A note on measurement of sound intensity with windscreened probes

Applied Acoustics 42 (1994) 41-53

A Note on Measurement of Sound Intensity with Windscreened Probes Finn Jacobsen The Acoustics Laboratory, Technical University of Denmark, Building 352, DK-2800 Lyngby, Denmark (Received 30 March 1993; accepted 20 May 1993)

ABSTRACT The influence of windscreens of porous foam on the performance of sound intensity probes is examined. It is shown that windscreens can lead to significant underestimation of the sound power of a source at low frequencies if the measurement is carried out in the reactive near field of the source, but have no appreciable undesirable effect on the result if the measurement surface is .further away from the source. In addition, some empirical observations on measurement of sound intensity in the presence of airflow are presented.

NOTATION c I Ix J k p Pa u Z

Speed of sound Sound intensity Component of intensity Reactive intensity Wavenumber Sound pressure Sound power Particle velocity Characteristic impedance

Fp xp

Propagation constant Compressibility

41 AppliedAcousticsOOO3-682X/94/$07.00 © 1994 Elsevier Science Limited, England. Printed in Great Britain

kTnn .lacohsen

42 p q5 ~o

Density of air Flow resistance Angular frequency Porosity Estimated value

1 INTRODUCTION A windscreen is a useful device; it reduces noise in the microphone signals from an intensity probe exposed to unsteady airflow, apparently without otherwise affecting the acoustic measurement, Accordingly, it expands the range of measurement. ~ ~ In addition it protects the probe agams~ mechanical and thermal damage; therefore windscreens are sometimes used even in the absence of flow. As shown by Munro and lngard the "two-microphone' technique ~,1 estimating sound intensity cannot be extended to situations with airflow strictly speaking the measurement principle is simply not valid in the presence of mean flow. 4 On the other hand, it can be shown that, with a moderate flow velocity, say, less than t5 m s--1, the resulting error is quite insignificant provided that the sound field is predominantly active, s,6 Under such conditions the noise generated by turbulence is likely to be a morc serious source of e r r o r ) and this noise will be reduced by a windscreen. However, whereas the beneficial effect of windscreens on measurement t,( sound pressure in the presence of airflow seems to be well established,: oni~ limited attention has been paid to the effect of windscreens on sound intensity measurement, and windscreens might give rise to measurement errors under some conditions. The purpose of this note is to examine the matter.

2 THEORY According to Morse and Ingard, 8 the equation of motion for air m a homogeneous, isotropic porous material is, in the absence of airflow. (j.)p,, + ~iu + Vp = 0

!ti

where pp is the effective density of the material and q~ is the flow resistivity. The characteristic impedance is Z

=

[(pp/Kp~'))( 1 -- j4~/O~p~,)]l 2

i2)

Measurement ol sound intensiO' with windwreened probes

43

where xp is the effective compressibility of the material and f~ is the porosity; and the propagation constant is Fp = jco[K~f~pp(1 - jqS/copp)]1/2

(3)

The windscreens under consideration are spheres or spheroids made of highly porous open-cell plastic foam. In this case the density and the compressibility approach the density and compressibility in the open, that is, pp ~ p

(4a)

Kp ~-- 1~pc 2

(4b)

the porosity is close to unity, and the frictional loss is moderate, q~<
(5)

It now follows that the characteristic impedance and the propagation constant of the material are Z ~- pc(1 - j c/~/2cop)

(6a)

F -~ jk(1 - jq~/2cop)

(6b)

where the small imaginary part of the factor in parenthesis is due to the losses of the foam. (The windscreen would evidently disturb the sound field if the characteristic impedance of the foam differed substantially from the characteristic impedance of air, and it would disturb the estimation if the wave velocity differed significantly from that of air in the open.) The two-microphone method of determining sound intensity relies on approximating the gradient of the pressure in the equation of motion in the open, Ux-

(7)

jcop ~x

with a finite difference, Ap/Ax. However, the frictional losses of the surrounding foam of a windscreen introduce a small phase error in the estimate of the particle velocity since, from eqn (1),

1 c~p ux =

1

jcop t3x 1 -jd?/cop

(8)

in the foam, from which it follows that the estimate may be written tJx _ u~(1 -jc])/cop) ~_ u~ exp (j0)

(9)

where 0 = -cUcop

(10)

44

kTnn Jacobsen

is the phase error. By contrast, the windscreen has no appreciable influence on the estimate of the pressure. It can now be seen that fx

= ~1 rf -n~g¢~ x ~ "" ~ Re ~~ptqg¢ exp(--j0)', Re (1, + j J x ) e x p ( - j 0 ) { - > 1~ - O ,I~

~Ii~

where J~ is the reactive intensity. It must be concluded that, in so far as the~c simple considerations are valid, the only (acoustic) effect of a windscreen on a 'p-p intensity probe' is to introduce a small negative bias error that i~ proportional to the reactive intensity. An expression that corresponds to eqn ( 11 ) for sound power estimation is easily obtained:

i

/',,, = ' [ ' d S . . . . . . . J. .• d.S .= . f' .~,

J- dS

~ 12~

where S is the surface that encloses the source. 3 DISCUSSION The model that led to eqns (9) and (11)is certainly a simplification: flow has been ignored and no account has been taken of the size and shape of the windscreen. One cannot derive a similar expression that takes flow into account since the particle velocity cannot be expressed in terms of the pressure and the gradient of the pressure in this c a s e ) There is no simple way of taking account of the size and shape of the windscreen either. However, it seems not unreasonable to expect the principal result of the considerations presented in Section 2, that viscous losses in the fl)am introduce a small phase error between the pressure and the particle velocity, to be of general validity. The dynamic flow resistance of porous materials is largely independent of the frequency; 9 therefore, the error will be a problem mainly at Im~ frequencies, the more so since large values of the reactive intensity occur mainly at low frequencies. 1° It is apparent that the local 'error indicator' is the quantity 6jl = l O l o g ( l J , / I x f ) 113! (the relativity); the influence of the windscreen is negligible unless this measure assumes an appreciable value, Obviously, the corresponding global error indicator is the quantity \JS

Measurement o['sound intensity with windwreened probes

45

which takes large values only when the enclosing surface is very near the source under test, 11 and since S J . d S is a positive quantity, 11 it can be concluded that the sound power will be underestimated when this is the case. (These considerations bear a strong resemblance to considerations presented in Ref. 11, where 'p-u phase mismatch' introduced by the vents of the two microphones of a p-p intensity probe was examined. Insufficient attenuation of the microphone vents gives rise to overestimation, though.) Finally it should be noted that the microphone separation distance is of no importance.

4 E X P E R I M E N T A L RESULTS To test the considerations presented in Sections 2 and 3 some experiments have been carried out, both without and with mean flow. An intensity probe, Briiel & Kjaer (B & K) 3545 with microphones of type B & K 4181 and spacers of 12 mm and 50 mm was used in combination with a 'real-time' analyser, B & K 2133. All measurements were performed in one-third octave bands. Possible p-p phase mismatch was eliminated by the 'switching technique'. 12 Two different windscreens of porous plastic foam were examined; a spherical one, B & K UAO782, and a larger ellipsoidal one, B & K UAO781. In the first experiment, which took place in an anechoic room, the intensity probe with the 50-mm spacer between the microphones was placed about 12 cm from the cone of a small enclosed loudspeaker driven with pink noise, and the sound pressure, the particle velocity, and the active and reactive intensity were determined without windscreen and with the ellipsoidal screen. The results are shown in Fig. 1, which certainly confirms that windscreens have no appreciable influence on estimation of the pressure, the particle velocity and the reactive intensity, but lead to underestimation of the active intensity at low frequencies in reactive sound fields; indeed, the windscreen changes the sign of the measured intensity at very low frequencies. In Fig. 2 are shown the results of a similar experiment, this time with a 12-mm spacer, with no windscreen, with the spherical screen and with the ellipsoidal screen. In this experiment the probe was even closer to the loudspeaker, and the sound field at the position of the probe was strongly reactive as can be seen from Fig. 2(a). Figure 2(b) shows the intensity estimates determined with the two screens, normalised with the 'true' intensity, which was determined without windscreen. Note that the ordinate axis is linear, not logarithmic. Also shown are curves determined from eqn (11) and the measured error indicator 61J (where I x has been measured without windscreen and Jx has been measured with windscreen) by adjusting

46

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Fig. 1. M e a s u r e m e n t about 12cm from a small enclosed loudspeaker. ( ) Aclivc intensity, no windscreen:{ -) active intensity, ellipsoidat windscreen:{ ) pressure, no windscreen: ( ) pressure, cllipsoidal w i n d s c r e e n : ( ) particle velocity, no windscreen: (.) particle velocity, ellipsoidal windscreen: ( reactive intensity, no windscreen: ( . . . . . . ) reactive intensity, ellipsoidal windscreen. * Negati~ c estimatc.

the u n k n o w n parameter 4) so as to obtain the best fit. There is excellent agreement between measured and fitted curves. It is apparent that the negative bias error caused by a windscreen can be up to 10 times larger than the intensity itself! For some reason the spherical screen gives errors about twice as large as the ellipsoidal screen, even though the two screens appear io be made of the same material. The third experiment was carried out in a large (200 m 3) strongly-damped room. The sound power of a box of steel plates driven with pink noise by an electrodynamic exciter was determined by integrating the intensity (i.e. bx 'scanning') over a 'conformal' surface as near as possible to the surface of the box. Figure 3 shows the results of four measurements, with each of the two spacers without windscreen, with the spherical screen combined with the 12-mm spacer, and with the ellipsoidat screen and the 50-ram spacer. There is very good agreement from 125 Hz and upwards, but the measurements at 50 Hz and at 100 Hz with both windscreens are totally wrong: the estimates are negative. The explanation can be deduced from Fig. 3(b): the sound field is particularly reactive in these two frequency bands. (The distance between the surface of the box and the centre of the probe is not the same in the two cases. With the ellipsoidal screen one cannot possibly come closer to the sur-

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Fig. 2. Measurement about 10cm from a small enclosed loudspeaker. (a) Error indicator: ( ---) eilipsoidal windscreen; ( - - - - ) spherical windscreen. (b) Ratio between estimated and 'true' intensity: ( ) measurement with ellipsoidai screen; ( - - - - ) prediction with ~b= 48 kg m - a s - ~; ( - - - - - - ) measurement with spherical screen; (. . . . - - ) prediction with ~ = 8 1 k g m - 3 s -1.

face of the source than about 10 cm. This is reflected in lower reactivity.t o, t 1 Figure 3(c) shows a comparison between measured and predicted (fitted) data. There is fairly good agreement, but whereas the best fit for the ellipsoidal screen is obtained with practically the same value of ~ as in the foregoing experiment, the best fit for the spherical screen is obtained with a somewhat smaller value of q~.(It is perhaps not unreasonable that the larger windscreen is in better agreement with the theory described in Section 2 than the smaller windscreen.) The results of yet another experiment are shown in Figs 4 and 5. The sound power of a dipole source (two loudspeakers mounted against each other) placed on the floor in the large damped room was determined by scanning over two different surfaces, one (of 5 m 2) about 0.5 m from the source, and another one (of about 0-4 m 2) very near the source. A fan placed approximately 3 m from the source generated an airflow speed of about 5 m s- 1 at the position of the source. As can be seen from Fig. 4(b), the sound field was very reactive on the measurement surface near the source. In consequence, the sound power estimates determined with the spherical windscreen without and with flow are negative from 125 Hz downwards. Again the estimation error is in good agreement with the theory as predicted

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Fig. 3. M e a s u r e m e n t o f s o u n d p o w e r o f vibrating box. (a) Estimated s o u n d power: (...... j 5 0 - m m spacer, no windscreen; (. . . . . ) 12-mm spacer, n o windscreen; (. . . . . . . . ) 5 0 - m m spacer. ellipsoidal windscreen; ( . . . . . ) 12-mm spacer, spherical windscreen. * N e g a t i v e estimates. (b) Error indicator: ( - - - ) ellipsoidal windscreen; (. . . . . . . ) spherical windscreen. (c) Ratio b e t w e e n e s t i m a t e d and 'true' s o u n d power: ( . . . . ) m e a s u r e m e n t with ellipsoidal windscreen; (. . . . . ) prediction with 0 = 4 5 k g m - 3 s ~ ; (. . . . ) m e a s u r e m e n t with spherical windscreen; (. . . . . . . . ) prediction with 0 = 62 kg m - 3 s- i.

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Fig. 4. Measurement of sound power of dipole source. (a) Estimated sound power: ( ) large surface, no flow, 50-mm spacer, no windscreen; ( - - - - ) small surface, no flow, 12-mm spacer, no windscreen; ( - - - - - - ) small surface, no flow, 12-mm spacer, spherical windscreen; (. . . . - - ) small surface, mean flow, 12-mm spacer, spherical windscreen. * Negative estimate. (b) Error indicator: ( ) small surface, spherical windscreen, no flow; ( - - - - ) small surface, spherical windscreen, mean flow; ( - - - - - - ) large surface, no windscreen, no flow. (c) Ratio between estimated and 'true' sound power: ( ) measurement with spherical windscreen, no flow; ( - - - - ) corresponding prediction with ~ = 60 kg m - 3 s - 1; (__ - - - - ) measurement with spherical windscreen, mean flow; ( - - . - - - - - ) corresponding prediction with ~b = 68 kg m - 3 s - 1.

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Fig, 5. M e a s u r e m e n t o f s o u n d p o w e r of dipole source. () Large surface, no l l m ~ 5 0 - r a m spacer, n o w i n d s c r e e n ; (t large surface, m e a n flow, 50-ram spacer, elliptical w i n d s c r e e n ; ( . . . . ) large surface, m e a n flow, 12-ram spacer, spherical windscreen: (...... ) small surface, m e a n flow, 12-ram spacer, no windscreen. * N e g a t i v e cslim~dc

by eqn (12), although the best fit is obtained with a slightly different value of qS. There is no significant difference between estimates determined with and without flow. However, Fig. 5 demonstrates that airflow can indeed have a significant effect on sound power estimation at low frequencies. At positions towards the fan on the large measurement surface the airflow speed was about 7 m s 1, and it is apparent that flow speeds of that size can generate strong "false' intensity signals. The large, ellipsoidal windscreen combined with the 50-ram spacer seems, not surprisingly, to be better at suppressing noise induced by flow than the spherical screen combined with the 12-ram spacer. In Fig. 6 are shown the results of measuring the sound power of ~ 'reference source', an aerodynamic source of type Airap A 14 manufactured by l~lectricit6 de France. The sound power was estimated by scanning over the three different surfaces, at a 'reasonable' distance from the source (50 cm), where the m a x i m u m airflow speed was about 4 m s - z, fairly near the source where the airflow speed assumed values of up to 5 m s - l , and as near as possible to the source, where the flow was very turbulent. Since the results determined on the large measurement surface with both windscreens and without windscreen but with the 50-ram spacer are in fairly good agreement, these results may be regarded as the 'true' sound power. (Comparing estimates determined with different measurement surfaces and with different microphone separation distances is probably the only practical way of testing the reliability of measurements made in the presence of airflow.) At the medium surface both windscreens are able to suppress the noise

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Fig. 6. Measurement ofsound power of reference source. (a) ( ) Large surface, 50-mm spacer, ellipsoidal windscreen; ( - - - - ) large surface, 50-mm spacer, no windscreen; ( - - - - - - ) large surface, 12-ram spacer, spherical windscreen; (. . . . --) large surface, 12-mm spacer, no windsreen. (b) ( ) Large surface, 50-mm spacer, ¢ilipsoidal windscreen; ( - - - - ) medium surface, 50-mm spacer, no windscreen; ( - - - - - - ) medium surface, 50-mm spacer, ellipsoidal windscreen; ( - - . - - . - - ) medium surface, 12-mm spacer, spherical windscreen. * Negative estimate. (c) ( ) Large surface, 50-ram spacer, ellipsoidal windscreen; ( - - - - ) medium surface, 12-mm spficer, no windscreen; ( - - - - - - ) small surface, 50-mm spacer, ellipsoidal windscreen. * Negative estimate.

52

kTnn Jacobsen

generated by turbulence, but since the sound field is strongly reactive the sound power is underestimated, in accordance with the theory. By contrast, the sound power is significantly overestimated by the measurement with the 12-mm spacer without windscreen. Very near the source not even the combination of the ellipsoidal windscreen and the 50-mm spacer can cope with the unsteady flow. It is apparent that turbulent airflow can give rise to overestimation as well as underestimation. It should be emphasised that the errors generated by airflow are reproducible, that is, systematic errors. All in all, the experimental results suggest that, at the relatively low airflow speeds considered here, turbulence is a more serious source of error than the more fundamental effects of mean flow described in Ref. 4, even in strongly reactive near fields. 5 CONCLUSIONS The effect of windscreens of porous foam has been examined. Windscreens seem to make it possible to use the two-microphone intensity technique even at low frequencies at airflow speeds of up to 4 - 5 m s - 1 . However, the frictional resistance of the foam gives rise to a phase error between the pressure and the particle velocity. The result is a negative bias error proportional to the reactive intensity. In strongly reactive near fields the sound power estimate becomes negative. On the other hand, the error decreases rapidly with the distance between the source and the measurement surface; with a 'reasonable' distance the error is negligible.

ACKNOWLEDGEMENT The author would like to thank Erling Frederiksen, Briiel & Kjaer, lot drawing his attention to the problem examined in this paper.

REFERENCES 1. Gade, S. & Ginn, K. B., Sound intensity measurements at 100 km/hour. In Proc. Inter-Noise 85, ed. E. Zwicker. Bundesanstalt fiir Arbeitsschutz, Dortmund. Germany, 1985. pp. 11514. 2. Fahy, F. J., Sound Intensity. Elsevier Applied Science, London, 1989, pp. 124-127, 241-245. 3. ISO 9614-1. Acoustics--Determination of sound power levels of noise sources using sound intensity--Part 1: Measurement at discrete points. ISO, Geneva, Switzerland, 1993. Annex C: The effects of airflow on measurement of sound intensity.

Measurement of sound intensity with windscreenedprobes

53

4. Munro, D. H. & Ingard, K. U., On acoustic intensity measurements in the presence of mean flow. J. Acoustic. Soc. Am., 65 (1979) 1402-6. 5. Chamant, M., Conception d'une sonde destin6e fi la mesure de rintensit6 acoustique dans un fluide en mouvement. Th6se present6e devant rUniversit6 Claude-Bernard, Lyon, France, 1981. 6. Jacobsen, F., Measurement of sound intensity in the presence of airflow. In Proc. 2nd International Congress on Acoustic Intensity, ed. M. Bockhoff. Centre Technique des Industries M6caniques, Senlis, France, 1985, pp. 193-200. 7. Skode, F., Windscreening of outdoor microphones. Briiel & Kjaer Tech. Rev., 1 (1966) 3-9. 8. Morse, P. M. & Ingard, K. U., Theoretical Acoustics. McGraw-Hill, New York, 1968, Section 6.2, pp. 241-56. 9. Ren, M. & Jacobsen, F., A method of measuring the dynamic flow resistance and reactance of porous materials. Applied Acoustics, 39(4) (1993) 265-76. 10. Ren, M., Jacobsen, F. & Ginn, K. B., Sound field description based on complex intensity. In Proc. Fourth Western Pacific Regional Acoustics Conference, Queensland Department of Environment and Heritage, Australia, 1991, pp. 544-51. 1I. Jacobsen, F. & Olsen, E. S., The influence of microphone vents on the performance of sound intensity probes. Applied Acoustics (in press). 12. Chung, J. Y., Cross-spectral method of measuring acoustic intensity without error caused by instrument phase mismatch. J. Acoust. Soc. Am., 64 (1978) 1613-6.