STANDING WAVE TUBE TECHNIQUES FOR MEASURING THE NORMAL INCIDENCE ABSORPTION COEFFICIENT: COMPARISON OF DIFFERENT EXPERIMENTAL SETUPS.

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1 STADIG WAVE TUBE TECHIQUES FOR MEASURIG THE ORMAL ICIDECE ABSORPTIO COEFFICIET: COMPARISO OF DIFFERET EXPERIMETAL SETUPS. Angelo Farna (*), Patrzo Faust (**) (*) Dpart. d Ing. Industrale, Unverstà d Parma, Va delle Scenze, 43 Parma, Italy (**) Isttuto d Ingegnera, Unverstà d Ferrara, Va Scandana, 44, Ferrara, Italy ITRODUCTIO The tradtonal standng wave tube technque s many years old: nevertheless, t s a current ssue, as the I.S.O. s revewng the test code (ISO/DIS 354). At the same tme, many alternatve measurng technques have been proposed, based on the dgtal sgnal processng of the sgnals comng from a par of phase-matched mcrophones, or from a seres of subsequent mcrophone postons. The numercal elaboraton can extract ether the Transfer Functon between these mcrophones or the Cross Spectrum, and the latter case can be seen as a sound ntensty technque. Also the exctaton sgnal can be of dfferent knds: the orgnal steady sne wave has been substtuted by a whte nose, by a swept sne and fnally by a pseudo-random Maxmum Length Sequence (MLS). In ths paper the results of a wde expermental research are presented. The authors employed three dfferent expermental setups, ncludng the tradtonal one, a multpont sngle-mcrophone arrangement, and a two-mcrophone tube. The acquston hardware consst of an analog meter, a two-channel FFT analyzer, a / octave dgtal real tme analyzer and a MLSSA system. The s used for these experments are varous knds of plasters and other mneral materals, avodng the commonly used soft layers of polyurethane foam or glass wool (wth these, n fact, all methods work well!). Furthermore, a new measurement technque was developed, whch combnes several dstnct measures made wth a sngle, movable mcrophone. A valdaton check s used to dscard data outsde the frequency range vald for the mcrophone spacng or below a mnmum coherence. In ths way, accurate measurements can be made also wth s of materals that usually produce poor results wth the other measurng technques. MEASUREMET TECHIQUES The frst measurement technque s the tradtonal one, descrbed n the test code ISO/DIS 534. o further explanaton s requred, but t must be noted that ths reference method requres a measurement at each frequency, as t employs pure tone exctaton. The followng pcture shows the apparatus: Pg.n

2 mcrophone probe sne generator amplfer narrow band flter Level Meter A B&K type 4 Standng Wave Apparatus has been employed, wth a B&K analog generator, flter and Level Meter. The absorpton coeffcent s then computed from the SPL dfference between a pressure maxmum and mnmum, L: α= 4 L/ L/ ( + ) The second technque s that descrbed n the test code ASTM E-5 (85): ths s substantally the same technque suggested by Chung and Blaser [], based on the measurement of the transfer functon H between the mcrophones: () mc. mc. loudspeaker s random generator amplfer dual channell spectrum analyzer In the present work, a / octave real-tme analyzer has been employed (B&K 33), connected wth a B&K type 46 tube. The absorpton coeffcent s then computed as follows: α= H e jks e H jks The same apparatus has been employed also for the thrd technque; the Sound Intensty software of the analyzer has been used to measure the three basc quanttes: Mean Pressure (MP), Partcle Velocty (PV) and Actve Intensty (AI). After smple manpulatons, from these quanttes t can be obtaned: AI α = ref = AI nc ρ c + MP PV ρ c ρ c + MP PV ρ c AI + AI The fourth technque s based on a mult-pont transfer functon measurement, nsde the same apparatus shown for the tradtonal method. () (3) A. Farna Pg.n

3 reference mcrophone loudspeaker movable mcrophone mcrophone postons amplfer PC wth A/D board and MLS generator -channell FFT anal. Ths system can measure the Transfer Functon between loudspeaker and movable mcrophone through deconvoluton of the MLS sgnal [] employng a MLSSA AD- 6 PC board, but t can also measure a tradtonal FFT transfer functon between the reference and movable mcrophones, wth an Ono Sokk CF9 analyzer. In ether way, one obtans Transfer Functons (H, H,..., H ), and these can be processed as suggested by Fujmor et al. [3] (neglectng the tube attenuaton) to gve α: α= H e H e jkx H e + H e jkx jkx jkx (4) The same apparatus s the one employed for the newly developed technque (the ffth), that conssts n a dfferent way of processng the measured Transfer Functons. The basc dea of the new method s to consder pars of mcrophone postons (not necessarly consecutve): for each par, the Transfer Functons between poston and j and the Coherence functon can be obtaned. The absorpton coeffcent α s then computed, at each frequency, as the average of all the vald α values calculated through eqn. ) from all the possble pars: a partcular value of α s consdered vald only f the Coherence s greater than.85 and the mcrophone separaton s comprsed between.88 and.353 tmes the wavelength. In ths way the data affected from poor measurement condtons (sgnal-to-nose rato, tube resonances, mcrophones too far or too close for the wavelength) are automatcally dscarded, and the averaged value s computed only on unbased data. EXPERIMETAL RESULTS The frst pcture shows the comparson between the ISO 534 tradtonal technque, the -mcrophone technque accordng to ASTM E-5 and the Intensty technque: A. Farna Pg.n 3

4 .8.6 Alfa Frequency (Hz) ASTM E-5 Intensty Method ISO 534 It can be seen that the -mcrophone technque s smlar to the tradtonal one, but much faster. On the other hand, the Intensty technque shows sgnfcant errors, probably because the gan and phase correcton procedure mplemented n the Intensty mode are not so effectve n removng these effects as the Chung and Blaser mcrophone swtchng method. The second pcture shows the mult-mcrophone results both wth the Fujmor formulas and wth the new data-dscardng method; these are compared wth the tradtonal pure tone method and wth the -mcrophones technque:.8.6 α Frequency (Hz) ASTM E-5 Fujmor (MLS) Farna (FFT) ISO534 It can be seen that the FFT analyss based on a reference mcrophone gves better results than the MLS deconvoluton of the speaker-to-mcrophone response, and ths s due to a hgher coherence n the measured transfer functons. Furthermore, t can be A. Farna Pg.n 4

5 seen that the new data-dscardng technque greatly reduce the spkness of the measured absorpton curve around tube resonances and n the hgh frequency regon. COCLUSIO After a wde comparson between avalable measurng technques, a new processng algorthm has been developed, whch makes t possble to measure the absorpton coeffcent of very reactve materals, followng the formulaton requred for compatblty wth ASTM E-5. The new technque only requres that the measurement s repeated a few tmes (typcally 7), and so t s only slghtly slower than the orgnal -mcrophone method. The comparson wth the other measurement technques shows that also wth the orgnal ASTM method, and wth a properly desgned tube and a powerful analyzer, reasonably good results can be acheved. However the new method s more versatle, as t can be used wth the old movng-mcrophone tubes, and t can be mplemented wth a low-cost PC and an MLS board. BIBLIOGRAPHY [] J.Y. Chung, D.A. Blaser - Transfer functon method of measurng n-duct acoustc propertes. part I Theory and part II Experment - J.A.S.A. 68(3), Sept. 98, pagg [] W.T. Chu - Impedance Tube Measurements - A comparatve study of current practces - ose Control Engneerng Journal, Vol. 37, n., July-August 99, pagg [3] T. Fujmor, S. Sato, H. Mura - An automated measurement system of complex sound pressure reflecton coeffcents - Proc. of Int. Conf. on ose Control Eng., G.C. Malng, 984. A. Farna Pg.n 5