INTERNATIONAL JOURNAL OF OCCUPATIONAL SAFETY AND ERGONOMICS 1996, VOL. 2, NO. 1, 1-15

Some Applications of the Sound Intensity Technique to Noise Control in the Workplace

Joseph C.S. Lai

Australian Defence Force Academy, Australia

Over a decade has elapsed since commercial sound intensity measurement systems became available. A literature search has shown that the sound intensity technique has found increasing applications in recent years. In this article, the principle and errors of the sound intensity technique are briefly described. Four case studies are given to illustrate how the sound intensity technique can be applied to determine sound power under both laboratory and field conditions, to identify noise source and to measure sound transmission loss o f composite partitions "in situ." It has been shown that, provided the lim itations o f the sound intensity technique are understood, results obtained by the sound intensity technique enable effective noise control to be implemented in the workplace.

sound intensity sound power sound transmission loss noise source identification noise control

1. INTRODUCTIONAlthough the first device for sound intensity measurements was patented by Olson in 1932, it was not until 1977 when Chung and Fahy independently applied digital signal processing techniques to the sound intensity theory that commercial systems became available. The increased interest in the sound intensity technique is reflected in Figure 1, which shows the distribution of papers published on the subject in English language journals since 1973. This information has been obtained using online search with the Science Citation database. A breakdown of a total number of 179 papers into two general areas, theory and application, reveals that the subject of using the sound intensity technique has matured as the number of application papers has dominated the theory papers. Around 1983-84, there was an explosion of papers on the subject, which coincided with the release of the first-generation commercial sound intensity systems in the early 1980s. There now exists an International Standard ISO 9614-1 (International Organization for Standardization [ISO], 1993a) on measurements of the sound power using the sound intensity technique. The sound intensity technique enables sound power measurements to be made directly instead of traditional methods conducted under a controlled acoustic environment (such as anechoic, semi-anechoic, or reverberant rooms) via sound pressure level measurements. It also offers other advantages such as external noise suppression capability, noise source identification, and noise ranking.

With improved understanding and availability of sound intensity m easurement systems, it seems worthwhile to examine how this new technique can be used to contribute effectively to noise control in the workplace. In this article, some applications of the sound intensity tech­nique undertaken at the Acoustics & Vibration Centre in the Australian Defence Force Academy will be described to illustrate the use of sound intensity measurements in the noise control process.

Correspondence and requests for reprints should be sent to Joseph Lai, Department of Aerospace & Mechanical Engineering, Australian Defence Force Academy, Campbell, ACT, Australia 2600. E-mail: <j-lai@adfa.oz.au>.

1

2 J.C.S. LAI

C/5L-0>

ol*

£

z

73-74 75-76 77-78 79-80 81-82 83-84 85-86 87-88 89-90 91-92

Period

Figure 1. Distribution of sound intensity papers published in English language journals since 1973.

2. THEORY

As the theory of the sound intensity technique has been described in detail in the literature (see, e.g., Fahy, 1989), the relevant equations underlying its principles are given in the A ppen­dix. It is the purpose of this section to highlight some of capabilities and limitations of the sound intensity technique.

2.1. Error ConsiderationsPossible sources of error in applying the sound intensity technique have been described by Gade (1985). It can be seen from Equations A3 and A4 in the Appendix that sound intensity measurements rely, respectively, on measuring the pressure gradient using finite difference approximations and measuring the phase gradient of the sound field accurately. Thus, the measurements are subjected to a low-frequency limit determined by the phase mismatching between the two microphone channels and a high-frequency limit determined by the finite difference approximation.

In determining the low-frequency limit of the measurements, Gade (1985) has shown that if the phase mismatch between the two microphone channels is <)>, then the measured intensity (Imeas) f°r plane sinusoidal waves is related to the actual intensity (I) by

^meas _ sin(kAr ± cj>)1 k S

where k is the wave number, and Ar is the separation distance between the two microphones.

NOISE CONTROL IN THE WORKPLACE 3

Equation 1 indicates that for sound intensity measurements to have an accuracy to within 1 dB, the phase change of the sound field (kAr) over the microphone separation distance Ar has to be greater than five times the phase mismatch (c|>).

The major error of sound intensity measurements at high frequencies is due to measuring the pressure gradient using finite difference approximation as given by Equation A3 in the Appendix. In determining the high-frequency limit, it can be seen from Equation 1 with 4> =0 that in order for the measured intensity (Imeas) to be a good approximation of the actual intensity (I), kAr has to be much smaller than 1. It follows then for measurements to have an accuracy to within 1 dB, the wavelength of the highest frequency of interest has to be greater than 6Ar.

2.2. Pressure-Intensity Index and Dynamic CapabilityVarious field indicators have been specified in ISO 9614-1 (ISO, 1993a) to help identify the grade of accuracy that can be achieved with sound intensity measurements. Basically, the grade of accuracy depends on both the nature of the sound field and the accuracy of the m easure­ment system and procedure. Only the pressure-intensity index and the dynamic capability of the measurem ent system will be discussed here. The pressure-intensity index (LK) is defined as the difference between the sound pressure level (Lp) and the sound intensity level (Lj) and is related to the phase change (c}>) over the spacer distance (Ar) for a given wavelength. LK gives an indication of the type of sound field in which the measurements are made. For example, the more diffuse the sound field or the larger the angle between the probe axis and the intensity vector, the larger the value of LK.

Owing to the phase mismatch between the two channels, the intensity measured is not zero, even if the two channels receive an identical signal and the pressure-intensity index measured under this condition is known as the residual pressure-intensity index (LK0). The error (Le) due to phase mismatch between the two channels can be expressed (see Gade, 1985) in terms of Lk and L j q as ^

Le = 10 log10[l ± 1001<l k " l ko> ] (2)

It can be seen from Equation 2 that for an accuracy to within 1 dB, LK has to be 7 dB less than L ko. The dynamic capability, LD, of a sound intensity measuring system can, therefore, be defined as (LK0 - 7) dB. Hence, it is important to monitor LK during measurements to ensure that it does not exceed LD. Ren and Jacobsen (1992) proposed a technique whereby the performance of the sound intensity measurement system may be improved by applying cor­rection based on the residual pressure-intensity index to the measurements. Various other field indicators are included in ISO standard 9614-1 and ISO CD 9614-2 (International Organiza­tion for Standardization [ISO], 1993b). A brief description of ISO 9614-1 (ISO, 1993a) is included in Fahy (1989). O ur experience, however, indicates that for most field measurements, monitoring LK appears to be adequate in checking the validity of the measurements.

3. APPLICATIONS TO NOISE CONTROLIn all the measurements described here, the sound intensity measuring system comprises a Bruel & Kjaer (hereinafter referred to as B&K) 2032 dual-channel FFT analyzer and a sound intensity probe made up of a pair of B&K 4181 phase-matched 0.5 in. microphones mounted in a face-to-face configuration. Most of the measurements were made with the microphones separated at a distance of 12 mm, covering a frequency range from 125 to 5000 Hz. There has been considerable debate in the literature regarding the accuracy between measurements obtained at discrete points and those obtained by the scanning technique. The current ISO standard 9614-1 (ISO, 1993a) relates to discrete point measurements, whereas a draft ISO CD 9614-2 (ISO, 1993b) relates to measurements by scanning. O ur experience, however, indicates

4 J.C.S. LAI

that as long as scanning is performed properly, the difference between the two techniques is insignificant. Furtherm ore, in field measurements, it is sometimes rather impractical to use discrete point measurements. All measurements described here have been obtained by scan­ning the sound intensity probe over a number of small segments. The narrow-band sound intensity data were processed and synthesized into 1/3 or 1/1 octave bands with a Hewlett- Packard series 300 microcomputer.

3.1. Measurement of Sound PowerThe sound power W of a sound source is related to the component Ir of the intensity vector normal to a hypothetical surface S enclosing the source:

W = JlrdS (3)s

Traditionally, the sound power of a noise source is determined by measuring the sound pressure level in some particular acoustic environment (such as anechoic or reverberant rooms), because under such conditions, the sound intensity level can be inferred from the measured sound pressure level. The International Standards ISO 3741-3746 (ISO, 1977) cover methods in this category.

According to Gauss theorem, if there is no source or sink within a measurement volume, then the sound power W as given in Equation 3 is zero. This property offers a significant advantage in using sound intensity technique for sound power determination, as external noise will not contribute to the sound power of the noise source under test provided that the external noise is stationary and there is no absorption within the measurement volume. Thus, in situ sound power measurements with high accuracy can theoretically be achieved. In practice, the accuracy is limited by the dynamic capability of the system as discussed in Section 2.2. The m easurement of sound power by the sound intensity technique in the presence of background noise has been studied theoretically and experimentally by Jacobsen (1992), and the various factors affecting measurement accuracy have been studied experimentally by Shirahetti and Crocker (1993). Two case studies on noise control in the workplace based on measurement of sound power will be discussed.3.1.1. Optical Mark ReaderA m odern office is usually equipped with a number of business machines which, although unlikely to cause hearing damage, can cause annoyance and have an adverse effect on comfort and performance. Managing the acoustic environment requires good management practices, forward planning, prediction of acoustic levels generated by machines to be purchased, and implementation of noise control strategies when necessary. In this section, the prediction and control aspects for the noise from 20 business machines, namely, optical mark readers (OMR), will be discussed. Each OM R is controlled by a laptop PC. The overall dimensions of an OM R are approximately 630 X 660 X 470 mm. The procedures adopted here include:

1. measurement of the sound power level of an OM R using the sound intensity technique,2. ranking of the noise sources of an OM R based on the sound intensity measurements,3. applying acoustic treatm ent to the OMR,4. predicting the sound pressure level at an operator’s position for the original and modified

OM R, and5. designing an optimum layout for the 20 OMRs to minimise operators’ exposure to noise.

In order to determ ine the sound power level and rank order the noise sources within the OMR, measurements were made with the sound intensity technique by scanning a sound intensity probe over nine surfaces of the OMR, as shown schematically in Figure 2(a). The ranking of the nine surfaces based on sound power under continuous paper feed operation is shown in Figure 2(b). It is interesting to note that Surface 7 is most dominant. The overall

NOISE CONTROL IN THE WORKPLACE 5

©

a

--------- 1------------ 1------------ r -

30 50Sound Power dB(A)

70

Figure 2 (a). Schematic of optical mark reader (OMR) showing measured surfaces (not to scale).

Figure 2 (b). Ranking of sound power of the measured surfaces.

sound power spectra obtained under both normal and continuous paper feed operations are shown in Figure 3. It can be seen that the peak sound power levels occur at about 500 Hz to 1 kHz. The overall A-weighted sound power level for the OM R is 72 dB(A) for normal paper feed operation and 76 dB(A) for continuous paper feed operation.

It has been noticed that under normal paper feed operation, the feed rate is not constant. From a typical time record of the sound pressure signal between paper feeds under normal feed operation, it has been estimated that the averaged duration for feeding a form is about0.33 s and the averaged duration for a form to be read is about 0.60 s, so that the difference between the sound power level for normal and continuous operations is about 4.5 dB(A). This value compares quite favourably with the measured sound power level difference of about 4 dB(A). It is considered that the result obtained under continuous paper feed operation is more reliable as the sound generated is constant. Consequently, most measurements were made under continuous paper feed operation, and the results were extrapolated to give the values for normal paper feed operations.

The sound radiation (directivity) pattern of an OM R over a reflecting plane has been measured inside an anechoic chamber at 1 m from the centre of the OM R and 300 mm above the reflecting plane in 15° increments. From the directivity pattern shown in Figure 4(a), the dominant noise propagates from the front surface of the OMR, and the directivity index along the 0° line is about 6 dB. These results agree with the ranking of noise sources based on sound power as shown in Figure 2(b).

The sound pressure level at distances 1 m, 2 m, and 4 m from the centre of an OM R and along the 0° line has been measured in a room of volume 275 m3 (referred to here as the test room). The reverberation time of the room is about 0.7 s at 500 Hz. These measurements indicate that the reduction in sound pressure level is about 4 dB per doubling of the distance from the OMR. Thus, in the near field of an OM R, its behaviour is between that of a point source and a line source. For the purpose of prediction for the worst situation, it has been assumed that the OM R behaves as a line source. Prediction of the sound pressure level has been made at 1 m from the centre of the OM R (i.e., about 500 mm from the paper tray) along the 0° line, using Equation 4 (see, e.g., Bies & Hansen, 1988). The sound pressure level for this location has been measured with a B&K 2231 sound level meter. As shown in Table 1, the

6 J.C.S. LAI

□ OMR - continuous paper feed E l OMR - normal paper feed ■ OMR with cover - continuous paper feed

125 250 500 lk 2k 4k A L Octave Band Centre Frequency (Hz)

Figure 3. Measured sound power spectra of an optical mark reader (OMR). (A refers to overall A-weighted level, and L refers to overall linear level.)

(a) Unmodified OMR. (b) OMR fitted with an acoustic cover.

Figure 4. Directivity pattern (in a horizontal plane).(Concentric lines indicate sound pressure level in increments of 10 dB.)Note. OMR—optical mark reader.

NOISE CONTROL IN THE WORKPLACE 7

predicted values for all cases agree with the measured values to within 1 dB(A), thus support­ing the prediction m ethod used.

_ ^W 10 +4'irr2 R (4)

where

Q e = directivity factor of the source in a particular direction 0 = 1001DID I = directivity index = Lp - Lp + 3 = sound pressure level (dB) at distance r and angle 0Lp = space-averaged sound pressure level (dB) _R = room constant, determined by the absorption of the room surfaces = a = average absorption coefficient of the room surfaces

and

S = total surface area (m2)

From Table 1, it can be deduced that in operating 20 OMRs under normal paper feed operations in a room with a room constant similar to that in the test room, the equivalent sound pressure level to which an operator would be exposed would be less than 85 dB(A) for an 8-h period, but would be close to 80 dB(A). Although this value satisfies the hearing conservation limit in Australia, it is considered to cause a fair degree of annoyance and fatigue. In order that individual comfort and performance would not be severely compromised, it was decided that the equivalent continuous sound pressure level for an 8-h period should not exceed 70 dB(A) for any operator’s position.

The noise from an OM R is basically generated by electric motors and the paper feed mechanisms. Any engineering solution would require redesign of the OMR, therefore, a retro-fit solution was the preferred strategy. As seen in Figure 2(b), the noise radiated from the front surface of the OM R is most dominant and it has also been noticed that a high-frequency interm ittent noise results from paper hitting the paper stop in the paper tray. A feasible solution to reducing the noise radiated from an OM R was to construct a flexible cover for the machine, with flaps to allow reasonably convenient access to the paper loading and unloading areas. The cover is made of a barium-loaded fabric. In order to reduce the noise resulting from paper hitting the paper stop, the paper stop was covered with a layer of soft foam material.

The sound power spectrum of a modified OM R has been determined for continuous paper feed operation and is shown in Figure 3. The overall A-weighted sound power level for continuous paper feed operation has been found to be 71 dB(A), and that for normal paper feed operation has been estimated to be 67 dB(A), about 5 dB(A) lower than an unmodified OMR.

The directivity pattern of an OM R fitted with an acoustic cover measured at 1 m from the centre of the OM R and 300 mm above the reflecting plane in 15° increments is shown in Figure 4(b). The directivity index along the 0° line is about 3 dB. The acoustic cover has generally rendered the noise radiation pattern less directional. The predicted and measured sound

TABLE 1. Comparisons Between Measured and Predicted A-Weighted Sound Pressure Lev­els, dB(A) at 1 m From the Centre of an OMR

Without Acoustic Cover With Acoustic Cover

Continuous Feed Normal Feed Continuous Feed Normal Feed

M P M P M P M P75.2 74.8 69.6 69.9 66.3 66.9 63 62

Note. M = measured; P = predicted.

8 J.C.S. LAI

^ E b

Operator'sPosition

^ B

^ E ]

^ b qa Bf"nq &^ E f

■ ^ b L500 mm

5m

Figure 5. Schematic of layout of 20 OMRs (not to scale). Note. OMR—optical mark reader

pressure levels of operating the modified OM R in the test room agree with each other to within 1 dB(A), as shown in Table 1.

Various configurations of the layout of 20 OMRs have been investigated for the noise exposure of an operator working in a large office (with a room constant of at least 200 m2). As the operation of a number of OMRs under normal paper feed operations is generally not synchronised, the equivalent sound power level for each OM R lies between that for normal paper feed operation and continuous paper feed operation. The equivalent sound power level of each OM R used for prediction is about 2 dB(A) higher than that for normal feed operation, that is, 74 dB(A) and 69 dB(A) for an OM R with and without an acoustic cover, respectively. One such configuration is shown in Figure 5, in which 20 OMRs are arranged in five modules, each module consisting of 4 OMRs. Within each module, adjacent OM Rs are separated at a distance of 2 m. Four modules are placed at a distance of 5 m from the centre module and at 90° intervals. By using Equation 4 and allowing for the reduction of 3 dB in sound pressure level per doubling of the distance from an OMR, the sound pressure level for the worst operator’s position for the layout as shown in Figure 5 has been predicted to be 70 dB(A) for OM Rs fitted with acoustic covers, compared with 78 dB(A) for unmodified OMRs.

3.1.2. Variable Air Volume (VAV) UnitIn this case study, cold air supplied by a central air-conditioning plant is mixed with secondary air in a distributed variable air volume (VAV) system which consists of over 24 units for an open office. It has been found that the office ambient sound level at low frequencies (below 500 Hz) is too high due to the operation of the VAV units. As shown schematically in Figure 6, a VAV unit consists of a box where the primary air and secondary air are mixed into a single stream (to achieve a certain preset tem perature) before being distributed to the office through the outlet discharge duct. The radiated sound power from various components of a VAV unit was measured in situ by scanning the sound intensity probe over the various components. The sound power spectra for the original unit (i.e., without the secondary air inlet silencer) in Figure 7(a) indicate that the secondary air inlet and the

NOISE CONTROL IN THE WORKPLACE 9

Secondary air

Silencerilencer \

I f e i l l 3 —

Primary air

Flexible coupling

n k .

VAV box

/

Figure 6. Schematic of a variable air volume (VAV) mixing unit showing various components.

VAV box are the dominant noise sources. It was then decided to treat the secondary air noise source by fitting the secondary air duct with silencers. As shown in Figure 7(b), the radiated sound power level determined using the sound intensity technique indicates that the contribution of the secondary air intake has been substantially reduced by the silencers, leaving the VAV box as clearly the dominant noise source. Subsequently, acoustic treatm ent (in the form of loaded vinyl) applied to the VAV box has brought the radiated sound power from the VAV units down to acceptable level.

Often in using the sound intensity technique to locate an air-conditioning noise problem, there is significant air movement in the space. Because currently available commercial sound intensity measuring systems do not account for errors introduced by air movement, it is im portant to monitor the air speed in the space to ensure that it is not too excessive to allow

80

70

Si 60

50

"= 40”D

'■5rzU 30

20

125 250 500 1000 Oclavc band centre frequency (Hz)

125 250 500 1000 Octave band ccnfrc frequency (Hz)

(a) Original VAV unit

Figure 7. Radiated sound power level spectra. Note. VAV—variable air volume.

(b) VAV unit fitted with silencer

□ VAV box a Flexi-coupling 13 Secondary air

10 J.C.S. LAI

measurements using a sound intensity probe fitted with a windshield. Our experience indi­cates that, generally, if the air speed is under 2 m/s, satisfactory measurements may be made.

3.2. Location of Noise SourceOwing to the directional response of a sound intensity probe as described in Section 2.0, the sound intensity technique has often been used to locate a noise source by the “null- search” method; that is, the intensity probe is swept with its axis parallel to that of a suspected noise source, and the location of the noise source is indicated by the reversal of the sign of the intensity spectrum as the probe is swept past the source. The sound intensity technique can be quite useful in identifying airborne noise transmission paths, particularly in building acoustics as dem onstrated by Lai (1991). In such applications, the sound intensity probe is pointed towards the suspected partition, and if the sound intensity spectrum is positive, then it can be inferred that the dominant noise is propagating through this partition. How­ever, great care must be taken in monitoring the pressure-intensity index LK in such appli­cations, because if the sound field is diffuse, then measurements may approach or even exceed the dynamic capability of the system, thus invalidating the use of the technique under such conditions.

A nother method of locating a source is to perform an intensity mapping. Figure 8 shows one such application in which contours of overall sound intensity (in the frequency range of 100 Hz to 6.4 kHz) have been obtained for a drill. The measurement grid, located at about 150 mm from the drill, is also shown and indicates that a total of 20 measurements have been made. The intensity contours clearly indicate the dominant noise source for this drill.

83 83 82 78

81

83

83

/ —’

✓ ^/ / —

' / Z'

_._ ^

s s

; > > > ^ \ \

*------- T \\ ' '

\ \ \ ' \ \ \

S \ V '\ \ \ \

k. s \ \ 'N \ v \ \

1 1 /! i ^

\ \

\ \ \ \ \s \ \ \ V

\ \ \ \ \ \% N \ \ \ \ \

V ' , W \ V .1 \ ’ jT"

\ \ \ (

\ \ \ f Nv \ \ v

\ \ \ r\ \ V > * .

"'■v/ L *

f t

/ /

' ! ! : i

' / / / / I !

/ / / 1 * / / ' 1 1

\ \

V ' C

i \\ ^ — V.

/

^ / / ■s

' ' / '

' / / /

/ /

85 86 84 82

Figure 8. Intensity map of a hand drill.

NOISE CONTROL IN THE WORKPLACE 11

3.3. Sound Transmission Loss MeasurementsVery often, noise control methods require the use of materials with good sound transmission

loss (or more commonly known in Europe as sound insulation) to reduce the level of intruding noise. Current methods of determining the sound transmission loss of materials are generally time consuming, expensive, and laboratory based. The sound intensity technique offers the advantage that field transmission loss measurements of composite partitions may be made, thus allowing the development of prototype materials with good sound transmission loss in the field (often on a building site where quick decisions have to be made).

In terms of the sound power Ws incident on the partition and the sound power Wr transmit­ted through and radiated by the partition, the sound transmission loss (STL) or as more commonly known in Europe as the sound insulation index is defined as:

STL = 10 log10(W /W r) (5)

Traditionally, a test partition is installed in between two reverberant rooms and the STL is determ ined from the averaged sound pressure levels measured in the source and receiving rooms.

Expressed in terms of the incident and the transmitted sound intensity levels, Lpi and LIt, respectively, and using the relationship for a diffuse sound field and the normal values for the density of air and the speed of sound, Equation 5 becomes

STL = (Lpi - 6) - LIt (6)

Hence, the sound transmission loss of a test partition can be obtained by measuring the averaged sound pressure level in the source room and the intensity transm itted through the partition into the receiving room. There has been considerable research conducted in estab­lishing the accuracy of sound transmission loss measurements using the sound intensity tech­nique in conventional laboratory facilities which consist of a source room and a receiving room (see, e.g., Halliwell & Warnock, 1985; Lai & Qi, 1993).

The real advantage of the sound intensity technique lies in field transmission loss m easure­ments where transmission loss of elements such as doors and windows in composite partitions can be determ ined, thereby revealing the weakest link in composite partitions. The application of the sound intensity technique to field transmission loss measurements of elements of composite partitions is quite promising, as reported by Lai and Burgess (1991).

Figure 9 shows schematically a room in a building site where the effect of applying different types of material to the concrete blockwork can be assessed. Note that the surroundings of the source room are basically open space. The averaged sound pressure level in the source room and the intensity transmitted through each specimen can be measured, thus allowing the STL of each specimen to be determined from Equation 6 and their acoustic performance to be compared. Figure 10 shows the field sound transmission loss measurements determ ined in this manner for a specimen comprised of a 200-mm thick aerated concrete block (with a nominal density of 500 kg/m3) with 28-mm thick rockwool and 6-mm thick villa board attached to its surface. The sound transmission class for this specimen has been determined to be STC 47.

Sound intensity measurements in “open air” are subjected to two major sources of error, namely, background noise and wind conditions. Because sound intensity measurements are generally made within 200 mm of a wall, the influence of background noise in open air is often not significant. As pointed out in Section 2, commercial sound intensity measuring systems assume no mean flow and turbulence in the medium; thus, substantial errors can result from making outdoor sound intensity measurements under windy conditions. To a certain extent, this error can be reduced by using movable sound-absorbing panels to shield the sound intensity probe from wind during measurements.

12 J.C.S. LAI

Figure 10. block.

Test specimen A Testspecimen E

Testspecimen B

Test specimen C

Test specimen Dj

Soundsource 4^—

a______ I___

Figure 9. Schematic of source room showing test specimens.

1/3 Octave Centre Frequency (Hr)

Determination of the sound transmission class for a composite 200-mm concrete

NOISE CONTROL IN THE WORKPLACE 13

4. CONCLUSIONS

Commercial sound intensity measuring systems have been available for over a decade. A literature survey has revealed that the sound intensity technique has matured and has found increasing applications. Examples have been given here to show that, provided the limitations of the sound intensity technique are understood, the technique can be used with good success for the determ ination of sound power in situ, the location of noise sources, and field measure­ments of transmission loss of elements of composite partitions. It has been demonstrated through the case studies on the optical mark reader and the variable air volume unit that ranking of noise sources based on sound intensity measurements (which are difficult, if not impossible, to do with traditional sound pressure level measurements) enables effective noise control to be implemented in the workplace. It has also been shown that prototype develop­ment of materials with suitable field transmission loss and their testing can be effectively carried out on site.

With the improvement in hardware and software, almost certainly accompanied by reduc­tion in price, sound intensity measurements will be more extensively used for noise control in the workplace, and the limits of applications will depend mainly on the ingenuity of the users.

A PPE N D IXBrief Description of the Theory of the Sound Intensity Technique

Unlike sound pressure which is a scalar quantity, sound intensity or sound energy flux density (i.e., the rate of energy flow per unit area) is a vector quantity. The time-averaged intensity vector I is defined as

II = ^ J p Q dt (A l)

wherep is the sound pressure u is the particle velocity vector.

The component Ir of the intensity vector I along a direction r can, therefore, be determined if the particle velocity ur can be measured. In the absence of a mean flow and turbulence in the medium, the particle velocity component ur in the r direction is related to the pressure gradient by E uler’s equation (Equation A2):

dur

p a f “ (A2)where p is the density of the medium.

The pressure gradient may be approximated by finite differencing so that in practice this can be determined from the pressure difference (pA - pB) detected by two microphones closely spaced at a distance Ar along the direction r. The pressure p in Equation A l can be obtained from the average of the two microphone signals. Integration of Equation A2 yields the particle velocity ur:

~ ^ ? J (PB -P A )dt (A 3)

It can be shown that the intensity vector component in the direction r can be calculated from Gade (1982).

T _ Prm s 1 9*1* / a \' ' ■ - p F t f c (A4)

14 J.C.S. LAI

where

34>/3r is the phase gradient of the sound field in the direction r; p2ms is the mean square pressure; pc is the acoustic impedance of the medium; and k is the wave number.

By substituting Equation A3 into Equation A1 and taking the Fourier Transform, it has been shown by Fahy (1989) that the active intensity spectrum Ir (to) in the r direction is related to the imaginary part of the cross-power spectrum GAB between the two microphone signals ;

Because Im (G AB) is related to the phase change of the sound field over the distance Ar separated by the two microphones, a typical sound intensity measuring system is comprised of a sound intensity probe made up of a pair of phase-matched microphones and a dual channel signal analyzer which could be either based on fast Fourier Transform (FFT) or digital filtering technique. Usually, the two microphones are mounted in a face-to-face configuration sepa­rated by a distance Ar. The response of a sound intensity probe follows approximately a “cosine” law (i.e., maximum along the axis of the probe and minimum normal to the axis of the probe). Hence, a sound intensity probe basically indicates the magnitude and direction of the net intensity along the axis of the probe. For sound incident to the probe axis at angles less than 90°, a net positive intensity would be measured, whereas at incident angles greater than 90°, a net negative intensity would be indicated. This directional property is often used as a quick check of the operation of a sound intensity measuring system when doing field m easure­ments.

REFERENCES

Bies, D.A., & Hansen, C.H. (1988). Engineering noise control Sydney: Unwin Hyman.Chung, J.Y. (1978). Cross-spectral method of measuring acoustic intensity without error caused by

instrument phase mismatch. Journal o f the Acoustical Society o f America, 6 4 ,1613-1616.Fahy, FJ. (1977). Measurement of acoustic intensity using the cross-spectral density of two microphone

signals. Journal o f the Acoustical Society o f America, 62, 1057-1059.Fahy, F.J. (1989). Sound intensity. New York: Elsevier Applied Science.Gade, S. (1985). The validity of intensity measurements. Bruel and Kjaer Technical Review, 4 ,3-31.Halliwell, R.E., & Warnock, A.C. (1985). Sound transmission loss: Comparison of conventional tech­

niques with sound intensity techniques. Journal o f the Acoustical Society o f America, 77,2094-2103.International Organization for Standardization. (1977). Determination o f sound power levels o f noise

sources (Standards No. ISO 3741-3745). Geneva: Author.International Organization for Standardization. (1993a). Determination o f sound power levels o f noise

sources using sound intensity— Measurement at discrete points (Standard No. ISO 9614-1). Geneva: Author.

International Organization for Standardization. (1993b). Determination o f sound power levels o f noise sources using sound intensity—Measurement by scanning (Standard No. ISO CD 9614-2). Geneva: Author.

Jacobsen, F. (1992). Sound power determination using the intensity technique in the presence of diffuse background noise. Journal o f Sound and Vibration 159,353-71.

Lai, J.C.S. (1991). Application of the sound intensity technique to noise source identification: A case study. Applied Acoustics, 34, 89-100.

Lai, J.C.S., & Burgess, M. (1991). Application of the sound intensity technique to measurement of field sound transmission loss. Applied Acoustics, 34,17-81.

NOISE CONTROL IN THE WORKPLACE 15

Lai, J.C.S., & Qi, D. (1993). Sound transmission loss measurements using the sound intensity technique.Part 1: The effects of reverberation time. Applied Acoustics, 40, 311-324.

Olson, H.F. (1932). System responsive to the energy flow o f sound waves (U.S. Patent No. 1,892,644). Ren, M., & Jacobsen, F. (1992). A simple technique for improving the performance of intensity probes.

Noise Control Engineering Journal, 3 8 ,17-25.Shirahatti, U.S., & Crocker, MJ. (1993). Studies on sound power measurements using the sound intensity

technique. Noise Control Engineering Journal, 41 ,323-330.