A method for field measurement of the transmission loss of building facades

Journal of Sound and Vibration (1974) 33(2), 127-141

A METHOD FOR FIELD MEASUREMENT OF THE TRANSMISSION LOSS OF BUILDING FACADES P. T. LEWIS

Welsh School of Architecture, University of Wales Institute of Science and Technology, Cardiff CF1 3BA, Wales (Received 15 August 1973) A method is described for measuring the transmission loss of building facades exposed to noise from road traffic. The principle of the method is the simultaneous tape recording of the sound level outside and inside the facade on site and analysis of the recordings in the laboratory. An assessment of the accuracy of the technique is given together with its theoretical basis. I. INTRODUCTION Although an important function of building facades is the control Of the entry of external noise, relatively little attention has been paid to the measurement Of iheir sound insulation. Of the work that hasbeen published [1-6] on this subject, the majority [1-4] has been concerned with laboratory measurement and the methods described have generally been unsuitable for field application. It is well known [6, 7] however, that the sound insulation of a structure when mounted in a building may differ considerably from that in a laboratory test. For some years, the author has been carrying out measurements on facades exposed to traffic noise [6, 8, 9] but no detailed description of the method has previously been published. This paper is based on a report which was submitted to the ISO Working Group preparing proposals [10] for measurement of the sound insulation of building facades. 2. DEVELOPMENT OF METHOD 2.1.

NATURE OF SOUND FIELD

The sound fields to which building facades are exposed are in general neither diffuse nor plane. In most cases sound arrives from a restricted range of angles with an intensity which varies with the angle of incidence. For example, the fifth floor level of a facade exposed to a road will typically receive no sound from angles less than 60 ~if there are no buildings opposite. In addition, the highest intensity will usually occur at the minimum angle. Since sound insulation is a function of angle of incidence [1-3], it is desirable that the test sound field be of a similar form if the result of a measurement is to reflect the performance of the facade in practice. 2.2.

EXISTING METHODS

The traditional method [I 1, 12] of transmission loss measurement is unsuitable for facades since the test structure needs to be fixed between two reverberant rooms and the incident sound field is diffuse. As a result an alternative technique has been evolved [1-4] in which the structure is, or is part of, an external wall of a reverberant room. The sound source is a loudspeaker system designed to produce a plane sound field at the facade. 127

128

P.T. LEWIS

To the author's knowledge, this has only been used in laboratory work up to the present time. In a field situation, difliculties are likely to arise due to the disturbance caused by the loudspeaker, its positioning (especially for the upper floors ofmulti-storey buildings) and the number of measurements with different angles ofincidence required to produce a representative result. Furthermore, the standard form of the method [1, 2, 4] requires the facade to be removed in order to measure an insertion loss, an impossible requirement in most cases. An alternative method has been to use a calibrated loudspeaker [3] but again there are problems in allowing for the image sources usually present. In the field measurements of Scholes and Parkin [5] a helicopter was used as the source and the insulation was determined as a normalized level difference from the readings of an external microphone 1 m from the facade and a microphone inside the room. Although the principle of direct measurement of the external sound level overcomes the difficulties given above, the interference which occurs between incident and reflected waves means that the nature of the sound field at a distance of 1 m is generally uncertain, especially at low frequencies. The sound source is also impractical for general application. 2.3. METHOD USING TRAFFIC NOISE The basis of the method described in this paper is the use of an existing source of external noise and direct measurement of the incident and radiated sound powers. Simultaneous recordings of the sound levels outside and inside the facade are made on a two channel tape recorder, which are subsequently analysed to determine the TL. The main differences between this and other methods are the use Of a naturally occurring noise source, the position of the external microphone, and the direct determination of the sound power incident on the facade. Its advantages are that there is no increased disturbance, a range of types of sound field can be considered (e.g., different floors of a building), the sound field is always of the appropriate form, the presence of image sources, due to other buildings for example, do not complicate the measurement of the incident power, and the determination of the incident power allows the transmission loss rather than a level difference to be found. 3. SUMMARY OF METHOD The equipment is shown in Figure 1. (1) A building is chosen which is exposed to an adequately high level of external noise. (2) The sound power incident on the facade is measured by means of a ~ i n c h omnidirectional microphone, fitted with a nose cone, mounted as close as possible to some large, hard, flat area of the facade (Plate 1). (3) The power transmitted through the facade is determined from the sound level in the room.

Tape I microphones 6 No.l"

J recorder Tape I

I IMeasuring H

Filter

I Microphone multiplexer

Frequency I 9 spectrometer

I

Level

I

I

Figurc I. Arrangement of equipment.

I I

I

Plate 1. A method of positioning a microphone close to a surface. The nose cone is not shown.

(facing p. 128)

FACADE TRANSMISSION LOSS

129

(4) The external and internal noise levels are simultaneously recorded on a two channel tape recorder. Two recordings are made: (i) of the unweighted microphone signals, (,ii) of the A-weighted microphone signals. --(5) The reverberation time of the room is determined by recording the decay of a number of pistol shots fired near the facade. (6) The recordings are analysed to determine the statistical distribution of external and internal sound levels. (7) The transmission loss of the facade is calculated from the equation TL = S L e - SLa + lOloglo(S/A) + 101ogto(COS0),

(1)

where T L = transmission loss of facade, SLE= mean sound level at surface of facade, SLR = mean sound level in receiving room, S = area of facade, A = absorption in receiving room, COS 0 = mean cosine of angle of incidence. (o)

Test e!ement of focode /

I<~-~_.

J P/"

Centre line . t

(b)

~-~"

.

Figure 2. Determination of cos0. (a)Facade parallel to road; zj, z2 =limits of road to which facade is exposed; (b) facade perpendicular to road; zl = ]imh of road to which facade is exposed.

(8) The value of cos0 is calculated as follows: (i) facade parallel to road:

zt

z2 f

d aZ+z~+aZ+z~ a tan -1 (zl/a) + tan -1 (z2/a) '

COS 0 = - -

(2)

P . T. L E W I S

(ii) facade perpendicular to road." a

1 COS 0 =

a z "Jr Z 2

tan-l(z/a)

9

(3)

e key to the symbols is given in Figure 2. If the distances zl, z:, z are infinite, these expresns simplify to 2d cos 0 = - -

and

a

2 cos 0 = - = 0.64

(4)

7z

facades parallel and perpendicular to the road, respectively. 4. DETAILS OF TECHNIQUE 9 MEASUREMENTS O F I N C I D E N T S O U N D P O W E R

When a sound wave is incident on a surface, interference patterns occur due to phase terence between the incident an d refleCted waves [13]. At a rigid perfectly reflecting surface, ,' incident and reflected waves wil! always be in phase and the sound level at the surface will :refore be a constant 6 dB higher than that of the incident wave. At other positions cluding, of course, 1 m from the'facade,) even for a fixed level of incident power, the form the interference pattern and hence the sound level at any point will vary according to the quency and angle of incidence of the wave. In practice the level cannot be measured at the surface due to the finite size of the microones. Since the sensitivity of a microphone reduces with its physical size, the choice of crophone must be a compromise. (The correction that has to be made for this is discussed Appendix II.) In the measurements reported here, a ~}-inch microphone was used which ts positioned close to a hard smooth flat surface, usually a window, so that its diaphragm ts at right angles tO the surface, horizontal and facing downwards (Plate 1); the correction 6 dB is then accurate to within 0.6 dB at frequencies up to 3150 Hz. The microphone can be positioned close to the facade in a number of ways. In the simplest se, access is available from inside the building: e.g., through an open window. The micro,one can then be supported by a rubber suction pad stuck to the facade (Plate 1) and the !crophone lead carried into the building through the frame by means of a "tape" cable. r using this method, the microphone can readily be positioned within 2 mm of the surface9 W h e n the facade is completely sealed this procedure is not possible and the microphone ts then either to be suspended from above or mounted on a mast from below. In all cases the microphone should be positioned in such a way that further complication i the interference patterns due to other reflecting features on the facade is avoided. I 2 9 MEASUREMENT OF RADIATED SOUND POWER

T h e radiated sound power is determined from the average sound level in the receiving room, ! in the normal double room procedure. The method used by the author was to position six inch microphones randomly through the volume of the room and to sample the level of .ch in turn for one second with a sequential multiplexer. The multiplexed signal was fed to te tape recorder 9 The majority o f the energy in traffic noise occurs at low frequencies, and since the sound sulation of most structures is greater at high frequencies than at low, this emphasis will :nerally be increased when the noise is transmitted into a building. In order to produce a

FACADE TRANSMISSION LOSS

131

spectrum which is more uniform with frequency, recordings are made of the A-weighted signals in addition to the linear signals. The reduction in low frequencies produced by an A-weighting filter allows a higher recording level to be used, with a corresponding increase in the signal to noise ratio at high frequencies. A further increase in signal to noise ratio can be obtained, if necessary, by using the 10Yo levels instead of mean levels in equation (I). 4.3. CORRECTION FOR ANGLE OF INCIDENCE

The correction given in section 3 for the angle of incidence of the noise applies only to that from a single carriageway. If the road has two distinct carriageways or if the presence of large reflecting objects create image sources, these may be treated separately. The value of can be calculated for each and an overall mean value ofcos 0 found by weighting the individual values according to the distance between the road (or image of road) and facade (at), and their relative strengths (k,): i.e.,

cos0=

'

I

5. MEASUREMENT ACCURACY 5.1. GENERAL It has been shown by:a number of researchers (see e.g., references [8], [14] and [15]) that different values of transmission loss can be measured for the same structure under different conditions. The implication is that a structure does not have a unique transmission loss as current standard procedures [11, 12] might suggest. Instead, it is a property of both the structure and the set of experimental conditions. The "accuracy" of the method cannot therefore be estimated by comparing the result of a field measurement with that for the same structure measured in a laboratory. However, a discussion of the likely sources of error and their magnitudes is not out of place. It will be more meaningful to compare the accuracy of the existing external source (EES) method described here with that ofthe established two roomrnethod rather than discuss it in isolation. 5.2. RANDOMERROR The repeatability/random error of the EES method was estimated by carrying out two independent measurements on each of six facades with a range of types of receiving room. By using standard statistical techniques for the analysis ofpaired observations, a 95 ~o confidence range (+2.6 standard deviations with six readings) for the results of a single measurement has bi:en determined at each frequency. The results are given in Table I. Figure 3 shows these values applied to a TL curve. In a study of the repeatability of field measurements with the two room method, Higginson [16] employed twelve teams to measure the TL of the same structure. When all followed a prescribed "rationalized" procedure, a typical value of the range +2 standard deviations was +_4 dB at low frequencies with a maximum of +_5 dB; when a single team followed a highly elaborate measurement procedure, the corresponding values were +2 dB and +-5 dB. For the EES method with road traffic as the noise source, the average value of the random error at low frequencies is +-2 dB, with a maximum of +3.4 dB (see Table l). The principal sources of error included are the variability in the level of traffic noise, the use of a single external microphone position, and the non-uniformity of the sound field in the receiving

132

P. T. LEWIS TABLE 1

95 ~ col~dencerangefor result of TL measurement Frequency band (H~

60

I

•

3150 2500 2000 1600 1250 1000 800 630 500 400 315 250 200

1"8 1-1 0"7 1"0 1"0 0"9 0-9 1"4 1"6 1"6 1"5 1-8 1"8

160

2"4

125 100

2"2 3"4

I

I

I

I

I

I Ik

1 2k

50

4O o

E

I--

20

I 63

I 125

I 250

I 500

I 4k

I

Frequency (Hz)

Figure 3. Repeatability of results :95 ~ confidence range (5-2 standard deviations) based on six readings. room. These results suggest that the repeatability of the EES method compares favourably with that of the traditional method. 5.3.

SYSTEMATIC

ERROR

5.3.1. Correction for position of external microphone The existence of a doubling of sound pressure at a plane, perfectly reflecting surface has been established theoretically [9]. In practice, an exact doubling of sound pressure will not be recorded by a microphone positioned close to a facade, for two reasons.

FACADETRANSMISSIONLOSS

133

First, no surface is perfectly reflecting. The pressure rise in this case is 2]0 + ct) [9] where ct is the absorption coefficient of the surface: i.e., increases in level of 5.8, 5.5 and 5-3 dB would occur with absorption coefficients of 0.1, 0.2 and 0.3, respectively. Thus, provided a surface such as that of glass is used, the error in assuming a 6 dB increase may usually be ignored; if not, a correction for it can be made. Second, the finite size of microphone does not allow measurement of the sound level actually at the surface. The magnitude ofthe error is determined by the ratio ofthe microphone size of the wavelength of the sound. No difficulty exists at low frequencies but at the highest frequency of 3150 Hz, the wavelength is only six times the microphone diameter. Whilst this ratio is sufficiently high to ensure that the microphone does not significantly distort the sound field when fixed as described in section 4.1, it cannot be assumed that a pressure doubling occurs over the whole of the microphone diaphragm. The allowance that should be made for this is discussed in Appendix II. It is shown that the error that can occur is typically less than 0.5 dB at 3150 Hz, and smaller at lower frequencies. It is pertinent to note that, in the double room method, the theoretical relationship between the mean source room level and the level of incident power seldom holds under field conditions. It is assumed that the energy density is uniform throughout the room, whereas the increase of energy density next to all surfaces [13] and the presence of room modes make this unlikely. These difficulties do not arise with a large external source like a road. 5.3.2. Correction for angle of hlcidence The purpose of the cosine correction, 101oglo(COS0), is the transformation of the sound level at the microphone to the sound power actually falling on the facade. The estimation of the value of this correction is a source of systematic error. However, it is generally insensitive to changes in the angle ofincidence. For example, ifthe angle arc cos 0 were assumed to be 60 ~ so giving a correction of 3 dB, and the true angle were in the range 51~ ~ the error would be less than 1 dB; ifthe true angle were in the range 37~ ~ it would be less than 2 dB. An indication of the range of angles that typically occurs in practice is given in the results of section 5.2 (see Table 2). It is again important to note. that the standard equation used in the double reverberant room method is also based on the assumption of a particular composition of the incident field, i.e., diffuse, which is difficult to achieve in practice even under laboratory conditions; in a field situation, the incident field is likely to depart widely from the assumed condition. 5.3.3. Frequency response The results were corrected for the measured frequency response of the whole record/replay chain. 5.3.4. Restricted source power When using a natural source of noise, the power output cannot be increased in the way that power from an oscillator]amplifier]loudspeaker system can and care has to be taken that the level in the receiving room is due predominantly to the energy transmitted from outside the building. The problem is most acute at high frequencies where the highest values of TL are being measured. In practice, however, this is unlikely to be a major difficulty and the level of traffic noise inside a building on a noisy site will usually be at or above that due to internal sources. The character of traffic noise, which makes it less disturbing than noise from most other sources at the same amplitude, and the cost and difficulty of achieving a high standard of sound insulation combine to ensure that few facades are "over-insulated".

134

P.T. LEWIS

These factors apply to normal conditions. For the purpose of measurement, therefore, a time can usually be found or internal noise sources controlled, or both, so that the required signal to noise condition is achieved. This will be assisted by the use of 10 ~o rather than mean sound levels. 5.4. OVERALLERROR

With regard to sources of error, the principal difference between the technique described in this paper and the standard field method for internal structures is in the method used to measure the incident sound power. From the above discussion it would seem that both random and systematic errors are likely to be of a similar magnitude or smaller than those of the traditional method. 6. EXAMPLE OF APPLICATION 6.1. GENERAL Although the EES method can only be used where a building is already exposed to a fairly high level of external noise, this has not been found to be a major disadvantage. For if an interest in the sound insulation of a particular facade exists, it is generally because there is an external noise problem. Alternatively, if a survey of field performance is being carried out, there will usually be an adequate number of buildings in noisy locations. 6.2. EXAMPLEOF RESULTS A small selection of the results that have been obtained are given in Figures 4--6. For each facade, the TL of an equivalent window measured in the laboratory [17] by the double room method is shown; the values have been adjusted to allow for the difference in the percentages of glazing. A summary of the principal experimental parameters is given in Table 2. TABLE2

Summary of measurement parameters Figure 4

Figure 5

,, J ~

Floorl Mean angle of incidence Proportion of glazing (9/o) Room dimensions (m) Mean reverberation time (s) Mean transmission loss 100/3150 (dB) Mean transmission loss (dB(A))

55 50 9.1x 4.6x 2.7 0-7

Floor5 66 50 4.4x 4.6x 2.7 0-5

Figure 6

A

Floor9 73 50 4.4x 4.6x 2-7 0-5

A 50 47 3.5x 4.3x 2.5 0-3

-%

B 60 42 2.9x 4.7x 2-8 0-5

Floor3 51 82 5.0x 5.1x 2-6 0.6

Floorl2 58 82 2-4x 5.1x 2.6 0-3

25

25

23

26

26

39

35

25

26

22

25

24

37

33

The facades to which the results refer were of the following types. Figure 4: location of rooms: I st, 5th and 9th floors of same building; facade construction: heavy, concrete frame with brick infill; window: 4 mm glass in metal frame, openable; facade exposure: parallel to road.

FACADE

60

TRANSMISSION

135

LOSS

i

I

I

I

I

I

I 125

I 250

I 500

I Ik

I 2k

I 4k

50

40

-~ ~0

I- 20

I0

0

I 63

(Hz)

Frequency

Figure 4. Facade with openable single windows, parallel to road: 9th floor; , laboratory result, random incidence.

.....

,

Ist floor; - - - , 5th floor;

......

,

Figure 5: location of rooms: (A) in bridge directly over road, (B) 5th floor ofsame building block; facade construction: heavy, concrete frame with brick skin; window: 4 mm glass in metal frame, openable; facade exposure: perpendicular to road. Figure 6: location of rooms: 3rd and 5th floors of same building; facade construction: heavy, pronounced concrete frame with windows directly inset; window: double; outer window 12 mm glass, fixed; inner window 6 mm glass, openable; some air paths between window cavity and room interior; facade exposure: building at intersection, roads parallel and perpendicular to facade.

60

I

I

I

I 12.5

I

I

I

i

I

I 250

I 500

I [k

I 2k

I 4k

I

50

~g

40

~3o

i

I-~ 2 0

o

Frequercy (Hz)

Figure 5. Facade with openable single windows, perpendicular to road: floor; , laboratory result, random incidence.

......

,

bridge over road; - - % 5th

136

P . T. L E W I S 60

I

I

I

I

I

I

50 9 -~-. ... 9"

i

/ i

-!

.6 3o

I-

20

~0

0

I 63

I t2,5

I 250

I 500

I Ik

I 2k

I 4k

Frequency (Hz)

Figure 6. Facade with double windows, at cross roads: ...... ,3rd floor; - - - , 12th floor; result*6 mm glass, 4 rnm glass, 200 mm cavity, random incidence.

, laboratory

6.3. NATUREOF INCIDENTFIELD It is of interest that the sound fields incident on a facade from roads vary over a smaller range than is sometimes thought. Indeed, the " m e a n " angle of incidence, which is weighted to take into account the reducing levels ofenergy arriving from more remote parts ofthe road, only varies between 50 ~ and 75 ~ for facades between the first and twelfth floors, both parallel and perpendicular to the road. 7. CONCLUSIONS In situations where the level of noise in a building due to internal sources is, or can be made to be, lower than that entering through the facade, the TL of the facade can be determined. The measurement accuracy is comparable with that obtained from the traditional field method for internal partitions. The application of the method is independent of the height of the facade above the ground and the inclination of the facade to the source and can be used with most types of external noise source.

ACKNOWLEDGMENTS The development of the measurement method was carried out at the Building Science Section, School of Architecture, University of Newcastle upon Tyne under the direction of Professor A. C. Hardy. It was sponsored principally by the Science Research Council. The author would like to express his appreciation of the invaluable help given by Mr J. Murta and Mr T. Cox in constructing the equipment and carrying out the measurements.

REFERENCES 1. A. ElSENBER~ 1958 Glastechnische Berichte 1, 597-602. Die Schalldammung yon glasern und verglassungen. 2. W. A. Oos'rING 1967 TNO and TH Technical Physical Service, Delft, Report 706.007. Onderzoek naar de geluidisdatie von vlakglas.

FACADE TRANSMISSION LOSS

137

3. M. JESSE and M. GILBERT 1968 Centre Scientifique et Technique du Bathnent Report DGRBT/ CSTB 64-FR-136. Transmission du bruit a travers les facades. 4. AMERICANSTANDARDSASSOCIATION1970 1970 Book of ASTM Standards. E336. 5. W. E. SCHOLLS and P. H. PARKIN 1968 Applied Acoustics 1, 37--46. The insulation of houses against noise from aircraft in flight. 6. P. T. LEWIS 1970 Building Acoustics (Ed. T. Smith, P. E. O'Sullivan, B. Oakes, R. B. Conn). Newcastle upon Tyne: Oriel Press. See Chapter 5, Real windows. 7. J. LANG 1972 Applied Acoustics 5, 21-37. Differences between acoustical insulation properties measured in the laboratory and results of measurements in situ. 8. A. C. HARDY and P. T. LEWIS 1969 Conference on "Road attd environmentalplannhTg and the reduction of noise", Unicersity of Southampton. Sound insulation standards for buildings adjacent to urban motorways. (Published 1971 Jottrnal of Sound and Vibration 15, 53-59.) 9. K. A. MULLHOLLAND 1971 Applied Acoustics 4, 279-286. Method for measuring the sound insulation of facades: factors to be considered. 10. INTERNATIONAL ORGANIZATION FOR STANDARDIZATION 1972 Fourth Draft ISO Proposal for

11.

FieM and Laboratory 3Ieasurenlents of Airborne Sound Insulation of IVindows, Doors, Facade Elements and Curtain Walls. INTERNATIONAL ORGANIZATION FOR STANDARDIZATION 1960 1S0 Reconlmendation RI40.

Field and laboratory measurement of airborne and impact sound transmission in buildings. 12. BRITiSn STANDARDSINSIrftrrlON 1956 British Standard 2750. Recommendations for field and laboratory measurement of airborne and impact sound transmission in buildings. 13. R. V. WA'rERHOUSE1955 Journal of the Acoustical Society of America 27, 247-258. Interference patterns in reverberant sound fields. 14. W . A . UTLEY 1968 Journal of Sound and Vibration 8, 256--261. Single leaf transmission loss at low frequencies. 15. T. KmLMAN and A. C. NILSSON 1972 Journal of Soundand Vibration 24, 349-364. The effects of some laboratory designs and mounting conditions on Reduction Index measurements. 16. R. F. HIGGINSON 1972 Journal of Sound and Vibration 21,405--429. A study of measuring techniques for airborne sound insulation in buildings. 17. P . T . LEwis 1971 Ph.D. Thesis, University of Newcastle upon Tyne. An investigation of variables associated with road traffic noise and its penetration into buildings.

APPENDIX I T H E O R E T I C A L BASIS GLOSSARY OF SYMBOLS

P; PE E~ J; JK po c cos0 S A

rms pressure of incident sound rms pressure at external surface of facade energy density of incident sound field sound power per unit area incident on facade sound power per unit area radiated by facade density of air velocity of sound in air mean of cosines of angles of incidence area of facade absorption in receiving room

INCIDENT SOUND POWER

(i) Pressure at surface of facade 2 Ifp~, P22 . . . . . p2 are the m e a n square pressures o f t h e s o u n d waves arriving at a p o i n t on the facade from n vehicles in the traffic stream, the total m e a n square pressure, p 2, in the absence o f the facade w o u l d be given b y = y (6) I

138

P.T.

LEWIS

At the facade, a pressure doubling will occur for the sound from each vehicle and so p2 = y. 4p~ = 4 ~ p~. l

(7)

l

Therefore, p~ = 4p~:

(8)

i.e., the sound level at the facade due to a stream of vehicles will be 6 dB higher than that which would occur if no surface were present. (ii) Sound power incident on facade parallel to road It is necessary to express the power per unit area, ./I, incident on the facade in terms of the pressure, pr, recorded by the microphone at the facade. This depends on the relationship between the intensity of the sound field and the angle of incidence. Provided the time interval over which the recording is made is long enough for a reasonable number of vehicles to pass, this relationship may be assumed to be the same as that of a line source, each element of which radiates with uniform power in all directions. Let the road radiate with power Wper unit length per unit solid angle. The energy density of the incident field at O is (see Figure 2(a)) gl

W f ds JEt = c a2 + s2

(9)

Z2

Therefore, W EI = - - [tan -1 (zJa) + tan -1 (z2/a)].

(10)

ac

Ez is related to the pressure at O by

p,~ Ez

=

p~

poc2 -- 4poea .

(11)

The power incident per unit area of the facade at 0 due to an element of road length 6z a t P is W~z Wd6z 'i3p2 cosZ..PON - (a z + z2) 312

(12)

Integrating over the length of road to which the facade is exposed gives Z2

J~ = W d

(13)

(a 2 "[- Z2)3/2 '

7[ z

(14)

From equations (10), (11) and (14),

~=

4poc a [ ' t a ~

1

u tan-l (z~/a)J

(15)

139

FACADE TRANSMISSION LOSS OI"

p~

06)

Jl = 4po c cos 0, where, F

ZI

Z2

0 ~/~+

~e-Z+z;

cos = ~ [ t a - ~ u

-]

I

(17)

arc cos0 can be interpreted as a mean angle of incidence. (iii) Sound power fltcident onfacade perpendicular to road Referring to Figure 2(b), one has, similarly, Et = W t a n - I (z/a)

(18)

tic

and Q

Jt = W

f

zdz

(a' + s2) 3/2"

(19)

0

Therefore,

w[ a]

(20)

From equations (11), (18) and (20), '

a

J' 4poCL

(21) tan--~(z-'~ J

or

Ji =

p~ 4po c

c o s 0,

(22)

where, in this case, a

1 COS 0 =

~/-~--a2+ z 2 tan -l (z/a)

(23)

RADIATED SOUND POWER

The average power radiated by unit area of the facade is related to the r.m.s, pressure in the room by

p~A

Jr . . . . 4po cS

(24)

140

P.T. LEWIS

TRANSMISSIONLOSSOF FACADE The T L of the facade is

,0,ogo()

(25)

From equations (16), (22), (24) and (25), p~2 S

T L = 10 Ioglo-LS--; cos 0. prA

(26)

Therefore, T L = SLr. - SLR + lOloglo(S]A) + loglo (cos 0).

(27)

APPENDIX II Consider a plane sinusoidal pressure wave ofunit amplitude incident on a surface at angle 0. This wave will be reflected by the surface and the mean square pressure at a distance x from the surface, which is the combination of the incident and reflected waves, is given by [13]

where f is the frequency of the wave and c is the speed of sound. This function is plotted a g a i n s t f x c o s O in Figure AI. The mean square pressure of the incident wave is 0.5, and so the presence of the surface causes an increase in sound level, D, given by

This function is also plotted in Figure A1. 6

~

~

I

I

i

tO 08

-~rns. pressure O6 4

Level-~

\

x

04 ~.

}

-02 ~ -04 -O6 I I0

I 20

I 30

I 40

I 50

f x cos ~(mHz)

Figure AI. Curves illustrative of error due to finite size of microphone and consequent finite distance of microphone centre from facade surface.

FACADE TRANSMISSION LOSS

141

The microphone used for the measurement ofthe incident sound had a diameter of 12.5 mm and was placed a distance of approximately 3 mm from the glass. It thus lay between 3 and 15.5 mm from the glass. At a typical angle of incidence, viz., 60 ~ the value o f f x c o s 0 varies between 5 and 25 and the sound level increase between 5.1 and 6.0 dB over the microphone diaphragm. This range reduces with reducing frequency and so in most cases this error can be ignored. If not, allowance for it can be made.