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MEASURING SOUND INSULATION OF BUILDING FAÇADES: INTERFERENCE EFFECTS, AND

REPRODUCIBILITY

U. Berardi, E. Cirillo, F. Martellotta

Dipartimento di Architettura ed Urbanistica - Politecnico di Bari, via Orabona 4, 70125 Bari, Italy

e-mail: {u.berardi, f.martellotta, e.cirillo}@poliba.it

Abstract Sound insulation in buildings is getting increased importance both in national regulations and in international standards. Consequently, accurate and reliable measurements are of the greatest importance in order to compare and discuss building performances. The determination of sound insulation of building façades requires the measure of both outdoor and indoor sound pressure levels. Unfortunately, the standard measuring procedure for façade insulation has shown several limits, especially with reference to outdoor pressure level. The placement of source and receiver, which is kept flexible to adapt to building characteristics, opens the way to possible interference effects which may affect different frequencies according to the given position. Comparisons between different source-receiver combinations are hence investigated theoretically and then compared with laboratory and on-site measures. The paper investigates possible destructive interference of sound waves and their influence on final results, after having described the elements that can influence the measure. Finally, the recent attention for reproducibility of acoustics measures implies the capacity to understand reasons for unexpected measures in order to be able to avoid them. The grade of reproducibility is investigated, and the variance of sound insulation of building façade is given.

Keywords: Measurement, sound insulation, building façades, wave interference.

1 Introduction

The measurement procedure for sound insulation of building façades is described in [1]. This establishes the position of the source and of the receiver out of the building façade. When the measure is performed using a loudspeaker, the standard indicates the distance both of the

INTERNOISE 2010 │ JUNE 13-16 │ LISBON │ PORTUGAL

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loudspeaker and of the microphone and the angle of the loudspeaker relative to the façade. Scope of the paper is to investigate the limits of the measurement technique, establishing its reproducibility according to [2]. The reason for this paper is that orientations of the source and of the receiver, as well as ground and façade impedances, determine interference patterns at the microphone. These interferences increase the uncertainty of the pressure level measurement at the external microphone. Ref. [1] states that for “uncontrolled interference effects, systematic errors will occur, particularly at low frequencies”. To assess the influence of these interference effects, the following parameters have been investigated: • the angle of the loudspeaker which is given by the line connecting the center of the façade with the source and the normal to the façades, θ=45° ± 5°, so that 40° ≤ θ ≤ 50°; • the position of the external microphone which can be on the surface of the façade (element method) or at 2 m distance, d=2 m ± 0.2 m, so that 1.8 m ≤ d ≤ 2.2 m, (global method); The influence of ground is evaluated together with the absorption and scattering properties of the façade. The aim is to evaluate circumstances that encourage destructive interference between direct and reflected sounds. The paper is composed by 5 sections. Next one contains a theory evaluation of the problem, then section 3 reports the experimental results and a comparison between theory and experiments. Reproducibility of measurements is discussed in section 4. Final section summarizes the conclusions of the work.

2 Theory

Among the methods accepted in Ref. [1], this paper considers only the possibility to calculate the sound insulation using a loudspeaker in front to the façade. This should form an angle of 45° with the normal to the façade passing for its center (figure 1).

Figure 1 – Position of loudspeaker and mic according to [1] and reflections at the microphone.

Many studies have investigated the possibility of destructive interference in front of the reflecting surfaces [3], and some of these specifically referred to façades [4]. These studies were oriented to measure exterior sound level for environmental monitoring, so they did not consider the specificities of sound insulation of building façades: for example they never considered the loudspeaker orientation. By taking into account different positions of loudspeaker and microphone it is possible to evaluate situations which could lead to interferences. To simplify the study the following assumptions are made:

a) loudspeaker is considered as a point source emitting spherical waves;


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b) ground and façade are perfectly reflecting with no phase change in the reflection; c) all reflections both of ground and of façade are specular; d) there is no other obstacle nearby the façade.

Scattering effects of façade and of balconies or other elements which protrude are neglected. Moreover Ref. [6] shows that building façades have low scattering in the first orders of reflections justifying hypothesis c). Zero absorption is assumed for the façade in the present work, also because when absorption has been considered no significant variation occurred in the interference results [7]. Assuming plane-wave propagation, the interference of a direct wave with reflection from a perfect reflecting surface can be calculated with equation (1) in Ref. [7] considering the two waves as fully coherent. The time-averaged Sound Pressure Level (SPL) is represented in fig. 2 where interferences are evident. Ref. [1] establishes that in the global method measurements microphone should be at 2 m from the façade or within an interval of ± 0.2 m. Large shifts happen for small changes in the position of the microphone from 1.8 to 2.2 m. Interferences also depend on the angle of incidence as shown by comparing sound pressure levels with the loudspeaker at 40°, 45° and 50°.

Figure 2 – Sound pressure level showing interferences between direct wave and reflection off the façade.

The above mentioned results were based on a theoretical evaluation of interferences performed considering the different waves arriving at the microphone. Their path differences compared to the direct sound are transformed into fly time delays. Supposing that the source is not positioned on ground, but at a height over the surface as shown in figure 1, four waves arrive at the microphone: the direct one (d1), that reflected from the ground (d2), that reflected from the façade (d3), and that reflected both from the ground and the façade (d4). The change in the sound pressure level due to the façade at each frequency is hence the ratio between the sums of the four waves over the two waves without the façade (d1 and d2):

2

31 2 42

1 2 3 4

22

1 2 1 2

1 2

exp( )exp( ) exp( ) exp( )

( ) exp( ) exp( )

t

t

ikdikd ikd ikd

p d d d d

p p ikd ikd

d d

−− − −+ + +

=+ − −

+

(1)

where t indicates the time-average value, k is the wavenumber, and other symbols refer to

figure 1. When two waves overlap a destructive interference occurs if the path lengths differ


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by an odd number of radians. In case of four interfering waves, the net value of numerator in eq. (1) is less easy to predict. Figure 3 reports the theory sound pressure level difference calculated with eq. (1) for a microphone at 1.5 m over the ground and the loudspeaker at 7.78 m from the center of the façade and at 0.22 m over ground.

Figure 3 – Theoretical interferences due to façade reflections with microphone positioned in the range from 1.8 to 2.2 m and loudspeaker at 45°. Relative height of microphone over height of the loudspeaker is 1.28 m. Eq. (1) is valid at any frequency. In order to calculate frequency band values, it is necessary to sum frequencies in each band. Hopkins and Lam elaborated the autocorrelation functions of the cross terms obtained from (1) in Ref. [4]. It is hence possible to calculate eq. (1) in frequency bands:

( ) ( ) ( ) ( ) ( ) ( )

( )

1 1 1

22 2 2 2 2

1 1 1 1 1 12 12 13 14 23 24 34

2 3 4 2 3 4 2 3 2 4 3 4

22

1 2 1 112

2 2

1 2 2 2 2 2 2

( )1 2

t

t

d d dd d d d d dR d R d R d R d R d R d

p d d d d d d d d d d d d

p p d dR d

d d

+ + + + ∆ + ∆ + ∆ + ∆ + ∆ + ∆

=+

+ + ∆

(2) where ( ...)R ∆ is the autocorrelation function between two waves. This is here calculated

following procedure proposed in [8]. As shown in figure 4, sound interference in front of façade depends on the position of the microphone and little displacement can lead to great differences in the SPL. For example at 80 Hz, the SPL difference is -5 dB at 1.8 m and +0.5 dB at 2.2 m. At high frequencies the change in the SPL due to the façade approximates energy doubling (+3 dB), according to the incoherent phases of reflections. On the contrary very near to a reflecting façade or at low frequency the phase is more coherent, and also pressure doubling (+6 dB) may occur. Energy doubling is generally assumed during environmental evaluation studies. However some standards do not accept this and suggest a correction coefficient different from +3 dB. For example the English Code for Road Traffic Noise gives a lower value of correction equal to 2.5 dB. Figure 4 shows that at low frequency the small phase difference lead to destructive interferences giving much lower levels than those predicted by the energy doubling assumption. As measurements of building façade insulation are significantly affected by behaviour at low frequency, it is hence fundamental to estimate the external SPL correctly.


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Figure 4 – Theoretical Sound Pressure Level different ce due to façade reflections with microphone positioned in the range between 1.8 and 2.2 m, and loudspeaker at 45°, in one-third octave frequency bands. Relative height of microphone over the loudspeaker is 1.28 m.

3 Experiment

3.1 Experiment setup

Measurements were carried out in the atrium of the faculty of Engineering at the Politecnico di Bari. The site was chosen as it reduced specific variables: there were no balconies or architectural decorative elements. Moreover the external ground floor consisted of hard ceramic material which guaranteed a high reflection coefficient. The wall had a window line from 1 to 2 m height, and plaster prefabricated panels above and below. Measurements were made in front of the glass. This permitted to assume perfect reflections as in theoretical assumptions. An omnidirectional sound source made up of twelve 120 mm loudspeakers was used. Source was positioned at 7.78 m from the façade at 40°, 45° and 50° angles, maintaining a constant distance (table 1). A logarithmic sine sweep signal was used for each combination loudspeaker-microphone, whereas a B-format microphone (Soundfield Mk-V) allowed studying the direction of reflections.

Table 1 – Positions of the loudspeaker during measurements.

Loudspeaker Angle Normal façade distance [m]

Parallel façade distance [m]

Façade distance [m]

40° 5.96 4,84 45° 5.50 5.35 50° 5.00 5.82

7.78

A calibrated measurement chain consisting of 01 dB Symphonie system and a GRAS 40-AR omnidirectional microphone was then used to measure the sound pressure level with non equalized white noise. The 1/2 inch GRAS microphone was preferred to comply with the distance limit prescribed in Ref. [1] for the element method.


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Coherently with distance from the façade prescribed in [1] for the global method, microphone should be at 2 m from the façade or within an interval of ± 0.2 m: five positions were hence chosen from 1.8 to 2.2 m in steps of 0.1 m. In the surface method, the two positions considered in [1] were selected: the microphone was hence positioned vertically and horizontally. Ideally random incidence microphones should show no variation in the measurements for different orientation, however only two orientations are prescribed in [1]. All microphone positions were at 1.5 m height over the floor. In Ref. [7] specific effects of scattering and reflections were responsible of differences of 1 dB among surface façade measurements, so in this study the microphone was positioned always in the same surface point in order to assume any specific scattering effect as constant.

Table 2 – Positions of the microphone during measurements.

Microphone Position Distance [m] Surface method 0.002 (perp.), 0.005 (vert.) Global method 1.8, 1.9, 2.0, 2.1, 2.2

3.2 Experiment results

The signals recorded by each microphone allowed to estimate the spectra in one-third octave bands from 50 Hz to 5 kHz. A preliminary assessment of the validity of the site respect to theoretical assumptions was carried out. Figure 5 shows the sound recorded by the Soundfield microphone positioned at 2 m in front of the façade with the source loudspeaker at 45°. Arriving sounds are clearly showed in overall time history at the microphone (channel W of the Soundfield microphone). The different reflections are clearly detectable in the normalized 3d sound plots, when the time window moves from 5 to 30 ms after the direct sound arrival. The low scattering of the plot confirms the agreement with theoretical assumptions. Figure 6 shows the horizontal projection of the sound incident with the microphone at 1.8 and 2.2 m from the façade when the source is at 45°. The directions are clearly defined and scattering is low. The normalized vectors of the reflections show that these have an absolute value comparable with the direct one. Figure 7 and 8 show the measured SPL differences due to the presence of the façade. These were obtained subtracting the SPL measured in front of the façade from the SPL measured with the same chain setup and at the same distance from the source but in a direction where there was no façade. In particular fig. 7 reports the average value among five positions of the microphone at 2 m from the façade (global method) with source at 45°, 40° and 50°, together with standard deviation in each one-third band. Standard deviation assumed maximum values at very low frequency for every angle of the source. Besides when source was at 45° a large standard deviation among measurements was observed in frequency bands from 400 Hz to 1 kHz. Figure 7 corresponds to the theoretical study in fig. 4. As evident at high frequency the difference among values approximates the increase of 3 dB with higher values for 45° respect to 40° source position. The interference is also constructive at low frequency, whereas in the middle frequency range negative values of the SPL difference suggest a destructive interference among sounds arriving at the microphone. Figure 8 shows the SPL measured with the element method, the loudspeaker positioned at the three angles and the microphone parallel or perpendicular to the façade. Results are surprising not only at low frequency but also at very high frequency. Even if standards suppose that whenever the microphone is positioned, the measure should be identical, differences of 4 dB among positions were found in low frequency bands. Greater differences were observed at high frequency independently of the angle position of the loudspeaker: when microphone was positioned perpendicularly, measured level was 7 dB higher than


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when parallel direction of the microphone was used. Measured SPL was particularly sensitive with the source at 40° in fact measurements with parallel microphone at 4 kHz were 8 dB lower than with perpendicular microphone. It should be noticed that theory considered no scattering from the façade, whereas at high frequencies this hypothesis is dubious given the wavelengths. In practice the center of the microphone should be maintained at 0.05 wavelengths from the surface [7]: for a 1/2 inch microphone, this means a frequency limit of validity below 2.5 kHz.

Figure 5 – Time history of 1 kHz sound incident at the Soundfield microphone positioned at 2 m from the façade with the loudspeaker at 45°, overall, Back-Front and Left-Right directions (above), and normalized 3d plots up to 5, 10 and 30 ms (below).

Figure 6 – Horizontal projection of 1 kHz sound incident at the Soundfield microphone positioned at 1.8 (left) and 2.2 m (right) in front to the façade with the loudspeaker at 45°.


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Limits in the measure of the sound insulation of building façades using a single stationary loudspeaker are evident in figures 7 and 8. Such differences appear only in the outdoor measurements while indoor ones are generally independent of source and receiver placement when these are lightly moved. This could hence induce errors in the calculation of the transmission loss of a building façade.

Figure 7 – Measured SPL difference for the presence of the façade at 2 m (global method): average values among microphone positions with the standard deviations.

Figure 8 – Measured SPL at the surface of the façade (element method) with the source at 45°, 40° and 50° and microphone perpendicular or parallel to the façade.

3.3 Comparison theory vs. experiment

Theoretical values of the interference are compared with measured results. Looking at theory estimation at 200 Hz with source at 45°, different values were expected among microphone positions at 2 m: in fact, standard deviation among measurements was high. At 250 Hz both theory and measurements agree with an increase of the SPL respect to 200 Hz and with a


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small standard deviation among microphone positions. A similar behavior occurs from 80 to 100 Hz: theory and measurements give an increase of the SPL and a high standard deviation among values at different microphone positions. Measured values at 1 kHz respect to the corresponding theoretical values are significantly lower, reversely at 100 Hz frequency band both theory and measured give a positive difference of the SPL. This demonstrates in phase interferences among reflections which lead to SPL differences greater than energy doubling. Measurements and theory also agree for destructive interference in frequency bands from 125 to 500 Hz with a clear dip down at 200 Hz.

4 Reproducibility of the measurements

The recent “Guide to the Expression of Uncertainty in Measurements” suggests considering the influence of uncertainty in sound insulation of building façades. Many international standards have discussed possible sources of uncertainty which have been often studied indirectly through the reproducibility of the measure. In particular uncertainty of building façade insulation measurements is described in [2]. This establishes that reproducibility for sound façade insulation is 2 dB for laboratory measurements both for the element and the global method. Greater differences are only supposed at frequency lower than 250 Hz. Measurement of the SPL has four main sources of uncertainties: instrumental (sensitivity, calibration), environmental, distances (loudspeaker and microphone both external and internal), and reflections. Other factors also affecting uncertainty of sound insulation of façade are the operator, post-processing algorithms, external factors or non stationary sounds. Previous elements were considered in [2]. In fact as reported in table 3, the repeatability values for the measure at different frequency bands were high, and the reproducibility values almost doubled previous ones.

Table 3 – Repeatability and reproducibility values among one-third bands for field test [2].

100 125 160 200 250 315 400 500 630 800 1k 1.25 kHz

Repeatability 4.5 4 3.5 3.5 2.5 2.5 2 2 1.5 1.5 1.5 1.5 Reproducibility 9 8.5 6 5.5 5.5 4.5 4.5 4 3.5 3 2.5 3

The present study has showed large variations in the measurements of the external SPL according to the configuration of loudspeaker and microphone. This problem not only occurs at low frequency, as expected also theoretically, but it influences high frequencies whenever element method is performed. In order to evaluate the effect of different measurement combinations on the sound insulation of building façade, the differences between external and internal measured SPLs were calculated. The single-number ratings of the sound insulation were hence assessed according to [1] for the any combination of loudspeaker-microphone position. Global method gave the same value among configurations, with a difference of 1 or 2 dB in some cases. This shows that the single-number rating was not significantly influenced by the configuration of measure even if external measured spectra were different. On the contrary, the single-number rating calculated with the element method gave different results: indices 3 dB greater than those obtained with the global method were calculated, even when average among spectra in different points was done as prescribed in ref. [1]. Among the source positions, maximum values of the single-number ratings were obtained when microphone was positioned perpendicularly to the façade whereas when it was parallel to the façade, the single-number ratings were 1 or 2 dB greater than those obtained with the global method. In conclusion it is evident that interference with global method can be predicted theoretically whereas when element method is used possible source of error increases. Besides the


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possible errors in reproducibility of field measurements of façade sound insulation showed in ref. [9], which was 0.8 dB only, underestimates the results of the present work. Integral equation methods could be used to theoretically predict the effect of the façade, or BEM simulations may be considered to take into account the scattering of the façade numerically in order to assess its influence on the external SPL in more complex cases.

5 Conclusions

The paper has shown the possible effects of interference in SPL measurements in front of a façade. Theoretical model was first considered. Measurements performed in field under strictly controlled conditions have then permitted to compare the results with theory predictions. The study has shown that different combinations of loudspeaker-microphone should be chosen because a single measure is unrepresentative of the SPL external to a façade and it can lead to several dB of error. The paper has finally investigated the influence of loudspeaker-microphone positions on measurement reproducibility of sound insulation of building façades.

Acknowledgments

The authors want to express their acknowledgments to eng. Antonio Scardigno who helped in performing the measurements. Helpful discussion of the first author with Dr. Carl Hopkins it is greatly appreciated.

References

[1] ISO, International Organization for Standardization 140-5: Acoustics - Measurement of sound insulation in buildings and of building elements - Field measurement of airborne sound insulation of façade element and facades, 1998.

[2] ISO, International Organization for Standardization 140-2: Acoustics - Measurement of sound insulation in buildings and of building elements - Determination, verification and application of precision data, 1991.

[3] Cox, T.J., Lam, Y.W., Evaluation of methods for prediction the scattering from single rigid panels, Applied Acoustics, Vol.40, 1993, pp.123-40.

[4] Hopkins, C., Lam, Y., Sound fields near building facades – comparison of finite and semi-infinite reflectors on a rigid ground plane, Applied Acoustics, Vol.70, 2009, pp.300-08.

[5] Hall, F.L., Papakyriakou, M.J., Quirt, J.D., Comparison of outdoor microphone locations for measuring sound insulation of building facades, J. Sound Vibr., Vol.92 (4), 1984, pp.559-67.

[6] Ismail, M.R., Oldham, D.J., A scale model investigation of sound reflection from building façades, Applied Acoustics, Vol.66, 2005, pp.123-47.

[7] Quirt, J.D., Sound fields near exterior building surfaces, J. Acoust. Soc. Am., Vol.77 (2), 1985, pp.557-66.

[8] Delany, M.E., Rennie, A.J., Collins, K.M., Model evaluation of the noise shielding of aircraft ground-running pens, NPL Report, Ac.67, 1974.

[9] Gerretsen, E., Interpretation of uncertainties in acoustics measurements in buildings, Proc. International INCE Symposium, Le Mans, 26-29 June 1995.

measuring sound insulation of building … sound... · 1 measuring sound insulation of building...

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