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The airborne sound insulation of glass: Part 1
THE AIRBORNE SOUND INSULATION OF GLASS: PART 1. JACQUELINE A. MARSH
Environmental Advisory Service, Pilkington Brothers Limited, St Helens, Lancs. (Great Britain)
(Received: 15 October, 1970)
SUMMARY
This paper is to be published in three consecutive issties of Applied Acoustics. This first part is a brief survey of the theory and practice of the measurement of the sound insulation of glass. In Part 2 the effects of changes in the various parameters will be discussed. The tabulated data supporting this discussion will constitute the final part. With the increase of noise in the external environment more attention is being focussed on the need for better sound insulation of buildings, l f high sound insulation is required, the window and its design become important. Although results of sound insulation measurements obtained in the laboratory are not strictly comparable with the values achieved hz actual buildings, laboratory measurements are necessary as a basis for design decisions. There is a need for a review of the currently available results of such measurements which this paper is intended to provide. The theoretical aspects of the sound insulation of both single and double panels are briefly outlined but the major part of this paper is concerned with the presentation of the results obtained by various experhnenters. Recommendations as to which window construction should be used for protection against a specific noise, such as traffic noise or aircraft noise, are not made, since this wouM require a discussion of the subjective aspects of noise, which is outside the scope of the present work. 1.
THEORETICAL ASPECTS
NOMENCLATURE a, b c d
dimensions of panel; m velocity of sound in air; 340 m/s separation of panels; m 55
AppliedAcoustics(4) (1971)-----~ Elsevier Publishing Company Ltd, England--Printed in Great Britain
56
J A C Q U E L I N E A. M A R S H
E
f f~ h m, n
M P Pp o"
0 T ¢0
2n
Young's modulus of elasticity; 7 x 10 t° N/m 2 (for glass) frequency; Hz critical frequency; Hz thickness of panel; m integers; mass per unit area of panel; kg/m 2 density of air; 1.2 kg/m 3 density of panel; 2.5 x 10 a kg/m a (for glass) Poisson's ratio; 0.22 (for glass) angle of incidence transmission coefficient angular frequency; rad/s wavelength; m wavelength of bending wave; m
For airborne sound the 'sound transmission coefficient', 3, of a panel is defined as the ratio of the transmitted to the incident sound energy. The transmission loss or sound reduction index is given by:
(1.i)
( T L ) = l0 loglo (~) dB
Single panels The transmission loss of a single panel depends on its mass, stiffness and dimensions. The behaviour of a panel can be divided into three frequency regions as shown in Fig. 1.
Mass: If stiffness can be ignored the transmission loss for an infinite panel, for sound incident at an angle 0, is given t by: (ogM cos
This 'mass law' equation predicts a 6 dB increase in insulation when the weight of the panel is doubled or when the frequency of the incident sound is doubled. The transmission loss will be greatest for normally incident sound, 0 = 0: (TL)o = 101oglo
1+
dB
(1.3)
If sound is incident at all angles, from 0 to O.mi, the total energy transmitted is the sum of that transmitted at each angle of incidence. An average transmission coefficient is obtained by integrating for the transmission coefficient as a function
THE AIRBORNE SOUND INSULATION OF GLASS" PART 1
57
of the angle of incidence over the range 0 to 0.mit. For random incidence, 0~i,.i, = 90 °, the expression for the transmission loss t is:
(1A)
(TL)..dom ~ (TL)o - 10 logto [0-23(TL)o] dB
In practice, sound is not usually incident at all angles up to 90 ° and a smaller limiting angle has been found to give a better agreement between theory and Mass control
Stiffness and resonance control
Wave coincidence
Ik,
Large I ~
//
i
/.~
/Medium
o*"
-"
Lf :\
i';-X..'
i%_.##
i
i
Frequency
Fig. 1.
fc
Theoretical transmission loss of a single panel (BeranekO.
experiment. 1 A value of 01im. = 80 ° is commonly chosen, for this limiting angle the transmission loss is: (TL) ~ (TL)o - 5 dB
(1.5)
Figure 2 shows the insulation for four thicknesses of glass calculated from eqn. (1.5). However, measured insulation values differ from the mass law predictions in certain parts of the frequency range because the mass law is derived assuming that the panel is infinite and that its stiffness can be neglected. A panel of finite size can resonate at certain frequencies, depending on its size, mass, stiffness and edge conditions. A thin rectangular Panel resonances:
58
J A C Q U E L I N E A. M A R S H
panel supported at its four edges can resonate at frequencies f=,. given 1 by:
~:r
--'EhL
fro,. ---- ~ Lppl2(l - a z)
] ~ [ m2 n2] ~ - + ~5 Hz
(1.6)
substituting in this equation the material constants for glass already given:
fm,n ~ 2"5 x 103h
+
Hz
(1.7)
Using this equation, the fundamental resonance frequencies, m = n = 1, have been calculated for three panel sizes and three thicknesses of glass (Table 1).
S0
-6
5"
40
J
10
0 100
200
4OO
6OO
8OO 1000
2O0O
40O0
Frequency in Hertz
Fig. 2. Theoretical transmission loss of single glass (mass law).
Coincidence effect: Above the resonance zone the transmission loss follows the mass law until a frequency is reached at and above which the projected wavelength of the incident sound on the panel can equal the wavelength of free bending waves in the panel (Fig. 3). In this region the transmission loss is reduced because of the efficient coupling between the panel and the air.2
THE AIRBORNE SOUND INSULATION OF GLASS: PART l
59
TABLE 1 FUNDAMENT~ ~NANCEFREQUENCIESFORG~PANE~
(m = n = 1)
Panel dimensions a (m)
b (m)
h (ram)
Resonance frequency (Hz)
0"5
1
1
1
2
1
4 6 12 4 6 12 4 6 12
50 75 150 20 30 60 12 19 38
Direction of bending wave
+
\ Reflected ~F Transmitted
/
Incident
Panel
Fig. 3.
T h e coincidence effect.
JACQUELINE A. MARSH
60 For coincidence:
2 sin 0
(1.8)
At a given frequency, f: c
2
f
CB
and
2s
f
5000
2000
-30
1000
- 45~
o
.e
N
5
Y2
.E
- 75"6 -905
zoo
==
<
kl.
3
12
4
24
Glass thickness in millimetres
Fig. 4.
Theoretical variation of coincidence frequency with glass thickness and angle of incidence.
The velocity of propagation of bending waves in a panel is given 2 by:
[
I m/s
cs = [2nf]~ L12pp(1 - a 2)J
(1.9)
but for coincidence: c
(1.10)
cB - - s i n 0
substituting for cs in eqn. (1.9) the frequency becomes: C2 rl2pe(1 - a2)], f - - 2 n s i n 20 L Eh z j Hz
(i.11)
61
THE AIRBORNE SOUND INSULATION OF GLASS: PART 1
for glass: 12 f ~ h sin2-"-'~Hz
(1.12)
The lowest frequency (critical frequency) at which coincidence can occur is found for 0 = 90 °, grazing incidence:
= ~2 Hz
fc
(1.13)
The critical frequency depends on the stiffness of the panel, for a given material it decreases as the thickness is increased. Figure 4 shows the variation of coincidence frequency with glass thickness for four angles of incidence.
14
Ma.~.air-mess resonance
bJ~
Cavity resonances
Mass control
144
Wave
coincidencegh4
T
Cavity resonances
rI
hJ
"!
I
f
12dB/0ctave
I--
Frequency Fig. 5. Theoretical transmission loss of a double panel (Ford and Lord4). The preceding discussion allows the frequency of the coincidence effect to be calculated but not the magnitude of the transmission loss. In the coincidence region, where the simple mass law is not applicable, the bending stiffness, including the damping or loss factor of the panel, must be taken into account as well as the
62
JACQUELINE A. MARSH
panel mass and the angle of the incident sound. The theory t for the transmission loss in this region indicates that the transmission loss decreases as the angle of the incident sound is increased and increases as the panel damping is increased. Double panels
In addition to the problems associated with single panels (low frequency panel resonances and the coincidence effect) other types of resonance influence the transmission loss of double panels. Figure 5 illustrates the behaviour of a double panel. The resonances will not always occur in separate regions, as shown. A theoretical treatment of the transmission loss of an infinite double panel with isolated leaves has been developed by London. 3 This theory is based on the assumption that the panels are identical and are excited below their critical frequency. Mass-air-mass resonance: London's theory predicts a minimum value of the transmission loss when:
1
[2pc2] t
f = 2ncos------~/MdJ Hz
(1.14)
where M is the mass of each panel. If the panels are not identical, as long as the difference between them is not too great, f--ncos0
M1 + M2) d
Hz
(1.15)
where M 1 and g 2 a r e the masses (kg/m 2) of the panels. The lowest frequency of the mass-air-mass resonance occurs for normally incident sound: f°=n
(M 1 + M2) d
Hz
(1.16)
[i
Hz
(1.17)
for glass:
1
fo ~ 120 Mt + M 2 ) d
Theoretically at fo and for obliquely incident sound at frequencies above fo the transmission loss of a double panel is zero. This does not occur in practice but the reduction in transmission loss at the lowest mass-air-mass resonance frequency can be considerable. Therefore, a double panel should be designed so that f~ is low, at least below 100 Hz. The variation of f~ with glass thickness and the separation between the panes is shown in Fig. 6.
T H E A I R B O R N E S O U N D I N S U L A T I O N OF G L A S S : P A R T
63
1
Cavity resonances: London's theory also predicts a reduction in transmission loss at higher frequencies because of resonances caused by standing waves in the air space between the panels. The transmission loss has a minimum value when C
f. = n ~
Hz
(l.18)
For normal incidence the first standing wave frequency (n = I) is
f=
C
2"d Hz
(1.19)
A theoretical transmission curve, for normal incidence, of a double panel is given in Fig. 7. For a finite double panel other resonances besides the mass-air-mass and high frequency cavity resonances may occur. These are caused by two-dimensional
Mass of panels (Mj + M2 ) in killogrammes per square metre 15
20
30
40
50
60
3OO
2O0
-,o
~-2o
100
=
8O
~-~
~
~.~,~
~
6O
._¢
6
8
12
16
20
24
Thickness of panels (hi + h: ) in millimetres
Fig. 6.
Theoretical variation of lowest mass-air-mass resonance frequency with total glass thickness and pane separation.
64
JACQUELINE
A. MARSH
standing waves in the air space in the plane of the panel, the frequencies of these waves are given 4 by f,... = } ~-T + b~j
Hz
(1.20)
provided that the wavelength of the incident sound is greater than twice the cavity width. 120
f-
100
80
Average
/
60
.;r
I
J
r
/
4O
.S
20
c ~"
0 10
20
40
60
100
200
400 600
1000
2000
4000 6000 10000
Frequency in I'lertz
Fig. 7. Theoretical transmission loss of a double panel. Normal incidence; panel separation 76 mm; mass of each panel 9.7 kg/m 2 (Beranek 1). The reduction in transmission loss due to the resonances associated with double panels can be diminished by placing absorbent material in the cavity between the panels. The preceding discussion has been restricted to a brief summary of the most commonly used equations for examining the transmission loss of panels. Recently, new theories have been published 5,6.7 and the development of these may lead to improved prediction of the transmission loss of panels.
THE AIRBORNE SOUND INSULATION OF GLASS: PART 1
2.
65
MEASUREMENT TECHNIQUES
Before reviewing the measurements of the sound insulation of glazing, the various methods of measurement must be considered (Fig. 8). If the glass panel is situated in the c o m m o n wall between reverberant rooms in which the sound field is diffuse, the transmission loss for random incidence can be expressed 8 as: S (TL) = L 1 - L 2 + 10 log10 ~ dB
(2.1)
Laboratory mmlsurement
Transmission loss
(TL}
8
/ t -- L2 + I0 log/~
diffuse sound field, all sound transmitted through test panel
Field mea~.urement
L~
I
.
~ Normalised Level Difference
A
D , = L t -- Lz + 10 log ~.
diffuse sound field, may be sOme flanking transmission
Laboratorymeasurement
T. (TL)e=Lt - La÷10log"~ •
!,
o
Loudsl)eak (variable position)
Fig. 8.
"~
I1~
L2,T,
directional incidence no flanking transmission
Representation of methods of measuring insulation.
where: L t = average sound pressure level in the source room; L 2 = average sound pressure level in the receiving room; S = area of panel and A = total absorption of the receiving room. This expression can be used provided that the sound pressure level in the source
66
JACQUELINE A. MARSH
room is much greater than that in the receiving room and that the sound is transmitted only through the panel under test. The average sound pressure level, Lt, is defined as: L I = 10 loglo p l
z + pzZ + . . . + p 2 dB npo2
(2.2)
where: Pl, P2 . . . . . Pn = rms sound pressures at n different positions and Po = reference sound pressure. L2 is similarly defined. The International Organisation for Standardisation s and the British 9 Standards on the measurement of sound insulation do not recommend a method for measuring the total absorption in the receiving room: the method usually used is to measure the reverberation time and then to calculate A. The reverberant room method of measuring transmission loss, including the determination of A.. has been the subject of critical examination by Mariner l° and Mulholland and Parbrook. 1 x, 12 When measurements of sound insulation are made in actual buildings, sound may be transmitted not only through the partition under test, but also via flanking paths. Because this differs from the conditions of laboratory tests two other quantities have been defined. Level difference: D = L t - Lz dB (2.3) Normalised level difference: mo
D~v = L t - L2 + 10 loglo -~- dB
(2.4)
where A = measured absorption, Ao -- reference absorption. BS 2750 gives two methods of normalisation (i) reference absorption Ao is taken to be equal to 10 m 2 at all frequencies (ii) for dwellings, since a large number of measurements have shown that the reverberation time of furnished rooms is about 0.5 seconds at most frequencies and from Sabine's formula reverberation time = 0.16 V/A, Ao is taken as 0.32 V (where V is the volume of the receiving room). The problems associated with conducting field measurements have been discussed by a number of authors, for example, Scholes, 13 Schulzi4 and Kasteleijn. 1s The American Standard 16 draws attention to the fact that since the sound transmission loss of a panel is determined for diffuse incident sound the results are most directly applicable to similar sound fields and are not necessarily appropriate in situations where the panel is exposed to a sound field containing only a small range of angles of incidence. To obtain measurements of sound insulation as a function of angle of incidence the following method has been used by Eisenberg 17 and later by Oosting. 1s The panel under test was placed in the external wall of a
THE AIRBORNE SOUND INSULATION OF GLASS: PART 1
67
reverberant room, a highly directional sound source was placed outside at such a distance from the panel that the incident sound waves could be considered to be plane. The source could be moved so that the angle of incidence of the sound was variable from 0 ° to 70 ° i s or 75 °. 17 The sound pressure levels in the reverberant room were measured before and after the installation of the test panel, the output of the source being kept constant; the reverberation times were also measured. If the sound field in the reverberation room can be assumed to be diffuse both with and without the test panel in place the insulation is given by:
Tz
(TL) = L 1 - L 2 + 10 logto "~t dB
(2.5)
where L~ - L2 = the difference in sound pressure levels between before and after installing the test panel; T~ = the reverberation time without the test panel and 7'2 = the reverberation time with the test panel. The transmission coefficient varies with frequency and so, in order to specify the transmission loss of a panel, measurements have to be made at a number of frequencies. The British Standard ~9 states that measurements should be made at third-octave intervals: 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1000, 1250, 1600, 2000, 2500, 3150 Hz The American Standard specifies the minimum range of measurements to be the series of contiguous third-octave bands with centre frequencies from 125 to 4000 Hz and adds: 'If desired, the range may be extended in further third-octave steps downward or upward. Note that extending to lower frequencies will require larger room volumes.' In Britain, prior to I948, measurements were carried out at the following frequencies: 100, 150, 200, 300, 500, 700, 1000, 1600, 2000, 3000, 4000 Hz and the previous American frequencies were: 125, 175, 250, 350, 500, 700, 1000, (1400), 2000, (2800), 4000 Hz Where sound insulation figures are given for specified frequencies there is little danger of confusion; the difficulties arise when trying to compare the average values. Because the sound transmission loss o f most panels is lower at low frequencies than at high, the American measurements (125 to 4000 Hz) tend to indicate a higher average transmission loss than the British (100 to 3150 Hz). 20 The signal used for transmission loss measurements is usually white noise but a warble tone may be used. The British Standard does not state how many sources or microphone positions should be used ' . . . as these will depend on the conditions and the accuracy required.'
68
JACQUELINE A. MARSH
For laboratory measurements the following conditions are stipulated: Volume of r o o m at least 100 m 3. Size of test specimen 10 m 2 minimum dimension 2-5 m. Edge conditions of test wall or floor should be as practical conditions and stated. Sound transmitted by any indirect path should be small compared with that through the test panel. Sound should be as diffuse and isotropic as possible. Size of test specimen and volume of reverberant room should be stated. The British Standard does not comment on measurements of building elements, such as doors, which are smaller than I0 m 2. The American Standard states that 'specimens of doors and other smaller building elements shall be their customary size. Preformed panel structures should include at least two complete modules (panels plus edge mounting elements)'. Although the introduction of similar standards makes the task of comparing results from different laboratories easier, the results may vary even when standard procedures have been adopted. Utley 2t has drawn attention to the discrepancies which may arise when the same panel is tested in different laboratories and he suggests that these discrepancies are not entirely due to the panel but to some property of the transmission suite. He did not ascertain which property accounted for the differences, which occurred usually at low frequencies, but pointed out that it would make comparison of measurements easier if transmission suites were more closely standardised or if the suites were 'calibrated' by measuring the transmission loss of a standard panel, a heavy limp panel such as lead. In a theoretical treatment of the sound transmission between two reverberant rooms for a single panel the effect of varying room conditions and number of sources has been investigated. 22 A computer was used to calculate the transmission loss and it indicated that any dissimilarity between the source room and receiving room would tend to increase the transmission loss. A comparison between the transmission loss for a 3 m m hardboard panel between identical rooms and the same panel tested with the source room longer than the receiving room predicted an increase in transmission loss for both high and low frequencies. A low frequency increase in insulation was also predicted if the velocity of sound in the source room differed from that in the receiving room, which could be caused by a temperature difference. If the source room is excited by two sources the calculations predicted that the transmission loss at low frequencies would be less than that obtained when only one source was used. This prediction was confirmed by measurements. Kihlman 23 has also studied the effect of r o o m dimensions and loudspeaker arrangements with particular reference to field measurements of airborne sound transmission in dwellings. From a theoretical analysis and measurements in model
THE AIRBORNE SOUND INSULATIONOF GLASS: PAR'[ 1
69
chambers he concluded, similarly, that insulation can be systematically lower if the r o o m s are equal t h a n if their d i m e n s i o n s are unequal. The effect on s o u n d transmission of a difference in air temperature between source a n d receiving r o o m s has been observed by Scholes 2'~ in field measurements of the insulation between two equal r o o m s (volume 40-3 mS). F o r example, when the temperature in the receiving r o o m was 3.5 deg C higher than in the source r o o m the s o u n d pressure level (for the third-octave b a n d centred o n 100 Hz) at one position in the receiving r o o m was 5 dB less t h a n the level at the same position when the temperatures of the two r o o m s were the same.
REFERENCES 1. L. L. BERANEK,The transmission and radiation of acoustic waves by solid structures, Noise Reduction, edited by L. L. Bcranek, McGraw-Hill, New York, 1960, 280. 2. L. CREMER,Sound-insulation of panels at oblique incidence. Noise and Sound Transmission. Report of the 1948 Summer Symposium of the Acoustics Group. The Physical Society, London, 1948, 23. 3. A. LONDON,Transmission of reverberant sound through double walls, J. Acoust. Soc. Am., 22 (1950) 270. 4. R. D. FORD and P. LORD, Practical problems of partition design, J. Acoust. Soc. Am., 43 (1968) 1062. 5. K. A. MULHOLLAND,A. J. PRICEand H. D. PARBROOK,Transmission loss of multiple panels in a random incidence field, J. Acoust. Soc. Am., 43 (1968) 1432. 6. M. J. CROCKERand A. J. PRICE,Sound transmission using statistical energy analysis, J. Sound and Vibration, 9 (1969) 469. 7. B. H. S. SHARPand J. W. BEAUCHAMP,The transmission loss of multi-layer structures, J. Sound and Vibration, 9 (1969) 383. 8. Field and laboratory measurements of airborne and impact sound transmission. ISO R140-1960 (E), International Organisation for Standardisation. 9. Rec•mmendati•ns f•r•e•d and •ab•rat•ry measurement •f a•rb•rne and impact s•und transmissi•n in buildings. BS 2750: 1956, British Standards Institution. 10. T. MARINER,Critique of the reverberant room method of measuring airborne sound transmission loss, J. Aeoust. Soc. Am., 33 (1961) 1131. 11. K. A. MULHOLLANDand H. D. PARBROOK,The measurement of sound transmission loss of panels with small transmission loss, J. Sound and Vibration, 2 (1965) 502. 12. K.A. MULHOLLANDand H. D. PARBROOK,The measurement of transmission loss (letter to the editor), J. Sound and Vibration, 5 (1967) 391. 13. W. E. SCHOLES, Sound insulation performance assessment, Symposh¢m on Sound Insulation Measurements and the Building Regulations, Building Research Station, December 1967. 14. T. J. SCHULTZ, A new standard for the field measurement of airborne transmission loss, 5e Congr~s International d'Acoustique, Universit~ de Lidge, 1965, Paper F 34. 15. M. L. KASTELEIJN,The statistical spread of measured airborne and impact sound insulation in the field, J. Soundand Vibration, 3 (1966) 36. 16. Tentative recommended practice for laboratory measurement of airborne sound transmission loss of building partitions, American Society for Testing and Materials, E90-66T, 1967. 17. A. EISENBERG, Die Schalldimmung von Gl~tsern und Verglasungen. I-Fest eingebaute Einfachscheiben (The sound insulation of glasses and glazing, l-Firmly fitted single panes), Glastechnische Berichte, 31 (1958) 297. 18. W. A. Oos'rtNG, Onderzoek naar de Geluidisolatie van Vlakglas (Investigation of the sound insulation of flat glass). Report 706,007, Delft, Building Acoustics, Technical Physical Service, TNO and TH, April 1967. See also: P. A. DE LANGE, Sound insulation of glazing with respect to traffic noise, Applied Acoustics, 2 (1969) 215. 19. Amendment No. 1 to BS 2750: 1956. British Standards Institution, 1963. 20. P. H. PARKIN, American and European standard methods for measurement of sound transmission in buildings (letter to the editor), J. Acoust. Soc. Am., 24 (1952) 542.
70
JACQUELINE A. MARSH
21. W. A. UTLEY, Single leaf transmission loss at low frequencies, J. Sound and Vibration, 18 (1968) 256. 22. Building Research Station, Private communication, 1969. 23. T. KmLMAS, Sound radiation into a rectangular room. Applications to airborne sound transmission in buildings, Acustica, 18 (1967) 11. 24. W. E. SCHOLES,A note on the repeatability of field measurements of airborne sound insulation, J. Sound and Vibration, 10 (1969) 1.
(To be continued)
Environmental Advisory Service, Pilkington Brothers Limited, St Helens, Lancs. (Great Britain)
(Received: 15 October, 1970)
SUMMARY
This paper is to be published in three consecutive issties of Applied Acoustics. This first part is a brief survey of the theory and practice of the measurement of the sound insulation of glass. In Part 2 the effects of changes in the various parameters will be discussed. The tabulated data supporting this discussion will constitute the final part. With the increase of noise in the external environment more attention is being focussed on the need for better sound insulation of buildings, l f high sound insulation is required, the window and its design become important. Although results of sound insulation measurements obtained in the laboratory are not strictly comparable with the values achieved hz actual buildings, laboratory measurements are necessary as a basis for design decisions. There is a need for a review of the currently available results of such measurements which this paper is intended to provide. The theoretical aspects of the sound insulation of both single and double panels are briefly outlined but the major part of this paper is concerned with the presentation of the results obtained by various experhnenters. Recommendations as to which window construction should be used for protection against a specific noise, such as traffic noise or aircraft noise, are not made, since this wouM require a discussion of the subjective aspects of noise, which is outside the scope of the present work. 1.
THEORETICAL ASPECTS
NOMENCLATURE a, b c d
dimensions of panel; m velocity of sound in air; 340 m/s separation of panels; m 55
AppliedAcoustics(4) (1971)-----~ Elsevier Publishing Company Ltd, England--Printed in Great Britain
56
J A C Q U E L I N E A. M A R S H
E
f f~ h m, n
M P Pp o"
0 T ¢0
2n
Young's modulus of elasticity; 7 x 10 t° N/m 2 (for glass) frequency; Hz critical frequency; Hz thickness of panel; m integers; mass per unit area of panel; kg/m 2 density of air; 1.2 kg/m 3 density of panel; 2.5 x 10 a kg/m a (for glass) Poisson's ratio; 0.22 (for glass) angle of incidence transmission coefficient angular frequency; rad/s wavelength; m wavelength of bending wave; m
For airborne sound the 'sound transmission coefficient', 3, of a panel is defined as the ratio of the transmitted to the incident sound energy. The transmission loss or sound reduction index is given by:
(1.i)
( T L ) = l0 loglo (~) dB
Single panels The transmission loss of a single panel depends on its mass, stiffness and dimensions. The behaviour of a panel can be divided into three frequency regions as shown in Fig. 1.
Mass: If stiffness can be ignored the transmission loss for an infinite panel, for sound incident at an angle 0, is given t by: (ogM cos
This 'mass law' equation predicts a 6 dB increase in insulation when the weight of the panel is doubled or when the frequency of the incident sound is doubled. The transmission loss will be greatest for normally incident sound, 0 = 0: (TL)o = 101oglo
1+
dB
(1.3)
If sound is incident at all angles, from 0 to O.mi, the total energy transmitted is the sum of that transmitted at each angle of incidence. An average transmission coefficient is obtained by integrating for the transmission coefficient as a function
THE AIRBORNE SOUND INSULATION OF GLASS" PART 1
57
of the angle of incidence over the range 0 to 0.mit. For random incidence, 0~i,.i, = 90 °, the expression for the transmission loss t is:
(1A)
(TL)..dom ~ (TL)o - 10 logto [0-23(TL)o] dB
In practice, sound is not usually incident at all angles up to 90 ° and a smaller limiting angle has been found to give a better agreement between theory and Mass control
Stiffness and resonance control
Wave coincidence
Ik,
Large I ~
//
i
/.~
/Medium
o*"
-"
Lf :\
i';-X..'
i%_.##
i
i
Frequency
Fig. 1.
fc
Theoretical transmission loss of a single panel (BeranekO.
experiment. 1 A value of 01im. = 80 ° is commonly chosen, for this limiting angle the transmission loss is: (TL) ~ (TL)o - 5 dB
(1.5)
Figure 2 shows the insulation for four thicknesses of glass calculated from eqn. (1.5). However, measured insulation values differ from the mass law predictions in certain parts of the frequency range because the mass law is derived assuming that the panel is infinite and that its stiffness can be neglected. A panel of finite size can resonate at certain frequencies, depending on its size, mass, stiffness and edge conditions. A thin rectangular Panel resonances:
58
J A C Q U E L I N E A. M A R S H
panel supported at its four edges can resonate at frequencies f=,. given 1 by:
~:r
--'EhL
fro,. ---- ~ Lppl2(l - a z)
] ~ [ m2 n2] ~ - + ~5 Hz
(1.6)
substituting in this equation the material constants for glass already given:
fm,n ~ 2"5 x 103h
+
Hz
(1.7)
Using this equation, the fundamental resonance frequencies, m = n = 1, have been calculated for three panel sizes and three thicknesses of glass (Table 1).
S0
-6
5"
40
J
10
0 100
200
4OO
6OO
8OO 1000
2O0O
40O0
Frequency in Hertz
Fig. 2. Theoretical transmission loss of single glass (mass law).
Coincidence effect: Above the resonance zone the transmission loss follows the mass law until a frequency is reached at and above which the projected wavelength of the incident sound on the panel can equal the wavelength of free bending waves in the panel (Fig. 3). In this region the transmission loss is reduced because of the efficient coupling between the panel and the air.2
THE AIRBORNE SOUND INSULATION OF GLASS: PART l
59
TABLE 1 FUNDAMENT~ ~NANCEFREQUENCIESFORG~PANE~
(m = n = 1)
Panel dimensions a (m)
b (m)
h (ram)
Resonance frequency (Hz)
0"5
1
1
1
2
1
4 6 12 4 6 12 4 6 12
50 75 150 20 30 60 12 19 38
Direction of bending wave
+
\ Reflected ~F Transmitted
/
Incident
Panel
Fig. 3.
T h e coincidence effect.
JACQUELINE A. MARSH
60 For coincidence:
2 sin 0
(1.8)
At a given frequency, f: c
2
f
CB
and
2s
f
5000
2000
-30
1000
- 45~
o
.e
N
5
Y2
.E
- 75"6 -905
zoo
==
<
kl.
3
12
4
24
Glass thickness in millimetres
Fig. 4.
Theoretical variation of coincidence frequency with glass thickness and angle of incidence.
The velocity of propagation of bending waves in a panel is given 2 by:
[
I m/s
cs = [2nf]~ L12pp(1 - a 2)J
(1.9)
but for coincidence: c
(1.10)
cB - - s i n 0
substituting for cs in eqn. (1.9) the frequency becomes: C2 rl2pe(1 - a2)], f - - 2 n s i n 20 L Eh z j Hz
(i.11)
61
THE AIRBORNE SOUND INSULATION OF GLASS: PART 1
for glass: 12 f ~ h sin2-"-'~Hz
(1.12)
The lowest frequency (critical frequency) at which coincidence can occur is found for 0 = 90 °, grazing incidence:
= ~2 Hz
fc
(1.13)
The critical frequency depends on the stiffness of the panel, for a given material it decreases as the thickness is increased. Figure 4 shows the variation of coincidence frequency with glass thickness for four angles of incidence.
14
Ma.~.air-mess resonance
bJ~
Cavity resonances
Mass control
144
Wave
coincidencegh4
T
Cavity resonances
rI
hJ
"!
I
f
12dB/0ctave
I--
Frequency Fig. 5. Theoretical transmission loss of a double panel (Ford and Lord4). The preceding discussion allows the frequency of the coincidence effect to be calculated but not the magnitude of the transmission loss. In the coincidence region, where the simple mass law is not applicable, the bending stiffness, including the damping or loss factor of the panel, must be taken into account as well as the
62
JACQUELINE A. MARSH
panel mass and the angle of the incident sound. The theory t for the transmission loss in this region indicates that the transmission loss decreases as the angle of the incident sound is increased and increases as the panel damping is increased. Double panels
In addition to the problems associated with single panels (low frequency panel resonances and the coincidence effect) other types of resonance influence the transmission loss of double panels. Figure 5 illustrates the behaviour of a double panel. The resonances will not always occur in separate regions, as shown. A theoretical treatment of the transmission loss of an infinite double panel with isolated leaves has been developed by London. 3 This theory is based on the assumption that the panels are identical and are excited below their critical frequency. Mass-air-mass resonance: London's theory predicts a minimum value of the transmission loss when:
1
[2pc2] t
f = 2ncos------~/MdJ Hz
(1.14)
where M is the mass of each panel. If the panels are not identical, as long as the difference between them is not too great, f--ncos0
M1 + M2) d
Hz
(1.15)
where M 1 and g 2 a r e the masses (kg/m 2) of the panels. The lowest frequency of the mass-air-mass resonance occurs for normally incident sound: f°=n
(M 1 + M2) d
Hz
(1.16)
[i
Hz
(1.17)
for glass:
1
fo ~ 120 Mt + M 2 ) d
Theoretically at fo and for obliquely incident sound at frequencies above fo the transmission loss of a double panel is zero. This does not occur in practice but the reduction in transmission loss at the lowest mass-air-mass resonance frequency can be considerable. Therefore, a double panel should be designed so that f~ is low, at least below 100 Hz. The variation of f~ with glass thickness and the separation between the panes is shown in Fig. 6.
T H E A I R B O R N E S O U N D I N S U L A T I O N OF G L A S S : P A R T
63
1
Cavity resonances: London's theory also predicts a reduction in transmission loss at higher frequencies because of resonances caused by standing waves in the air space between the panels. The transmission loss has a minimum value when C
f. = n ~
Hz
(l.18)
For normal incidence the first standing wave frequency (n = I) is
f=
C
2"d Hz
(1.19)
A theoretical transmission curve, for normal incidence, of a double panel is given in Fig. 7. For a finite double panel other resonances besides the mass-air-mass and high frequency cavity resonances may occur. These are caused by two-dimensional
Mass of panels (Mj + M2 ) in killogrammes per square metre 15
20
30
40
50
60
3OO
2O0
-,o
~-2o
100
=
8O
~-~
~
~.~,~
~
6O
._¢
6
8
12
16
20
24
Thickness of panels (hi + h: ) in millimetres
Fig. 6.
Theoretical variation of lowest mass-air-mass resonance frequency with total glass thickness and pane separation.
64
JACQUELINE
A. MARSH
standing waves in the air space in the plane of the panel, the frequencies of these waves are given 4 by f,... = } ~-T + b~j
Hz
(1.20)
provided that the wavelength of the incident sound is greater than twice the cavity width. 120
f-
100
80
Average
/
60
.;r
I
J
r
/
4O
.S
20
c ~"
0 10
20
40
60
100
200
400 600
1000
2000
4000 6000 10000
Frequency in I'lertz
Fig. 7. Theoretical transmission loss of a double panel. Normal incidence; panel separation 76 mm; mass of each panel 9.7 kg/m 2 (Beranek 1). The reduction in transmission loss due to the resonances associated with double panels can be diminished by placing absorbent material in the cavity between the panels. The preceding discussion has been restricted to a brief summary of the most commonly used equations for examining the transmission loss of panels. Recently, new theories have been published 5,6.7 and the development of these may lead to improved prediction of the transmission loss of panels.
THE AIRBORNE SOUND INSULATION OF GLASS: PART 1
2.
65
MEASUREMENT TECHNIQUES
Before reviewing the measurements of the sound insulation of glazing, the various methods of measurement must be considered (Fig. 8). If the glass panel is situated in the c o m m o n wall between reverberant rooms in which the sound field is diffuse, the transmission loss for random incidence can be expressed 8 as: S (TL) = L 1 - L 2 + 10 log10 ~ dB
(2.1)
Laboratory mmlsurement
Transmission loss
(TL}
8
/ t -- L2 + I0 log/~
diffuse sound field, all sound transmitted through test panel
Field mea~.urement
L~
I
.
~ Normalised Level Difference
A
D , = L t -- Lz + 10 log ~.
diffuse sound field, may be sOme flanking transmission
Laboratorymeasurement
T. (TL)e=Lt - La÷10log"~ •
!,
o
Loudsl)eak (variable position)
Fig. 8.
"~
I1~
L2,T,
directional incidence no flanking transmission
Representation of methods of measuring insulation.
where: L t = average sound pressure level in the source room; L 2 = average sound pressure level in the receiving room; S = area of panel and A = total absorption of the receiving room. This expression can be used provided that the sound pressure level in the source
66
JACQUELINE A. MARSH
room is much greater than that in the receiving room and that the sound is transmitted only through the panel under test. The average sound pressure level, Lt, is defined as: L I = 10 loglo p l
z + pzZ + . . . + p 2 dB npo2
(2.2)
where: Pl, P2 . . . . . Pn = rms sound pressures at n different positions and Po = reference sound pressure. L2 is similarly defined. The International Organisation for Standardisation s and the British 9 Standards on the measurement of sound insulation do not recommend a method for measuring the total absorption in the receiving room: the method usually used is to measure the reverberation time and then to calculate A. The reverberant room method of measuring transmission loss, including the determination of A.. has been the subject of critical examination by Mariner l° and Mulholland and Parbrook. 1 x, 12 When measurements of sound insulation are made in actual buildings, sound may be transmitted not only through the partition under test, but also via flanking paths. Because this differs from the conditions of laboratory tests two other quantities have been defined. Level difference: D = L t - Lz dB (2.3) Normalised level difference: mo
D~v = L t - L2 + 10 loglo -~- dB
(2.4)
where A = measured absorption, Ao -- reference absorption. BS 2750 gives two methods of normalisation (i) reference absorption Ao is taken to be equal to 10 m 2 at all frequencies (ii) for dwellings, since a large number of measurements have shown that the reverberation time of furnished rooms is about 0.5 seconds at most frequencies and from Sabine's formula reverberation time = 0.16 V/A, Ao is taken as 0.32 V (where V is the volume of the receiving room). The problems associated with conducting field measurements have been discussed by a number of authors, for example, Scholes, 13 Schulzi4 and Kasteleijn. 1s The American Standard 16 draws attention to the fact that since the sound transmission loss of a panel is determined for diffuse incident sound the results are most directly applicable to similar sound fields and are not necessarily appropriate in situations where the panel is exposed to a sound field containing only a small range of angles of incidence. To obtain measurements of sound insulation as a function of angle of incidence the following method has been used by Eisenberg 17 and later by Oosting. 1s The panel under test was placed in the external wall of a
THE AIRBORNE SOUND INSULATION OF GLASS: PART 1
67
reverberant room, a highly directional sound source was placed outside at such a distance from the panel that the incident sound waves could be considered to be plane. The source could be moved so that the angle of incidence of the sound was variable from 0 ° to 70 ° i s or 75 °. 17 The sound pressure levels in the reverberant room were measured before and after the installation of the test panel, the output of the source being kept constant; the reverberation times were also measured. If the sound field in the reverberation room can be assumed to be diffuse both with and without the test panel in place the insulation is given by:
Tz
(TL) = L 1 - L 2 + 10 logto "~t dB
(2.5)
where L~ - L2 = the difference in sound pressure levels between before and after installing the test panel; T~ = the reverberation time without the test panel and 7'2 = the reverberation time with the test panel. The transmission coefficient varies with frequency and so, in order to specify the transmission loss of a panel, measurements have to be made at a number of frequencies. The British Standard ~9 states that measurements should be made at third-octave intervals: 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1000, 1250, 1600, 2000, 2500, 3150 Hz The American Standard specifies the minimum range of measurements to be the series of contiguous third-octave bands with centre frequencies from 125 to 4000 Hz and adds: 'If desired, the range may be extended in further third-octave steps downward or upward. Note that extending to lower frequencies will require larger room volumes.' In Britain, prior to I948, measurements were carried out at the following frequencies: 100, 150, 200, 300, 500, 700, 1000, 1600, 2000, 3000, 4000 Hz and the previous American frequencies were: 125, 175, 250, 350, 500, 700, 1000, (1400), 2000, (2800), 4000 Hz Where sound insulation figures are given for specified frequencies there is little danger of confusion; the difficulties arise when trying to compare the average values. Because the sound transmission loss o f most panels is lower at low frequencies than at high, the American measurements (125 to 4000 Hz) tend to indicate a higher average transmission loss than the British (100 to 3150 Hz). 20 The signal used for transmission loss measurements is usually white noise but a warble tone may be used. The British Standard does not state how many sources or microphone positions should be used ' . . . as these will depend on the conditions and the accuracy required.'
68
JACQUELINE A. MARSH
For laboratory measurements the following conditions are stipulated: Volume of r o o m at least 100 m 3. Size of test specimen 10 m 2 minimum dimension 2-5 m. Edge conditions of test wall or floor should be as practical conditions and stated. Sound transmitted by any indirect path should be small compared with that through the test panel. Sound should be as diffuse and isotropic as possible. Size of test specimen and volume of reverberant room should be stated. The British Standard does not comment on measurements of building elements, such as doors, which are smaller than I0 m 2. The American Standard states that 'specimens of doors and other smaller building elements shall be their customary size. Preformed panel structures should include at least two complete modules (panels plus edge mounting elements)'. Although the introduction of similar standards makes the task of comparing results from different laboratories easier, the results may vary even when standard procedures have been adopted. Utley 2t has drawn attention to the discrepancies which may arise when the same panel is tested in different laboratories and he suggests that these discrepancies are not entirely due to the panel but to some property of the transmission suite. He did not ascertain which property accounted for the differences, which occurred usually at low frequencies, but pointed out that it would make comparison of measurements easier if transmission suites were more closely standardised or if the suites were 'calibrated' by measuring the transmission loss of a standard panel, a heavy limp panel such as lead. In a theoretical treatment of the sound transmission between two reverberant rooms for a single panel the effect of varying room conditions and number of sources has been investigated. 22 A computer was used to calculate the transmission loss and it indicated that any dissimilarity between the source room and receiving room would tend to increase the transmission loss. A comparison between the transmission loss for a 3 m m hardboard panel between identical rooms and the same panel tested with the source room longer than the receiving room predicted an increase in transmission loss for both high and low frequencies. A low frequency increase in insulation was also predicted if the velocity of sound in the source room differed from that in the receiving room, which could be caused by a temperature difference. If the source room is excited by two sources the calculations predicted that the transmission loss at low frequencies would be less than that obtained when only one source was used. This prediction was confirmed by measurements. Kihlman 23 has also studied the effect of r o o m dimensions and loudspeaker arrangements with particular reference to field measurements of airborne sound transmission in dwellings. From a theoretical analysis and measurements in model
THE AIRBORNE SOUND INSULATIONOF GLASS: PAR'[ 1
69
chambers he concluded, similarly, that insulation can be systematically lower if the r o o m s are equal t h a n if their d i m e n s i o n s are unequal. The effect on s o u n d transmission of a difference in air temperature between source a n d receiving r o o m s has been observed by Scholes 2'~ in field measurements of the insulation between two equal r o o m s (volume 40-3 mS). F o r example, when the temperature in the receiving r o o m was 3.5 deg C higher than in the source r o o m the s o u n d pressure level (for the third-octave b a n d centred o n 100 Hz) at one position in the receiving r o o m was 5 dB less t h a n the level at the same position when the temperatures of the two r o o m s were the same.
REFERENCES 1. L. L. BERANEK,The transmission and radiation of acoustic waves by solid structures, Noise Reduction, edited by L. L. Bcranek, McGraw-Hill, New York, 1960, 280. 2. L. CREMER,Sound-insulation of panels at oblique incidence. Noise and Sound Transmission. Report of the 1948 Summer Symposium of the Acoustics Group. The Physical Society, London, 1948, 23. 3. A. LONDON,Transmission of reverberant sound through double walls, J. Acoust. Soc. Am., 22 (1950) 270. 4. R. D. FORD and P. LORD, Practical problems of partition design, J. Acoust. Soc. Am., 43 (1968) 1062. 5. K. A. MULHOLLAND,A. J. PRICEand H. D. PARBROOK,Transmission loss of multiple panels in a random incidence field, J. Acoust. Soc. Am., 43 (1968) 1432. 6. M. J. CROCKERand A. J. PRICE,Sound transmission using statistical energy analysis, J. Sound and Vibration, 9 (1969) 469. 7. B. H. S. SHARPand J. W. BEAUCHAMP,The transmission loss of multi-layer structures, J. Sound and Vibration, 9 (1969) 383. 8. Field and laboratory measurements of airborne and impact sound transmission. ISO R140-1960 (E), International Organisation for Standardisation. 9. Rec•mmendati•ns f•r•e•d and •ab•rat•ry measurement •f a•rb•rne and impact s•und transmissi•n in buildings. BS 2750: 1956, British Standards Institution. 10. T. MARINER,Critique of the reverberant room method of measuring airborne sound transmission loss, J. Aeoust. Soc. Am., 33 (1961) 1131. 11. K. A. MULHOLLANDand H. D. PARBROOK,The measurement of sound transmission loss of panels with small transmission loss, J. Sound and Vibration, 2 (1965) 502. 12. K.A. MULHOLLANDand H. D. PARBROOK,The measurement of transmission loss (letter to the editor), J. Sound and Vibration, 5 (1967) 391. 13. W. E. SCHOLES, Sound insulation performance assessment, Symposh¢m on Sound Insulation Measurements and the Building Regulations, Building Research Station, December 1967. 14. T. J. SCHULTZ, A new standard for the field measurement of airborne transmission loss, 5e Congr~s International d'Acoustique, Universit~ de Lidge, 1965, Paper F 34. 15. M. L. KASTELEIJN,The statistical spread of measured airborne and impact sound insulation in the field, J. Soundand Vibration, 3 (1966) 36. 16. Tentative recommended practice for laboratory measurement of airborne sound transmission loss of building partitions, American Society for Testing and Materials, E90-66T, 1967. 17. A. EISENBERG, Die Schalldimmung von Gl~tsern und Verglasungen. I-Fest eingebaute Einfachscheiben (The sound insulation of glasses and glazing, l-Firmly fitted single panes), Glastechnische Berichte, 31 (1958) 297. 18. W. A. Oos'rtNG, Onderzoek naar de Geluidisolatie van Vlakglas (Investigation of the sound insulation of flat glass). Report 706,007, Delft, Building Acoustics, Technical Physical Service, TNO and TH, April 1967. See also: P. A. DE LANGE, Sound insulation of glazing with respect to traffic noise, Applied Acoustics, 2 (1969) 215. 19. Amendment No. 1 to BS 2750: 1956. British Standards Institution, 1963. 20. P. H. PARKIN, American and European standard methods for measurement of sound transmission in buildings (letter to the editor), J. Acoust. Soc. Am., 24 (1952) 542.
70
JACQUELINE A. MARSH
21. W. A. UTLEY, Single leaf transmission loss at low frequencies, J. Sound and Vibration, 18 (1968) 256. 22. Building Research Station, Private communication, 1969. 23. T. KmLMAS, Sound radiation into a rectangular room. Applications to airborne sound transmission in buildings, Acustica, 18 (1967) 11. 24. W. E. SCHOLES,A note on the repeatability of field measurements of airborne sound insulation, J. Sound and Vibration, 10 (1969) 1.
(To be continued)