Characterization of acoustic properties of materials by means of the impulse response measurements. 1 Introduction

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1 Characterization of acoustic properties of materials by means of the impulse response measurements Simone Geroso, Alessandro Schiavi, Andrea Pavoni Belli, Francesco Russo, Mario Corallo Istituto Elettrotecnico Nazionale Galileo Ferraris, Torino, Strada delle Cacce 91, Italia, {geroso, schiavi, pavoni, russo, A linear and time-invariant system can be considered as a black-box, characterized by its impulse response h(t), that is the relationship between the output and the input signals of the system. The method of impulse response is based on this concept. In this paper are showed the results obtained applying the impulse response method for the determination of sound insulation of building elements and of sound absorption coefficient of objects and materials. The influence on the results of some parameters used in the determination of the impulse response has been analysed, in particular: number of measurement points, number of signal sequences, signal type, signal power. The measurements of sound insulation have been carried out in two ways: first with the traditional technique indicated in EN ISO 140-3, using two continuously moving microphones, and then with the impulse response method in some stationary microphone positions. Also the sound absorption coefficient measurements have been carried out in two ways: interrupted noise method and impulse response method in the same microphone positions. All results have been and some conclusions of interest are drawn concerning the respective uncertainties of measurements. 1 Introduction A linear and time-invariant system is considered like a black-box, characterized by its impulse response h(t). This impulse response is defined as the output of the same system when the input is the generalized Dirac delta function δ(t). This function is infinitely peaked at t=0 with the total area of unity. For this system the following equation is valid + () t x( t u) h( u) y = du (1) where y(t) is the output signal of the black-box and x(t) is the input signal. The relation (1) is the convolution of the input signal with the impulse response of the system. On the whole y(t), in a generic instant t, is obtained as linear combination of all past and future values of the input signal x(t). The impulse response h(t) behaves like weight-function of the linear combination. This interpretation of the input-output relation can intuitively justify the property of the system of being linear and time-invariant (LTI). In order to obtain the impulse response of an acoustic system, the Dirac delta signal δ(t) is not reproducible: therefore, by signal analysis theory, it is possible to use a particular signal like the MLS or the Sweep frequency. The application of the described signal analysis techniques to acoustic systems is increasing in these years. The introduction of Schroeder's backward integration has allowed to obtain the reverberation times from h(t). This has introduced measurements of impulse response of acoustic systems together with the traditional and always valid acoustic measurements: Standard ISO 354/2003, measurement of sound absorption in a reverberation room, introduces the impulse response method for measurements of reverberation time; Standard ISO 3382/97, measurement of the reverberation time of rooms with reference to other acoustical parameters, uses the impulse response measurement also for the calculation of acoustic parameters characterizing confined rooms. In this communication the results obtained applying the method of impulse response for the determination of the airborne sound insulation of buildings elements and the sound absorption coefficient of objects and materials are showed. Standard ISO 354/2003 admits the measurement of sound absorption coefficient in a reverberation room with the impulse response technique, considering the reverberation room system (with and without test material/object) and the relative microphone-source position as an LTI acoustic system. For the laboratory measurement of airborne sound insulation of building elements, Standard EN ISO 140-3/95 does not foresee the use of the impulse response method; however, it is possible to consider an LTI acoustic system constituted by two rooms separated by the test element, together with the relative position between the microphones (one in the source room and one in the receiving room) and the source. The influence on the results of some parameters used in impulse response determination has been analysed, such as: number of measurement points, number of signal sequences, signal type, signal power. The measurements of sound insulation have been made in 2245

2 two ways: first with the traditional technique indicated in EN ISO 140-3/95, using two continuously moving microphones, and then with the impulse response method in some stationary microphone positions. About the sound absorption coefficient, the values obtained with the interrupted noise method and those deducted from the impulse response method in the same microphone positions are compared. The results concern the respective measurements uncertainties. 2 Methodologies and instrumentation for sound absorption coefficient α/α w measurement The measurement of sound absorption coefficient have been executed in the reverberation room of the IEN Galileo Ferraris in compliance with the prescription and the conditions of test from Standard EN ISO 354/2003. With both methods of calculation of the reverberation time - interrupted noise (traditional) method and impulse response method -, four series of consecutive reverberation times have been made with and without the test specimen, each for four microphone positions. The traditional method is a reverberation time measurement through a multispectrum: the obtained 64 reverberation times, corresponding to the four microphone positions, are averaged. With impulse response method, the length of signal used (MLS or Sweep) is determined on the basis of the highest value of reverberation time. The values of reverberation time measured in the four microphone positions are averaged. The instrumentation is different for the two methodologies, except for the two omnidirectional sources Brüel & Kjær Type 4296 used together. For the traditional method we have used a condenser microphone ½ B&K type 4166 with preamplifier B&K type 2619, a four channels one-third-octave digital real time frequency analyzer Pulse B&K type 3560c, a digital equalizer Yamaha type DEQ 5 and a final power Amcron Crown type MICRO-TECH For the impulse response method we have used the program Dirac Room Acoustics Software B&K type 7841 installed on notebook with the audio card Vxpocket v2 Digigram, a microphone Neumann TLM170Rni, a one channel microphone power source G.R.A.S. Power Module type 12AK used as microphone amplifier signal and a power amplifier Crown D-75 A. 3 Methodologies and instrumentation for airborne sound insulation index R/R w measurement Airborne sound insulation index measurements were performed in the laboratory in compliance with Standard ISO 140-1/97: in particular, a source and a continuously moving microphone is placed in the source room while in the receiving room a second identical continuously moving microphone is placed for the space-temporal integration; the measurements is repeated for three different positions of the source. By means of an omnidirectional acoustic source it has been measured the reverberation time of the receiving room as the average on four microphone positions and two source positions; therefore all the elements necessary in order to calculate the defined airborne sound insulation index are stated. The instrumentation used for this measurement is: two condenser microphones ½ B&K type 4166 with preamplifier B&K type 2619, two rotary rod B&K type 3923, the analyzer is still Pulse B&K type 3560c therefore like the equalizer, the final power and the source. The measurements of airborne sound insulation index by means of the impulse response method have been executed using Dirac Room Acoustics Software B&K type 7841 [3]. This software is suitable for the measurement of room acoustic parameters, as specified in Standard ISO 3382/97. Among these parameters, the quantity G rel is defined as a relative sound pressure level i.e. the relationship between the measured sound pressure level in the enclosure and the input excitation signal power level, in logarithmic scale. This parameter measured in m microphone positions in the source room (G si ) and in n microphone positions in the receiving room (G ri ) allows to calculate the airborne sound insulation R, as a function of frequency, through the formula m GS, i n R = 10 log log 10 m i 1 n j= 1 S T + 10 log 0.16 GR, j 10 = V (2) where S is the area of test specimen, T the reverberation time and V the volume of the receiving room. The first term represents the average relative sound pressure level in the source room, the second term is the average relative sound pressure level in the receiving room and the last is a correction term due the reverberation time of receiving room. The instrumentation consists of two ½ B&K type 4166 microphones with preamplifier B&K type 2619, a dual microphone supply B&K type 5935 used also as amplifier microphone signal and power amplifier 2246

3 Crown D-75 A. The sources are the same as in the measurement described previously. 4 Results integrated impulse response method in accordance to EN ISO 354/2003). Description of the testing material is unimportant in this context because the objective is the comparison of the two different methods. For example, the graphs relative to the measurement of test specimen n 3 are shown in Figures 1 and Sound absorption coefficient α/α w Three measurements have been performed with two methods (typical interrupted noise method and Sound Absorption Coefficient with IR-MLS Sound Absorption Coefficient with IR-eSweep Sound Absorption Coefficient with Interrupted Noise [-] Figure 1: Sound absorption coefficient α of test specimen n [-] Uncertainties over the Sound Absorption Coeff. with IR-MLS Uncertainties over the Sound Absorption Coeff. with IReSweep Uncertainties over the Sound Absorption Coeff. with Interr. Noise Figure 2: Sound absorption coefficient α of test specimen n 3 and the uncertainties 2247

4 In Fig. 1 it can be noticed that the curves continuously intersect, in Fig. 2 the uncertainties on the measurement of sound absorption coefficient are shown. For the other test specimens the corresponding value of α w reported in table 1 shows an adequate agreement. Table 1: Weighted Sound absorption coefficient α w α w Test n.1 Test n.2 Test n.3 Imp. Resp. with MLS Imp. Resp. with lsweep Imp. Resp. with esweep Traditional Method R [db] R with IR- MLS R with IR- esweep R with Trad. Standard Method Figure 3: Airborne sound insulation R and the uncertainties Test specimen n Airborne sound insulation index R/R w measurement established in Standard ISO 140-2/91. For the other test specimens, the corresponding value of R w reported in table 2 shows an adequate agreement. Six measurement of airborne sound insulation have been performed. Description of the testing material is unimportant. The graphs obtained in the measurement of test specimen n 2 are shown in Fig. 3. The curves with the different types of signal used in impulse response method are within the uncertainty of 2248

5 Table 2: Weighted Airborne sound insulation R W (db) Test number Impulse Response Method Traditional Method In order to verify the compatibility between both measurement methods, it has been tried to reduce randomly the measurement points in the receiving and source rooms. The diagram in fig. 4 points out the curves of R obtained with different number of microphone positions: the observed variations among the curves are not significant. These variations are within the uncertainty of measurement. Also for R w index there are variations within ±1 db, as shown in Table [db] R 10 Mic. Points R 9 Mic. Points R 8 Mic. Points R 7 Mic. Points R 6 Mic. Points R 5 Mic. Points R 4 Mic. Points R 3 Mic. Points R 2 Mic. Points R 1 Mic. Points R Trad. Method Figure 4: Airborne sound insulation R reducing of the points of measurement and the uncertainties (test specimen n. 3) Table 3: Weighted Airborne sound insulation R W of test specimen n. 3, with measurements points reduced Number of measurements points R w IR Method / Trad. Method Trad. Method

6 5 Conclusions There is an adequate agreement between the measurements carried out with the traditional method and those carried out with the impulse response method, in order to evaluate the sound absorption coefficient and the airborne sound insulation. In the diagrams it is shown the validity of results within the uncertainty of the traditional measurement. Particularly, in sound absorption coefficient measurement the formula of the uncertainty has been extended also to the measurements performed by means of the impulse response method. As far as the airborne sound insulation it has been possible to verify that with impulse response method few microphone points of measurements are required, it means a fastest measurement than the traditional measurement with continuously moving microphone. This is also an interesting application in the measurement in situ. Finally both the verification of measurements compatibility and measurement uncertainties calculation must be extended and investigated, specially for the measurements of airborne sound insulation by means of the impulse response method. References [1] ISO/FDIS 354:2003 Acoustics -- Measurement of sound absorption in a reverberation room [2] ISO 3382:1997 Acoustics -- Measurement of the reverberation time of rooms with reference to other acoustical parameters [3] Acoustics Engineering, Technical Notes Insulation Measurements using Dirac, August 2003, [4] EN ISO 140-3:1995 Acoustics -- Measurement of sound insulation in buildings and of building elements -- Part 3: Laboratory measurements of airborne sound insulation of building elements [5] ISO 140-2:1991 Acoustics -- Measurement of sound insulation in buildings and of building elements -- Part 2: Determination, verification and application of precision data [6] M. Schroeder, New method of measuring reverberation time. J. Acoust. Soc. Am., Vol. 37. pp (1965) 2250