The measurement of sound radiation from room surfaces in lightweight buildings

THE MEASUREMENT OF SOUND RADIATION FROM ROOM SURFACES IN LIGHTWEIGHT BUILDINGS

J. A. MACADAM

Building Research Establishment, Department of the Environment, Garston, Hertfordshire (Great Britain)

SUMMA R Y

When investigating the transmission of sound within a building it is useful to measure the sound powers being radiated by individual room surfaces. This is normally accomplished using the 'accelerometer method'. This method is shown to be unsuitable for use in lightweight buildings, and a new 'direct' method, suitable for general application, is described. The equipment required by the direct method is detailed, and the magnitudes of the inaccuracies involved in its use are estimated. An account is given of the successful testing o f the method on lightweight panels radiating into an anechoic chamber, and the application of the method to actual constructions is described.

INTRODUCTION

The overall transmission of sound within buildings can be studied in the field and in experimental constructions. 1-9 In both cases it is useful to measure the sound powers being radiated by individual room surfaces. The dominant radiating surfaces can then be identified, and for adjacent source and receiving rooms the direct and structure-borne flanking components of transmission can be separated. Knowledge of the sound powers radiated by individual surfaces also helps in the tracing of flanking paths through a construction.

ACCELEROMETER METHOD

The sound power radiated by a room surface is normally measured by the accelerometer method due to Westphal. io This method is based on the relation: 103 Applied Acoustics (9) (1976)--© Applied Science Publishers Ltd, England, 1976 Printed in Great Britain

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n = pcu 2 As (1) where: p = density of air; c = velocity of sound in air; A = area of radiating surface; u = rms (with respect to both position and time) transverse velocity of surface and n = radiated power, s is dimensionless and is known as the surface's 'radiation factor'. This factor is in general a function of frequency (of surface vibration and radiated sound) and of the characteristics of the structure and the manner in which it is excited into vibration. However, at frequencies greater than the structure's 'critical frequency '1~ s tends to unity independently of structural and excitational characteristics. Therefore, over the frequency range of interest, from about 100 Hz to about 3 kHz: 7z - p c u 2 A if fc < 100 Hz (2) where:fc = critical frequency. Critical frequencies for structures contained in traditional heavy types of buildings do just about satisfy this criterion 11; therefore the accelerometer method, assuming a radiation factor of unity, is perfectly satisfactory for this type o f building. For a particular frequency--or, more usually, frequency b a n d - - o f excitation the rms transverse velocity is measured at five or six positions on the surface using a vibration transducer (accelerometer). The mean square value of these readings is an estimate of u 2, and the radiated power follows from eqn. (2). However, the method is subject to sampling error. This increases as the complexity of the structure increases, but decreases as the bandwidth of excitation is increased. Furthermore, the measured velocities contain a component due to the vibration of the structure by the sound-field in the receiving room. This component is generally much smaller than the velocities associated with the radiation of sound by the surface, 12 but inaccuracies can occur where little power is being radiated. An obvious example is that of a window opposite a strongly radiating party wall.

LIGHTWEIGHT BUILDINGS

Lightweight buildings contain structures with critical frequencies well within the frequency range of interest from 100 Hz to 3 kHz. Radiation factors can, therefore, no longer be assumed to equal unity. This is illustrated by Fig. 1, which shows the radiation factor, in the form 10 logloS, for a stud-frame panel subjected to mechanical excitation at its centre. In most instances this form of excitation is equivalent to the edge excitation which occurs with structure-borne flanking transmission. 13 Figure 2 shows the third-octave sound powers radiated by the panel with constant rms transverse velocity at the point of excitation. Also shown are the powers as calculated from the accelerometer method assuming a radiation factor of one. It can be seen that the accelerometer method cannot be applied to lightweight buildings where the precise construction is not known.

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airborne (direct) excitation than for edge (flanking) excitation, and a difference of l0 dB can exist below the critical frequency. This is illustrated by Fig. 3 which shows the radiation factors for airborne and mechanical excitation of a l0 m m thick steel plate. The critical frequency of this plate is around 1.25 kHz.

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Since the accelerometer method cannot be used in lightweight buildings a new 'direct' method has been developed. The sound power being radiated by a vibrating surface is equal to the rate at which the surface does work on the air in contact with it. The mean radiated power is therefore given by: rt =

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The value of the work function at (x,y) is the mean rate at which work is being done per unit area at (x,)'). Then: n = WA (5) where: W = mean value of the work function over the surface. The direct method determines the value of the work function at several points on the surface, the mean value is calculated, and the radiated power follows from eqn. (5). The value of the work function at a particular point is measured using eqn. (4). The equipment required to do this is shown in Fig. 4. The acoustic pressure is measured by a half inch microphone, the diaphragm of which is placed as closely as possible to the surface without touching. The surface transverse velocity is measured with a 30 gramme piezoelectric accelerometer waxed to the surface as close to the microphone as possible, again without touching. A low capacity cable

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required for the lower frequency bands of random excitation, where relatively long-term variations in pressure and velocity occur. The output from the 'multiplier-integrator' is examined on an oscilloscope. From eqn. (4) this output is proportional to the value of the work function at the measuring position. The constant of proportionality depends on the microphone sensitivity, the accelerometer and integrating preamp sensitivity, the spectrometer gain settings, and the integration time employed. INACCURACIES

The small separation, of about 5 mm, of the microphone diaphragm from the surface and the small offset, of about 15 ram, of the accelerometer from the measuring position introduce an inaccuracy into the radiated power as measured by the direct method. However, this inaccuracy is less than 1 dB for all practical situations. 12 The method is also subject to sampling error, to about the same extent as the accelerometer method. 12 For instance, the spread in six work function readings over a clinker-block wall subjected to airborne excitation was 9 dB for the 100 Hz third-octave and 2-4 dB for the 3-15 kHz third-octave. The direct method measures the resultant power radiated by a room surface. That is, it measures the difference between the power as radiated into free-field conditions and the power absorbed through the vibration of the surface by the sound-field in the receiving room: Zru = ~R - r~A (6) where: ~M = radiated power measured by direct method; 7rR = actual power radiated into free-field conditions and zrA = power absorbed through vibration of surface by receiving room sound-field. In an empty receiving room with little porous absorption, ~zA is in the order of ~s. zrA must, therefore, be removed. This is achieved by reducing the level of the receiving room field using sheets of flexible polyurethane foam. Ten 2.44 m × 1.37 m x 50 mm sheets, suspended so as to present a large absorbing area without hindering access to the room surfaces, give a 9 dB to 12 dB reduction in this field. This level of absorptivity is to be expected from the Eyring absorption coefficients of the foam in 'dead' conditions. However, the foam will not completely remove ha, so there is still some inaccuracy in the measured radiated power. 12 If the reduction in the receiving room field is 10 dB, this error is less than 1 dB for those room surfaces which, in the empty receiving room, absorb through vibration less than twice the power they radiate. For those surfaces which absorb through vibration less than 3.7 times the power they radiate this error is less than 2 dB. PERFORMANCE

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chamber. ~~ Figure 6 indicates the accuracy of the method in measuring the thirdoctave sound powers radiated by a I0 mm thick steel plate subjected to airborne excitation. Six measuring positions were used and the major source of inaccuracy was sampling error, which is greatest at the lower frequencies. Mechanical excitation is more localised than airborne excitation, leading to a less uniform velocity distribution and greater sampling error. This is illustrated by Fig. 7 which shows

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the actual and measured radiated powers for mechanical excitation of the steel plate. The sampling error would be expected to be greatest for the mechanical excitation of inhomogeneous structures. This is in fact the case, as is shown in Fig. 8. However, the performance of the direct method is still good, especially when compared with that of the accelerometer method, assuming a radiation factor of one, shown in Fig. 2. The direct method has also been applied to two instances of sound transmission between adjacent rooms in buildings.'2 The first construction featured a clinker-

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block p a r t y wall which was weak, in s o u n d insulation terms, c o m p a r e d with the flanking structures. T h e s o u n d powers r a d i a t e d by this p a r t y wall into the receiving r o o m were a r o u n d 20 dB greater than those r a d i a t e d by a n y o t h e r r o o m surface. A c o m p a r i s o n between the powers r a d i a t e d by the p a r t y wall, m e a s u r e d b y the direct m e t h o d , a n d the actual total powers r a d i a t e d into the receiving r o o m a p p e a r s in Fig. 9. A g a i n , the direct m e t h o d p e r f o r m s well. T h e second c o n s t r u c t i o n featured a heavy p a r t y wall s e p a r a t i n g the light s t u d frame flanking walls a n d ceilings o f the two rooms. T h e r a d i a t i o n f r o m the p a r t y wall was f o u n d to be greater t h a n that from all o t h e r receiving r o o m surfaces, except for the 125 a n d 160 H z third-octaves. This can be seen in Fig. 10. Virtually all the flanking r a d i a t i o n c a m e from the stud-frame walls a n d ceiling. These structures were f o u n d to have a mass-spring-mass r e s o n a n c e n e a r 160 Hz. So it can be s u p p o s e d t h a t a r o u n d 160 H z energy was transferred f r o m the p a r t y wall to these r e s o n a t i n g flanking structures, which then r a d i a t e d c o r r e s p o n d i n g l y more. The total powers r a d i a t e d into the receiving r o o m as m e a s u r e d by the direct m e t h o d again s h o w g o o d agreement with the actual values, as can be seen in Fig. 1 !.

ACKNOWLEDGEMENTS This w o r k was p a r t o f the p r o g r a m m e o f the Building R e s e a r c h E s t a b l i s h m e n t o f the D e p a r t m e n t o f the E n v i r o n m e n t a n d this p a p e r is p u b l i s h e d b y p e r m i s s i o n o f the Director.

REFERENCES 1. J. E. R. CONSTABLE,The transmission of sound in a building by indirect paths, Proceedings of the Physical Society, .50 (1938) pp. 368-73. 2. J. E. R. CONSTABLE,Transmission of sound between neighbouring rooms in a brick building, Proceedings of the Physical Society, 51 (1939) pp. 53-61. 3. H. J. PUIZKISand P. H. PARKIN, Indirect sound transmission with joist and solid floors, Acustica, 2 (1952) pp. 237-41. 4. R. MARTIWand H. W. MOLLER,Ober k6rperschalluntersuchungen in wohnbauten, Acustica, 6 (1956) pp. 88-90. 5. W. WESTPHXL,Ausbreitung yon k6rperschall in gebiuden, Acustico, 7 (1957) pp. 335-48. 6. T. KmLMAN,The influence of flanking transmission on insulation against airborne sound as specially applied to buildings with lightweight concrete inner walls, Transactions of Chalmers University of Technology, Gothenburg, 254 (1961). 7. O. BRANDTand S. WAHt$rR6M, Experimental buildings for sound insulation studies. Congress Report I of the Fourth ICA, paper L57 (1962). 8. O. BRANDTand S. W^HLSTR6M,Studies on flanking transmission in an experimental building. Congress Report I of the Fourth ICA, paper M35 (1962). 9. R. F. HIC,OINSON,A laboratory facility for testing sound insulation of building constructions. Unpublished note, Building Research Establishment, 1972. 10. W. WESTVHAL,Zur schallabstrahlung einer zu beigeschwingungen angeregten wand, Acustica, 4 (1954) pp. 603-10. 11. L. L. BERANEK,The transmission and radiation of acoustic waves by structures, I.M.E. 45th Thomas Hawksley Lecture. 1958.

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12. J. A. MACADAM,The measurement of sound powers radiated by individual room surfaces in lightweight buildings. Building Research Establishment Current Paper 33/74, 1974. 13. E. C. SEWELL,Radiation from panels. Unpublished note, Building Research Establishment, 1970. 14. K. GOSELE, Abstrahlverhalten von w/inden, Acustica, 6 (1956) pp. 94-8. 15. P. W. SMITH, Coupling of sound and panel vibration below the critical frequency, Journal of the Acoustical Society of America, 36 (1964) pp. 1516-20.