SHUNT LOUDSPEAKERS FOR MODAL CONTROL IN ROOMS

Transcription

1 SHUNT LOUDSPEAKERS FOR MODAL CONTROL IN ROOMS Hervé Liek, Romain Boulandet Laboratoire d Electromagnétime et d Acoutique, Ecole Polytechnique Fédérale de Lauanne, Station 11, CH-1015 Lauanne, Switzerland, herve.liek@epfl.ch Pierre-Jean René Acoutical Engineering and Reearch, rue de l Ale, 5, CH-1003 Lauanne, Switzerland, e- mail: pjrene@a-e-r.ch Engineer dealing with noie reduction in habitation cloe to tranportation traffic or indutrial facilitie encounter everal problem to decreae noie level in room at low frequencie. Paive material and current building contruction knowledge enable to avoid noie tranmiion in habitation at medium and high frequencie and the regulation baed on the dba cale can often be repected. But thee regulation do not take into account the real annoyance of noie for the inhabitant who are till diturbed by low frequency noie. Becaue of the modal behavior of room, air-borne and tructure-borne noie generate high ound preure level at the firt modal frequencie, even with mall amount of energy. In order to lower the annoyance induced by low-frequency behavior in room, huge compliant wooden panel can be ued, though with quite low performance in term of reonance damping. An alternative can be found with ba-trap, compriing a mechanical reonator and a cloedbox, with fixed acoutic performance at pecific frequency. Enhanced performance can even be obtained with cloed-box hunt loudpeaker, where the acoutic impedance of the loudpeaker' diaphragm around it reonance can be modified (in term of magnitude and alo in frequency) by way of a imple paive electrical device, providing the requeted complementary complex acoutic impedance for perfect aborption at the firt modal frequencie. The preent work decribe the deign of a mall array of low-frequency hunt loudpeaker, dedicated to damp a certain amount of mode within a known room. Aement in laboratory condition (impedance tube, reverberant chamber) will then be preented and compared to imulation, leading to concluding remark on practical iue on the applicability of the concept of hunt loudpeaker for low-frequency noie reduction in habitation. 1. Introduction About 80 million people in the European Union are expoed to noie level that are conidered a unacceptable. Health, worker productivity, or comfort at home, are directly impacted by noie. Though, depite the complexity of noie annoyance, regulation are often baed on indicator that obviouly decreae the influence of low frequencie (roughly below 00 Hz) on the referenced level. The quetion ha then raied whether thee metric are accurate when aeing the annoyance repone to noie containing trong low-frequency component, and ome alternative meaure have been propoed to correlate the actual annoyance to objective aement 1,. Thi ituation might explain that only few low-frequency oundproofing olution exit on the market. ICSV16, Kraków, Poland, 5-9 July 009 1

2 In fact, uual acoutic treatment can be found with pretty good performance in the high and middle frequencie range, but preent little performance for low frequencie. For the low frequency range, ome panel aborber 3 olution exit, coniting of wide flat wooden panel (that can alo be of metal, gypum board, or platic material), that are arranged in front of an encloed air volume (partly or completely filled with porou material). Such a ytem ha everal reonance frequencie that can be excited by airborne ound. But their dimenion, a well a their weight, reduce their interet for uual room. Thee compliant tructure are then mainly ued to provide enhanced aborption in the low frequency range for demanding condition uch a concert hall. A more practical low-frequency aborber i the ba-trap, coniting of a mall dicrete membrane reonator, aembled within a cloed-box, which reonance frequency i tuned o that to provide ufficient aborption within a narrow frequency band. Thi paper aim at preenting a ytem dedicated to reduce low frequency noie, inpired by the ba-trap technique, but involving electroacoutic tranducer in a paive reonator ue, allowing tuneable acoutic performance. Thi technique i baed on an electromechanical tranducer loaded with a paive electrical circuit o that to obtain an optimal damping around it reonance frequency. A quick preentation of the technique will be provided, together with numerical imulation of the acoutic behaviour in tandard configuration (impedance tube), and experimental aement in actual room to highlight it performance.. Influence of room modal behavior on indoor noie In the low frequency range, a room acoutic repone i driven by the modal behavior which i characterized by high level at eigenfrequencie that can be very annoying inide room 3,4. Several meaurement have been performed near the Geneva Airport. Figure 1 illutrate the modal behaviour in an office, located under the take off path of airplane. Figure 1: pectrograph meaured during aircraft flyover outide a room (left chart) and inide (right chart). When comparing the noie outide and inide the room, one can oberve that the noie pectrum inide the room appear to be concentrated on modal frequencie (traight horizontal red line), wherea the noie outide i trictly characteritic of the ource (with the Doppler effect illutrated by the curved red area). To reduce the annoyance in the room, the ound preure level ha to be reduced at thee identified frequencie. If the mode of the room are excited with the broadband low frequency noie excitation of an air plane, it become obviou that the main energy concentrate on the eigenfrequencie in the room, and at the main annoying frequency, the noie level inide the room i higher than outide the building. The former example highlight the neceity to perform a damping of the firt modal frequencie in a room to reduce the noie annoyance. Thi can be performed with the hunt loudpeaker concept decribed in the following.

3 3. Shunt loudpeaker 3.1 Deign of hunt loudpeaker An electrodynamic loudpeaker i a phyical ytem that i generally decribed with differential equation 5. From Newton law of motion, it mechanical dynamic auming piton-like vibration, can be modeled by a econd-order differential equation, given a 1 mxt () + xt () + Rmxt () = ( Bl) it () Spt () (1) C where m, C m m, Rm are the ma, compliance and mechanical reitance repectively of the loudpeaker moving part, ( Bl) the force factor, x() t the diaphragm poition, it () the driving current, S the effective piton area, and pt () the exogenou preure diturbance acting on the loudpeaker diaphragm. The electrical dynamic can alo be modeled by a firt order differential equation after mehe law, given a di() t ut () = Rit e () + Le + ( Bl) xt () () dt where ut () i the applied voltage, Re and L e the dc reitance and inductance of the voice coil, and ( Bl) x () t the back emf induced by the motion of the voice coil within magnetic field. Equation (1) and () form a coupled et of differential equation decribing the loudpeaker ytem. Expreing the preceding relation in complex quantitie (phaor repreentation) yield the characteritic equation of the generalized electrodynamic loudpeaker, given a ( ω m 1 ω m) ( ) ( ω ) ( ) Sp = j m + R + j C v Bl I U = Re + j Le I + Bl v (3) Under driving operation, Sp = 0 and no external force i applied to the mechanical ytem; under generating operation U = 0 and there i no voltage ource at the electric terminal of the loudpeaker. For imulating the dynamic of a loudpeaker we ue an approach baed on electroacoutic analogy. By taking account of the internal radiation impedance induced by the boxed environment we obtain the analytical decription of the loudpeaker ytem, be it mechanical or acoutical, in the form of a ynthetic circuit illutrated on the figure below. v Rm m C m SR ab Sm ab S Cab ( Bl) I Re Le R g Sp F mag U emf U U g F U mag emf = ( Bl) I = ( Bl) v Figure : Circuit repreentation of generalized cloed-box loudpeaker ytem whereu and R are the voltage ource and internal reitance of the audio amplifier. g g Starting from the circuit repreentation, if we remove the audio amplifier on the electric ide to replace it by hunt impedance Z, the driving current in the coil become equal to = ( + ) I Uemf Ze Zh where e h Z i the blocked electrical impedance of the coil ( v = 0 ). Solving 3

4 the equation (3) when the loudpeaker ytem i connected to a hunt impedance yield to the pecific acoutic impedance Z, given a Z m = = SZab + + ( Bl) ( + ) p Z v S S Z Z where Zab i the acoutic impedance correponding to the cloed-box and Zm the mechanical impedance of the diaphragm. At lat, the acoutic aborption coefficient under normal incidence i defined a: Z / ρc 1 α = 1 (5) Z / ρc+ 1 where ρ and c are the denity of air and the celerity of ound in the air. 3. Numerical imulation The figure below illutrate the effect of adding a ma to the moving part of the loudpeaker (dotted line with cro marker curve), and then connecting a uitable reitive load to it electrical terminal (dotted line with circular marker curve), compared to the cae of the open cloed-box loudpeaker (continuou line curve). The reult are expreed in term of acoutic impedance (left chart), and aborption coefficient (right chart). Thee reult give the evidence of the performance of the hunt loudpeaker technique for ue a locally reacting low-frequency noie aborber, for example in the cope of damping low-frequency modal behaviour in a room. e h (4) Figure 3: computed normalized acoutic impedance Z / c ρ (left) and aborption coefficient α (right) of the hunt loudpeaker ytem 3.3 Obervation A baic analytical decription of the loudpeaker in the frequency domain i able to model it dynamic in piton mode, and hence to predict it acoutic performance. By conducting a hort enitivity analyi on the loudpeaker parameter we can tune the reonant part of it frequency repone toward a deired value. Then, by connecting uitable hunt impedance, the quality factor can be enhanced to provide an improved aborption Damping of room modal behaviour with hunt loudpeaker Having hown the capability of the hunt loudpeaker concept to adapt the acoutic impedance of a loudpeaker diaphragm to a deired value, it can be aeed a a olution for lowfrequency aborber epecially in the frame of the damping of modal behaviour in room. The following intend to demontrate the performance of the hunt loudpeaker technique a lowfrequency aborber for cloed pace. 4

5 4.1 Simulation In order to perform both computational and experimental aement within the facilitie of the Laboratory of Electromagnetic and Acoutic at EPFL (LEMA), we have choen the reverberant chamber, of about 00 m 3, the complex geometry of which doe not allow the ue of an analytical olution for the tationary wave decription. It ha then been choen to deign a pecific finiteelement model of the reveberant chamber, with the help of Comol Multiphyic 3.5a oftware Simulation etup The following characteritic have been conidered: - the reverberant chamber geometry ha been accurately modelled a illutrated on Figure 4, the 6 wall being denoted in the following Sx 1, Sx, Sy 1, Sy, Sz 1, Sz, - the acoutic domain ha been et up, with frequency dependant parametric olver, - the wall of the reverberant chamber have been conidered a having a uniform pecific impedance Z wall = 10 6 Pa..m -1 (determined after a preliminary aement of the quality factor of the mode (1,1,0) in the room), - all loudpeaker in the model (ource and aborber) are conidered a circular piton with pecific boundary condition (velocity for the ource, impedance for aborber), o a circular piton of radiu a=150 mm repreent the acoutic ource (loudpeaker), embedded within wall Sx 1, roughly at a corner of the room. The excitation conit of a velocity depending on frequency after the mechanical impedance of the loudpeaker, auming a frequency independent electro-mechanical Laplace force at the loudpeaker diaphragm, o a horizontal array of 10 circular piton of radiu a=150 mm repreent the variable aborber, embedded within wall Sx, roughly along the bottom line of the face. They are computed a impedant boundary condition, the value of which can be et to Z wall or to Z, depending on the computation cae (rep. for hard wall and hunt loudpeaker condition). Figure 4 : the reverberant chamber at LEMA (left: CAD model in Comol Multiphyic, right: photograph taken from the entrance) 4.1. Simulation reult The ound preure level at corner #4 (a defined on Figure 4) computed with Comol Multiphyic, without any treatment ( hardwall ), and with an array of 10 low-frequency hunt loudpeaker along one face of the room are given in Figure 5. 5

6 Figure 5: Sound preure level computed between 0 Hz and 50 Hz, at corner 4, for different treatment (hard wall and hunt loudpeaker) It can be oberved that a mall urface of treatment (not more than 0.7 m ) i ufficient to damp of about 1 db the main reonance frequencie in the reverberant chamber. In the following, we will focu on the 34.9 Hz reonance frequency of the room, correponding to mode (1,1,0) (thi notation i not rigorou ince the room i not a parallelepiped). The experimental aement will then addre the blue zone in the room repone illutrated above. 4. Experimental aement In order to ae the accuracy of the model, and verify the performance of the hunt loudpeaker in room, it ha been decided to et up an experimental etup with imilar pecification than the numerical computation. For the purpoe of the preent paper, we have only focued on the mode 110 at 34.9 Hz, for which the hunt loudpeaker have been optimized. Then the following experimental aement will only addre the [30 Hz-40 Hz] frequency bandwidth Experimental etup - the ource i a home-made ba-reflex loudpeaker ytem, deigned to provide the requeted acoutic power in the requeted frequency bandwidth, - the excitation i a dicrete wept ine with 0.1 Hz frequency tep from 30 Hz to 40 Hz, each tep lating 30, allowing the extinction of any prior mode, and the etablihment of tationary ound field at each frequency tep (thi technique, illutrated on Figure 7 and Figure 8, provide better reult than other excitation a explained in a prior tudy 3 ), - an array of 10 hunt cloed-box loudpeaker (Monacor SPH-300 each in a 50 dm3 cloedbox) i put parallel to the bottom line of wall Sx, the loudpeaker face pointing along direction x, - a Brüel & Kjaer Type 4165 electret microphone (enitivity 50 mv/pa) ene the acoutic preure at corner 4 of the room. 4.. Experimental reult The reult of aement of the influence of the array of aborber on the identified mode at 35 Hz i given in Figure 6, and compared to the ame meaurement with no aborber ( hardwall ). It i alo to be compared with computation reult given in the preceding ection. 6

7 Figure 6: Stationnary ound preure level meaured in the LEMA reverberant chamber, between 30 Hz and 40 Hz, at corner #4, for different treatment (hard wall and hunt loudpeaker) It can be oberved that a imple array made of 10 paive hunt loudpeaker i ufficient to reduce of more than 10 db the level of the 34.9 Hz reonance of the room. Thee performance are obviouly trongly dependant on the poition of the aborber, and a further enitivity tudy hould be performed for a better undertanding of the concept within wide reverberant room. Figure 7: temporal behaviour of the acoutic preure in the vicinity of the mode, with hard wall (left: 34.9 Hz; right: 35.0 Hz) Figure 8: temporal behaviour of the acoutic preure in the vicinity of the mode, with 10 hunt loudpeaker (left: 34.9 Hz; right: 35.0 Hz) 7

8 5. Concluion It ha been proven that hunt loudpeaker i an efficient technique for providing enhanced acoutic aborption in the low-frequency range, and allowing a rather broad variability. An experimental proof of concept ha been performed with an Impedance Tube aement, after ISO tandard, and the aement in a 3D ituation uch a the reverberant chamber how the efficiency of thi concept in an almot realitic condition, with a broadband noie excitation. Further experimental validation hould be performed with le impedant wall, uch a thoe of actual habitation, and with real low-frequency noie ource. REFERENCES K. Peron Waye, M. Björkman, R. Rylander, Loudne, annoyance and dba in evaluating low frequency ound. Journal of Low Frequency Noie and Vibration, 9, 1990, C. H. Hanen, The Effect of Low-Frequency Noie and Vibration on People, Multi- Science Publihing Co. Ltd, United Kingdom, 008 H. Kutruff, Room Acoutic, 4 th edition, Spon Pre, London, United Kingdom, 000 P.-J. René, Contribution aux étude ur le couplage électroacoutique dan le epace clo en vue du contrôle actif, PhD Thei, 006, Ecole Polytechnique Fédérale de Lauanne. M. Roi, Audio, Pree Polytechnique Univeritaire Romande, Lauanne, Switzerland, 008 H. Liek, F. Sandoz, From the Electrical Shunting of a Loudpeaker to Active Impedance Control, Proc. of Acoutic 08, Pari, 008 8