are results of experiments made at 300 Hz in a rectilinear duct 8 cm on each side, with perfectly reflecting walls. Of course this was only a trial device and it presented several disadvantages already reported [8]. In the first place the inefficiency of the drivers made the sources unsuitable for generation o f low frequency sound below 300 Hz say. Further, the system was non-auton-
335
ACTIVE SOUND ABSORPTION
-B
80
\
~/-\ ~
\
{~_Inc'~dent
l
A
Horn drivers (0)
(i)
60
40
/-----
20
(ii) 60 & 4O
20
80
(iii) --
9
-
-
-
-
v
.
-
60
40
20 I 0
I 5O Distance
I I00 along
the
I
150
guide (cm)
(b)
Figure 2 (a) Radiation of the absorber in the guide. (b) Sound pressure curves in an experimental guide, where attenuation is achieved by horn drivers; the measurements are made at 300 Hz; (i) along the wall near the dipole; (ii) along the axis of the guide; (iii) along the wall near the monopole.
omous in that each driver was powered by its own amplifier and tuned one at a time by hand, so that individual adjustment was necessary for each different frequency of incident sound studies. In this configurationthen, the tripole was able to absorb only a pure tone since it could not automatically track the incident wave. Thus we sought to develop an apparatus which could at the same time be efficient at low frequencies and automatically self-controlled in order to obtain a broader band of sound absorption. 3. REALIZATION OF A BROAD BAND ACOUSTIC DIPOLE Our first objective, following these preliminary experiments was to construct an acoustic doublet having a dipolar radiation pattern whatever the frequency and the level of the sound signal to be emitted. This device would then be used as the dipole component of the tripolar source.
336
G. CANEVET
\
/
/
\
r~
>->'.-(~<
r-'
3
Figure 3. Pattern of a broad band dipole.
270~ 90"
270* 90*
O" I
IBO ~
270*
B
0
*
~
-
0~
270~
Figure 4. Radiation pattern of a broad band dipole in an anechoic room, for various frequencies: (a) 100 Hz; (b) 500 Hz; (c) 700 Hz; (d) narrow band noise (Af= 100 Hz, central frequency 300 Hz). Scale: l0 dB between each circle; outer circles at 80 dB.
337
ACTIVE SOUND ABSORPTION
To reach this objective several systems have been tested and that of Figure 3 has been selected. It comprises two identical loudspeakers mounted back to back in an enclosure. The interesting possibility of this set is the close coupling of the loudspeaker diaphragms through their back radiation, if they are driven 180 ~ out of phase with one another, this having the effect of improving the acoustical symmetry of the set and equilibrating the sound level emitted by each mouth. In addition, the loudspeaker dimensions are not limited in this design so very low frequency or high power absorbers can be constructed in the same way. The dipolar properties of this source have been verified by two kinds of experiments. In the first its radiation pattern was studied in an anechoic room. The enclosure itself was put on a turntable (Briiel & Kjaer 3922). The analysis microphone (Briiel & Kjaer I0 mm) was located one meter from the enclosure axis in the plane of the mouths. The sound pressure level and phase were then recorded, the phase on the axis (zero degree on the curves) being used as a reference. The results illustrated by Figure 4, demonstrated that the source radiation was fairly symmetrical over the frequency range it was intended for. ~
Frequency
Generolor
A
analyser
~
I
Oi~ote I, r-'-x ; Q
Monitorinq microphone
.
Anechoic lerminatlon
(mineral ~001)
(a) I
I
I
O
50
70 60 50 (i)
-- 70
_.e w
60
5O
60 50 iii)
-IOO
I -50
10(2
Distance along the guide(c~) (bl
Figure 5 (a) Experimental arrangement for dipole radiation analysis in an infinite waveguide. Co) Acoustic pressure along the axis of the waveguide for various freqeuneies: (i) 500 Hz; (ii) 700 Hz; (iii) 900 Hz; the dipole is centered at x = 0.
338
G. CANEVET
Secondly the dipolar source was mounted on a hard-walled wave guide, both ends of which were blocked with mineral wool to form anechoic terminations. Under these conditions the sound pressure along the axis of the wave guide was plotted. Once more the results, some of which are shown in Figure 5(b), confirmed the dipolar behaviour of our source. It must be pointed out that the bandwidth of such a source suffers a few natural limitations at low frequencies as well as at high ones. At low frequencies two factors arise. First, one must choose the dimensions and the efficiency of the loudspeakers to give adequate, frequency response down to the lowest frequency of the noise to be reduced. Secondly, the proximity of the dipole mouths, a d d e d to the fact that their radiations are out of phase, produce as a consequence an absorption of the acoustical energy of one by the other, which considerably reduces the radiated power, especially as the frequency decreases. This problem, already pointed out by Poole and Leventhall [5], can be quantified by writingdown the equation for the radiation from two simple sources out of phase and having the same amplitude: A p(/~t) -- - -
A e -J~tr-a~ -- - -
-r-d
e -J~t'+d),
r+d
p(M) being the resulting acoustic pressure at the point M produced by the two sources, separated by the distance 2d. The radiation of each ofthe component sources is assumed to be spherical and of amplitude A. The modulus of the pressure is then deduced as
Ip(M)I' = r - d cosk(r - d) - r---~-~cos k(r + d) -,4 s i n k ( r - d ) + sink(r +d) + r-d r+d
'
or
I p ( M ) ] = A JCr---7-S~ + (r +1 d) 2
r 2 _2 d2 cos2kd.
Figure 6 gives an illustrative example where A is chosen to be unity, and with a distance o f 14 cm between the mouths, which was the exact value for one of the dipoles used experimentally. This amplitude variation can for the most part be corrected electronically by using an equalizing circuit. I
! m
4 ta.
t~
3
"'.
2 I I 500 Frequency
I IOOO (Hz)
Figure 6. Frequency response of an acoustic doublet.
339
ACTIVE SOUND ABSORPTION
90*
90*
90*
270* (i)
( ii ) {o}
2?'0~ (iii}
8of' 70 8O
t
(ii)
e= 70 ~" 6O
w 50
8 70 - I00
0 I - 50
~
t .
I I 0 50 Distance along the axis (cm)
I00
(bl
Figure 7. Radiation of a dipole when increasing frequency. (a) Free field directivity pattern (pressure and phase) for various frequencies (2 < 2d): (i) 900 Hz; (ii) 1500 Hz; (iii) 2000 Hz; 2d= 28 cm. Scale: 10 dB between each circle; outer circles at 90 dB for (i) and (iii), 80 dB for (ii). (b) Effect of the duct on the radiation of a dipole: (i) 2000 Hz; (ii) 2150 Hz; (iii) 2665 Hz; 2d= 19 cm. At high frequencies there are also two parameters which limit the performance of such a source. On the one hand, the distance separating the mouths is not infinitely small, so our source ceases to be dipolar as 2 decreases below 2d, after which the radiation pattern becomes highly variable as the frequency is progressively increased further. In addition, since our device is intended for the absorption of plane waves, it will cease to be efficient as soon as the wavelength of the signal becomes smaller than that of the first oblique propagational duct mode; and thus high frequency performance is limited by the cross-sectional dimensions of the duct; Figure 7 illustrates these limitations. Notwithstanding these qualifications it is nevertheless conceivable that such a device could be capable of significant absorption in the frequency range for which it is designed. As an example, the application of active sound absorption of noise propagating in an air conditioning duct is given below.
340
G.
CANEVET
4. EXPERIMENTS OF SOUND ABSORPTION IN AN AIR CONDITIONING DUCT A square air conditioning duct, 43 cm on each side, was constructed of sheet metal I mm thick. It was fed from an air conditioner AirWell 552 AR by a centrifugal fan. The air conditioner and fan were located outside the main laboratory in a separate unit, which was mounted on vibration isolators (see Figure 8).
_rt Analysis ~ i I '..4 microphcre I '
' /
I I i i
Ii,--,-~j I ooa,y,~,
~
/-~
Driving microphone I ~
/
L--TT ~
shifte;s
Air
r~'VCq-lc~'ooe, on~
I
H
I;
, I
W
f
" I
Figure 8. Block diagram of the experimental set-up.
During the experiments the air velocity in the duct was maintained at 6 m/s. The anti-noise source was fed by a microphone located upstream of the absorber designed to monitor the sound wave to be reduced and thus to make the system autonomous, in contrast to the configuration mentioned in section 2 and that discussed by Mazanikov and Tyutekin [14]. This driving microphone has of course been chosen to be as directional as possible in order to avoid possible feedback; specifically the experiments were conducted with a Phillips N 8500 electret microphone equipped with a windscreen. The absorbing source consisted of one monopole and one dipole (see Figure 9), the monapole being a simple loudspeaker housed in an enclosure and connected to the duct by an appropriate converging horn. Three identical loudspeakers were used to make the absorbing
r
1
Figure 9. Disposition of the absorber (monopole + dipole) on the duct.
341
ACTIVE SOUND ABSORPTION
source. They were loudspeakers of 13 cm diameter and each was capable of handling 20 watts rms of electrical power. The apparatus used to drive the loudspeakers is shown in schematic form in Figure 8. It will be seen that, starting from the microphone Me, the signal to be reproduced is first filtered. This filtering improves the stability ofthe system, already aided by the marked directionalities of the microphone M, and of the absorbing source, and it also selects the operational frequency range of the absorber. The signal is then fed to the monopole and the dipole simultaneously through two separate amplifying channels. The phase shifters incorporated in the circuit delay the signal in order to compensate for the sound wave propagation time from the microphone M, to the source, the loudspeakers' inertia also being taken into account of course.
The performance of this tripolar absorber has been tested on various kinds of noises, and the results of the experiments are described in the following sections. ABSORPTIONOF A PURE TONE First, pure tone absorption was tested. Since the noise produced by the air conditioning unit and propagated down the duct had an almost fiat pressure spectrum, no pure tone
4.1.
9. g s o
)
o
z50
5oo (a)
7'50
Iooo o Frequency (Hz)
:'50
,soo
7'50
rooo
(b)
Figure 10. Active absorption of a pure tone superimposed on the air conditioner noise. (a) Pure tone of 250 Hz, at a level orS0 dB (the 0 dB revel is arbitrary): (i) absorber o n ; (ii) alJsorber off. (b) Pure tone at 500 Hz at the same level: (i) absorber o n ; (ii) absorber off.
emerged with sufficient distinctness to adequately test the performance of the absorber in this mode. We thus introduced, near the air conditioning unit an additional noise source, a high power loudspeaker mounted in a baffle and capable of producing a pure tone of sound pressure level 40 to 50 dB higher than that of the machinery noise. Under these conditions it was verified that the anti-noise device was able to attenuate any pure tone between approximately I00 Hz and 800 Hz by about 40 dB, the frequency limits depending, let us recall, on the loudspeakers used and on the dimensions of the duct. Figures 10(a) and 10(b) illustrate these results by two examples. They represent the sound pressure spectrum of the noise received by the analysis microphone Mo (Figure 8) downstream of the absorber when the system was in operation (Figures 10(a)(i) and 10(b)(i)) and when it was switched off (Figures 10(a)(ii) and 10(b)(ii)). In these examples the pure tones superimposed on the natural noise of the air conditioner have frequencies of 250 and 500 Hz respectively. Note that these results as well as the following were obtained from a real-time analysis (Ubiquitous Spectrum Analyzer UA--500 A) of the
342
G. CANEVET
acoustic signal, the air temperature being continuously about 25~ about 6 meters per second.
and the flow velocity
4.2. ABSORPTION OF A N A R R O W B A N D NOISE Under the same conditions as before narrow band noise was added to the air conditioner noise. This narrow band noise was a signal which was produced by a random noise generator (Sine-Random generator Briiel and Kjaer type 1024), filtered by a gate before amplification, and then supplied to the primary source. The gate is a spectrometer Briiel and Kjaer type 2112, acting as a ~ octave filter. Two examples ofthe results obtained appear in the Figures 11(a) and 50~(i)
~
J
250
500
t
I
i}
,
i
250
95 0 0
,
i
750
I000
25
O
750
10OO
Frequency
{Q)
0
"
(Hz)
[b)
Figure 11. Active absorption of a narrow band noise superimposed on the air conditioner noise. (a) Narrow ban d centered at 250 Hz: (i) absorber on; (ii) absorber off. (b) Narrow band centered at 500 Hz: (i) absorber on; (ii) absorber off.
1l(b), showing the absorption of a band of noise, the first one centered at 250 Hz, the other at 500 Hz. As a general rule, for this kind of narrow band noise situated in the low-frequency range, it was found that a tripolar sound absorber could produce about 15 dB of attenuation. Thus the performance of a tripolar source formed by the juxtaposition of one monopole and one dipole is reasonable. Nevertheless it deteriorates significantly as soon as the noise bandwidth is appreciably broadened. This results from several causes, but especially from the different behaviour of the monopole and of the dipole as the frequency of the signal is varied. More precisely, the response curves of the monopole and of the dipole being necessarily different, their relative phase and level adjustment, appropriate for one frequency, ceases to be appropriate for the next one. As a consequence the set ceases to be a tripole and the active absorption conditions are no longer satisfied. For these reasons we were led to conceive another kind of source, where monopole and dipole would be integrated in the same enclosure. The model we have built is described in the following section. 4.3. BROADBAND NOISEABSORPTION;INTEGRATEDTRIPOLARSOURCE Independence o f the monopole from the dipole being a cause of imperfection, we tried to construct a compact tripolar source, driven from a single amplifying channel. In our model (Figure 12) the three loudspeakers are mounted in the same box, two forming the dipole as before, and the third connected in parallel with one of the others forming the monopole. This set radiates through the mouths D~', M and D-, the radiation of D + and 3 f being in
343
ACTIVE SOUND ABSORPTION
( Figure 12. Integrated tripolar source.
50
_~ 4o ~
30
-o
g
20
~
~0
o ~:
o
30
40
50 70
1(30
150
200
300
400 500
700
I000
FrequenCy (Hz)
Figure 13. Frequency response of the integrated tripolar source: curve a sound pressure level at one meter from D+; curve b sound pressure level at one meter from D-.
50~
'
F ~ ~
'
o
C
25
0
125
250
375
500
Frequency (Hz)
Figure 14. Low frequency spectrum of the air conditioner noise: (a) absorber off; (b) absorber on.
344
G. CANEVET
phase but out of phase with that of D-. One can imagine that the resulting radiation of the set is a cardioidal one, or at least has a marked directivity. T o assess this directivity, the sound pressure level of the source was measured as a function of frequency along the axis ofthe holes, in the plane ofthe mouths, first at one meter from D § (Figure 13, curve a), then at one meter from D - (Figure 13, curve b). This study showed the tripole radiation to be relatively directional between 70 and 300 Hz roughly. Indeed when installed on the experimental rig it was found to be able to attenuate the fan noise about 10 to 15 dB in this frequency range (note the shaded area in Figure 14). Of course these results must be improved to make the integrated tripolar source usable in practical applications. In particular, more accurate electronic control of the response o f the loudspeakers--that is, more precise servo-control--should contribute to improved performance. 5. CONCLUSION Active sound absorption seems to be, nowadays, a well posed problem, and theoretically solved. It is solved too, for the most part, experimentally, for modern technology no longer raises important obstacles to practical realizations. In fact, the actual problem lies in conceiving the sources themselves: that is, in producing the required acoustical characteristics and in elaborating their control system. Active absorption, indeed, is necessarily associated with very stringent equipment requirements, because not only must the sources be very high fidelity emitters in terms of their temporal response, but also their radiation pattern must be very well defined and suited to the particular application. Before active absorption may be applied to low frequency noise, suitable sources must be found which satisfy these requirements, the latter especially posing difficulty. It seems that up to now highly directional low frequency sources have not been developed. This is one of the most important problems remaining in active sound absorption. ACKNOWLEDGMENT The author is grateful to J. Stuart Bolton for his assistance in preparing the English version of this paper. REFERENCES I. P. LUEG 1936 U.S. Patent No. 2 043 416. Process of silencing sound oscillations. 2. G. MANGtANTE1974 Th~se de Doctorat d'Etat, Facldtd des Sciences de Marseille. Application du principe de Huygens a rabsorption acoustique active. 3. M.A. SWINBANKS1973 Journal of Sound and Vibration 27, 411--436. The active control of sound propagation in long ducts. 4. H. G. LEVENTHALL1976 Noise Control Conference, Varsovie, 33-42. Developments in active attenuators. 5. J. H. B. POOLEand H. G. LEVENTHALL1976 Journal of Sound and Vibration 49, 257-266. An experimental study of Swinbanks' method of active attenuation of sound in ducts. 6. M. JESSEL1972 Revue d'Acoustique 5, 37-42. La question des absorbeurs acoustiques actifs. 7. G. CAN~VETand M. JESSEL1971 7th bzternational Congress on Acoustics, Budapest, Paper 20 E 5. Les absorbeurs acoustiques actifs. 8. G. CAN~VETand G. MANGIANTE1974 Acustica 30, 40-48. Absorption acoustique active et antibruit fi une dimension. 9. G. MANOtAN'rE1976 Acustica 36, 287-293. Application du principe de Huygens aux absorbeurs acoustiques actifs. I. Th~orie des absorbeurs actifs. 10. M . J . M . JESSELand G. A. MANGIANrE1972 Journal of Sound and Vibration 23, 383-390. Active sound absorbers in an air duct.
ACTIVESOUNDABSORPTION
345
11. G. MANGIANTEand G. CANFVET1976 Revue du Cethedec 48, 109-137. Principe de Huygens et absorption aeoustique active. 12. G. MANGtAr,,q'E1977 Acustica 37, 175-182. Application du principe de Huygens aux absorbeurs acoustiques actifs. II. Approximation du principe de Huygens. 13. G. MANGIANTE1977 Journal of the Acoustical Society o'fAmerica 61, 1516-1523, Active sound absorption. 14. A. A. MAZ-~N~KOVand V. V. TYU'r~KIN1976 Akustische Zeitschrift 22, 729-734. Autonomous active systems for the suppression of sound fields in a single-mode waveguides.