Vibration and Radiation Behavior of Loudspeaker s Membrane

Hands-On Training 2 Vibration and Radiation Behavior of Loudspeaker s Membrane 1 Objetive of the Hands-on Training - Understanding the need for distributed parameters to model loudspeakers at higher frequenies - Applying laser sanning tehniques to eletro- aoustial transduer - Interpreting the results of modal analysis - Refreshing the basi theory of sound radiation and propagation - Performing sound radiation analysis - Developing skills in loudspeaker diagnostis to assess quality and hoose between design hoies 2 Requirements 2.1 Previous Knowledge of the Partiipants It is reommended to do the previous Klippel Training 1 Linear Lumped Parameter Measurement before starting this training. 2.2 Minimum Requirements The objetives of the hands-on training an be aomplished by using the results of the measurement provided in a Klippel database (.ksp) dispensing with a omplete setup of the KLIPPEL measurement hardware. The data may be viewed by downloading the SCN Analysis Software (version 2.0.11 or later) and the measurement software db-lab from www.klippel.de/training and installing them on a Windows PC. 2.3 Optional Requirements If the partiipants have aess to a KLIPPEL R&D Measurement System we reommend to perform some additional measurements on transduers provided by instrutor or by the partiipants. In order to perform these measurements, you will also need the following additional software and hardware omponents: Sanning Control Hardware 3D Sanner Distortion Analyzer DA2 Laser Sensor + Controller Amplifier Driver Stand 3 The Training Proess 1. Read the theory that follows to refresh your knowledge required for the training. 2. Wath the demo video to learn about the pratial aspets of the measurement. 3. Answer the preparatory questions to hek your understanding. 4. Follow the instrutions to interpret the results in the database and answer the multiple-hoie questions off-line. 5. Chek your knowledge by submitting your responses to the anonymous evaluation system at www.klippel.de/training. 6. Reeive an email ontaining a Certifiate of Mastery, Knowledge or Partiipation (depending on your performane). 7. Perform some optional measurements on transduers if the hardware is available. 1

4 Introdution At low frequenies the motor and mehanial system of the loudspeaker an be modeled by an equivalent iruit using lumped parameters. The eletrial signals (voltage u and urrent i) at the terminals generate the eletro-dynamial fore F oil driving the moving mass M ms, stiffness of the suspension K ms and mehanial resistane R ms and generating the voie oil veloity v oil. An eletrial signal (e.g. voltage u) and a mehanial signal (e.g. veloity v) desribe the transfer of the audio signal in one-dimensional signal path (see Training 1). At higher frequenies a distributed model omprising a multitude of parameters and state variables is required to desribe the vibration of the diaphragm and suspension system. The veloity v(r ) in normal diretion at any point r on the radiating surfae generates the sound pressure values p(r n ) and p(r a ) in the near and far field, respetively. u terminals i Motor F oil Voie oil v oil Vibration F( r ) radiator s surfae v( r ) Radiation near field p r ) ( n far field p( r a ) Eletrial Measurement Mehanial Measurement Aoustial Measurement TS parameters Lumped Parameters vibration, geometry Far Field Response Distributed Parameters Figure 1: Loudspeaker parameters Although mehanial vibration plays an important role in the generation of the reprodued sound, its measurement has been muh more diffiult in the past than the measurement of eletrial input signals and aoustial output signals. Modern Laser sanning tehniques measure the mehanial vibration and the geometry of the one at high auray. The SCN Analysis Software supports the visualization and animation of the measured data and provides new kinds of analysis of one vibration and predition of the radiated sound pressure. 4.1 Displaement Transfer Funtion The laser sanner provides the omplex transfer funtion H x ( j, r ) X ( j, r ) U( j) (1) between the voltage signal u at the loudspeakers terminal and the displaement x at an arbitrary point r on the radiating surfae. The exat position of the measuring points is reorded and desribes the geometry of the membrane surfae. The number of sanning points on the measured grid varies between 50 to 3200, depending on the appliation (see demo video). 2

[db] KLIPPEL E-Learning, Training 2 3/7/2013 Figure 2 shows an example of transfer funtion response of a loudspeaker. The red arrow indiates the resonane frequeny of the woofer at f s 50 Hz. Below the resonane the transduer generates onstant voie oil displaement beause the entire exitation fore flows into the mehanial suspension assuming onstant stiffness. Above resonane the response falls by 12 db/otave approximately. Above 1 khz there are signifiant deviations due to vibration modes breaking up on the one whih will be disussed in the following setions. 0 Magnitude of the Displaement Transfer Funtion -10-20 -30-40 -50 Effets of break-up modes -60-70 -80-90 Fundamental resonane 12dB/otave -100 f s 10² 10³ 10 4 f [Hz] Figure 2: Magnitude of Transfer Funtion H x (jω, r ) between input voltage and displaement at point r 4.2 Aumulated Aeleration Level The amplitude of the vibration of the radiator may be summarized in an Aumulated Aeleration Level (AAL) defined by paa( a AAL db (2) a p r ) ( r ) 20 log 2 o using the sound pressure potential p 2 0 aa( ra ) S v( r ) r a r ds (3) with ρ 0 S C r r a p 0 density of air surfae of the membrane point in the surfae element ds observation point in the far field referene sound pressure and the veloity v( j, r ) jh ( j, r ) u( j) (4) x 3

expressed by using the terminal voltage u and the transfer funtion H x (jω,r ) measured by laser sanning. The sound pressure potential p aa desribes the maximal sound pressure at point r a in the far field while negleting phase information due to the distane r a r and onsidering the magnitude of veloity v only. Therefore the AAL is always larger than the Sound Pressure Level (SPL) as shown in Figure 3. 80 [db] Rigid body mode Figure 3: Comparison AAL and SPL urves at the same observation point r a At low frequenies, below one break up (at 800 Hz, in Figure 3), the SPL is idential with the AAL. At higher frequenies the AAL reveals distint peaks whih orrespond to modal resonanes on the one. Contrary, the SPL response shows at higher frequenies signifiant dips whih orrespond to destrutive interferenes in the aoustial radiation. 4.2.1 Modal Analysis The peaks in the AAL response orrespond to resonanes of distributed modes whih are similar to the fundamental resonane f s where the loudspeaker an be modeled by lumped parameters. The natural frequenies are mutually orthogonal and an be used as strutural funtions in a series expansion a( r ) H i0 r i ( i j ( r ) (5) i where ) desribes the loal distribution of the vibration mode and H i (jω) the frequeny response for eah vibration mode: 2 H i j 1i j / i i The modal loss fator 2 1 f2 f1 i (7) f i i / 2 at the natural frequeny ω i an be determined after reading the 3dB bandwidth f 2 - f 1 as illustrated in Figure 4. (6) 4

[db] 92,5 90,0 [db] 87,5 85,0 82,5 AAL 0 db - 3dB 80,0 77,5 f 1 f 0 f 2 6*10 2 7*10 2 8*10 2 9*10 2 10 3 f [Hz] Figure 4: Reading the relative 3 db bandwidth in the AAL urve 4.2.2 Axial Symmetrial Deomposition If the loudspeaker one has a round shape the total vibration an be split in radial and irumferential (irular) omponents. The modes propagating in radial diretion an be alulated by averaging the vibration v versus the irumferential angle φ giving the radial veloity as illustrated in Figure 5. The irumferential modes are the differene between total vibration and the radial omponent: v 1 2 rad ) vtotal( d 2 (8) vir vtotal v rad 0 (9) Figure 5: Separation of radial and irumferential mode in transduers with round geometries Figure 6 shows that the Aumulated Aeleration Level (AAL) of the irumferential modes rises with the frequeny. Cirumferential modes with high amplitude may produe signifiant nonlinear distortion but produe low Sound Pressure Level (SPL) on-axis. However, irumferential modes generate signifiant side lobes resulting in a low Diretivity Index (DI). The lowest irumferential omponent is a roking mode whih may ause voie oil rubbing in the gap. 90 85 Aeleration Level Cirular Component SPL [db] 80 75 70 65 60 55 50 45 40 0.1 1 10 f [khz] Figure 6: AAL of the total vibration (red) and AAL of the irumferential omponent (blue) versus frequeny 5

4.3 Sound Radiation The sound pressure p(r a ) at an observation point r a generated by a vibrating surfae S an be approximately alulated by desribing the sound radiation at eah point r on the surfae by a monopole generating a volume flow dq =v(r )ds aording to the veloity v and the orresponding area ds. Figure 7: Sound Radiation modeled by equivalent monopoles on the one s surfae If the radiator s surfae is mounted in a baffle the total sound pressure at a point r a in the far field an be alulated by integrating the ontribution of all monopoles using the first Rayleigh integral (10) p j 0 v( r ) jk ra r ( ra ) e ds (10) 2 r S a r jk r r a using density of air 0. The exponential e produes the phase shift, whih results from the time required for the sound wave traveling from the soure point r to the observation point r a. The denominator r a - r desribes the attenuation of the sound with rising distane between soure and observing point. The Sound Pressure Level (SPL) is defined by p j, ra SPL a p (, r ) 20log 2 o db (11) using referene sound pressure p 0. 4.3.1 Beam Pattern Figure 8 shows the beam pattern whih is the variation of the relative sound pressure on a sphere in the far field over an azimuthal angle ϕ and an elevation angle. 6

Figure 8: Beam Pattern The beam pattern is defined by b( p r,,, ) 20log H(, ) db 20log p r,0,0 db (12) as the level of the diretional fator H (, ) whih is the ratio of the sound pressure p r,, at an observing point at angles,θ and radius r and the on-axis sound pressure pr,0,0 at distane r. Thus the sound pressure level on- axis SPL ax (r) an be desribed as SPL ax p( r,0,0) r db p ) 20log o ( (13) 4.3.2 Sound Power In far field the total aousti sound power radiated by the soure an be obtained by integrating the mean square of the sound pressure on the surfae S over the angles and by the following equation 1 0 S p( r,, ) 2 ds using the speed of the sound. The sound power level L Π db P log 10 0 (14) 10 (15) using the referene power P 0 = 10-12 W. L (in db) is defined as 4.3.3 Diretivity The diretivity defined by S D 2 H (, ) ds (16) and the derived Diretivity Index in db DI 10log10( D) db (17) desribe the beaming of the soure. For a monopole having an omni-diretional radiation harateristi the Diretivity Index equals 0 db. Operating a radiator (e.g. one) in an infinite baffle and radiating into half spae, it is possible to find a distane r 0.4 m between soure and observation point where the Diretivity Index (DI) is the differene between the sound pressure and sound power level: DI SPL ax ( r 0.4m) L (18) Figure 9 shows the most important three responses of a radiator mounted in a baffle. At low frequenies, there is no differene between the three urves beause the radiator vibrates as a rigid body and the loudspeaker generates an omni-diretional radiation pattern beause wave length is muh larger than the geometrial dimensions of the radiator. At higher frequenies, where the break-up modes our, the aoustial anellation ause a differene between AAL and SPL. The differene between SPL on-axis and 7

Sound Power response at higher frequenies orresponds with the rising Diretivity Index and the beaming of the soure. (db) 80 Rigid body mode AAL ax 75 SPL ax Aoustial Canellation 70 Omni direional soure 65 60 Sound Power L Diretivity Index DI 55 100 1k Frequeny (Hz) Hz 10k Figure 9: AAL response, sound power response and on-axis SPL responses at a distane r = 0.4 m of a radiator operated in an infinite baffle 4.3.4 Sound-Pressure-Related Deomposition To explain the aoustial anellation it is useful to deompose the total vibration into three vibration omponents: v( r ) vin ( r ) vanti ( r ) vquad ( r ) (19) generates sound redues sound no sound Figure 10: sound-pressure-related deomposition The in-phase omponent v in (r ) is a onstrutive ontribution to the sound pressure p(r a ) at the observation point r a. The anti-phase omponent v anti (r ) is a destrutive ontribution and redues the sound pressure p(r a ). The quadrature omponent v quad (r ) will be ompletely ompensated by the ontributions from other points on the radiator surfae and has no effet on the sound pressure p(r a ) at the observation point r a. The KLIPPEL engineering poster Loudspeaker Sound Radiation gives a detailed desription of sound pressure deomposition method. 8

SPL [db] KLIPPEL E-Learning, Training 2 3/7/2013 (db) 85 80 75 70 65 60 55 50 45 40 35 30 Quadrature Component AAL quad In- Phase Component SPL in =AAL in 100 1k Frequeny [Hz] TotalAAL Total SPL Anti- Phase Component SPL anti =AAL anti Figure 11: Comparison sound pressure omponents with AAL and SPL 10k The three vibration omponents an be explained in greater detail in Figure 11 whih ompares the omponents with the AAL and SPL responses: 1. The responses SPL in =AAL in of the in-phase omponent may be larger than the total SPL but never exeeds the total AAL. These urves oinide below one break-up where the anti-phase and quadrature omponents are negligible. 2. The responses SPL anti =AAL anti of the anti-phase omponent rise rapidly at the break-up frequeny (here about 1 khz) but never exeed the values of SPL in =AAL in in the in-phase omponent. 3. The quadrature omponent produes no sound pressure but the AAL quad may exeed the in-phase omponent. The peak at 380 Hz indiates a roking mode. 4.3.5 Aoustial Canellation Signifiant dips in the SPL response are aused by aoustial anellation whih ours if the anti-phase omponent is not negligible and the differene between in-phase omponent SPL in and anti-phase omponent SPL anti beomes smaller than 10 db as shown in Figure 12. 1078,1 p Hz ( r ) p ( r a ) a in anti 90 80 70 SCN Result Curves - SPL Deomposition Total SPL In-Phase Component Anti-Phase Component 60 50 40 p( r ) p ( r ) p ( r ) 0 a in a anti a 30 20 10 0 10 2 10 3 10 4 f [Hz] 4.4 Roking Mode Figure 12: Aoustial anellation generating dips in the total SPL response The first irumferential mode on the surround auses a roking of the one and a tilting of the voie oil former at low frequenies. This may result in voie oil rubbing in the gap produing impulsive distortion. 9

voie oil rubbing Figure 13: Roking mode (left) and voie oil rubbing (right) The roking mode provides poor radiation onditions, sine the radiation surfae behaves as two soures (dipole) generating positive and negative volume flow of almost equal soure strength generating low sound pressure on-axis. The quadrature omponent AAL quad is a very good indiator of roking modes on radiators of arbitrary shape (e.g. retangular diaphragm). 4.5 Effetive Radiation Area The effetive radiation area S D is an important lumped parameter desribing the sound radiation by replaing the radiator s surfae by a rigid piston moving with the mean value of the voie oil veloity v oil and generating the same volume veloity q with the piston s surfae S D as the radiator s surfae S. The mean value of the voie oil veloity v oil is alulated by integrating the veloity on a irumferene with the voie oil radius r oil whih suppresses roking and other asymmetrial vibration modes. Radiator s surfae replaed by a Rigid piston SD ( ) S v ( ) S v(, r ) ds oil (20) () v oil S D () v, r ) ( using mean voie oil veloity r oil q() v oil ( ) 2 0 v(, r oil 2, ) d (21) q() Figure 14: Calulation of the effetive radiation area S D (ω) versus frequeny Following the definition above, the effetive radiation area S D (ω) is a funtion of frequeny ω. This funtion may be used to predit the sound pressure at points with arbitrary distane on the radiation axis. In most ases a single value S D = S D (ω 0 ) is derived from the response by reading the value at the resonane frequeny ω 0. 10

Voie oil m 2 3,0 2,5 2,0 1,5 1,0 0,5 Reading the absolute value at fundamental resonane gives SD S D ( 0 ) S D () f 0 1 10 Frequeny [khz] Figure 15: Position of the voie oil (left) and the graphi of the effetive radiation area (right) For woofers, where the width of the surround is small ompared to the inner diameter of the one, the effetive radiation area may be approximated by the area using the average of the surround s outer and inner diameter. This approximation fails in miro speakers and transduers for headphones and headsets where the surround area is relatively large and the urved geometry generates a nonlinear deay of the exursion versus the surround. 5 Preparatory Questions Chek your theoretial knowledge before you start the regular training. Answer the questions by seleting all orret responses (sometimes, there will be more than one). QUESTION 1: How do the one and the dust ap move at low frequenies? MC a: The one and the dust ap vibrate as an almost rigid body. All points move with the same amplitude and phase. MC b: The one and the dust ap vibrate as an elasti body. The points on the surfae move with different amplitude and phase. MC : At partiular frequenies the points on the one and dust ap may vibrate at different amplitude and phase. This is aused by a roking mode whih deforms the surround and spider but tilts the one and dust ap as a rigid body. QUESTION 2: What happens to the sound pressure level (SPL) at the reeiving point r a in the far field if the distane between the membrane and the reeiving point is doubled? (Use the equation (11) to answer this question) MC a: The sound pressure inreases by 2 db. MC b: The sound pressure inreases by 6 db. MC : The sound pressure dereases by 2 db. MC d: The sound pressure dereases by 6 db. QUESTION 3: Compare the equation (11) for the alulation of the sound pressure level (SPL) at the observation point r a with the equation (2) for the aumulated aeleration level (AAL). Whih relationship exists between AAL and SPL? MC a: The AAL and the SPL are almost idential at low frequenies, where the radiator (diaphragm, one) vibrates as a rigid body and the wave length is muh larger than the geometrial dimensions of the radiator. MC b: The SPL is never larger than the AAL at the same observation point r a. MC : The SPL alulation onsiders the phase angle of the mehanial vibration and the phase shift aused by the propagation between the soure point r and the reeiving point r a. 11

MC d: The AAL alulation neglets any phase information and orresponds with the maximal sound pressure whih would be generated if all points r on the membrane would ontribute onstrutively to the total sound pressure SPL at the point r a. QUESTION 4: Whih relationships exist between in-phase, anti-phase and quadrature omponents? MC a: The AAL in of the in-phase omponent is never smaller than AAL anti of the anti-phase omponent. MC b: The AAL anti is always larger than the SPL anti of the anti-phase omponent. MC : The SPL quad of the quadrature omponent is always larger than the SPL in of the in-phase omponent. MC d: AAL quad is idential with SPL quad of the quadrature omponent. MC e: AAL in is idential with the SPL in of the in-phase omponent. 6 Interpretation of Sanning Data (no hardware required) Step 1: Step 2: View the demo movie Vibration and Radiation Behavior of Loudspeaker Membrane to see how a pratial analysis is performed. Download from the website www.klippel.de/training the Klippel Sanning System SCN and the db- Lab and install them on your omputer. Advie: It is reommended to do the following exerises offline and to note the answers of the multiple hoie questions on a paper! 6.1 Displaement on the Radiator s Surfae Step 3: Step 4: Step 5: Clik on file honeyomb.ksp to ativate the SCN Analysis Software to view the results of a laser san applied to a flat radiator made of honeyomb material. Selet the tab Cross Setion View. Press the button Animation and adjust the Amplitude Enhanement to generate a natural vibration of the radiator. Clik with the right mouse button on the diagram and ativate the Show Current Point.. Set the ursor to the entre of the radiator to see the magnitude of the transfer funtion H x (f) between terminal voltage U(f) and displaement X(f, r ) at this partiular point r. QUESTION 5: How does the magnitude of the transfer funtion H x (f) hange by doubling the frequeny f (70 Hz < f < 5 khz)? Step 6: MC a: The magnitude of the transfer funtion Hx(f) falls with 6 db per otave approximately. MC b: The magnitude of the transfer funtion Hx(f) falls with 12 db per otave approximately. MC : The magnitude of the transfer funtion Hx(f) falls with 18 db per otave approximately. Set the frequeny ursor in the lower diagram Displaement Transfer Funtion to 140 Hz in the file honeyomb.ksp. View the magnitude of the transfer funtion H x (f = 140 Hz, r) as a funtion of the radius r by setting the blue marker at different loations on the setional view in the upper diagram. QUESTION 6: How does the magnitude of the transfer funtion H x (f) hange versus radius r at low frequenies (f = 140 Hz)? MC a: The magnitude is almost onstant over the one area beause this part has a high bending stiffness and moves as a rigid body at low frequenies. MC b: All of the deformation ours in the surround where the magnitude dereases linearly from the inner edge to the outer edge. Thus the displaement on the middle of the surround is always 6 db lower than the one displaement. This is the basis for an aurate alulation 12

MC : 6.2 Modal Analysis Step 7: of the equivalent radiation surfae S D by alulating the mean value of inner and outer diameter of the suspension. The magnitude dereases nonlinearly from the inner edge to the outer edge of the surround. The displaement in the middle of the surround in the partiular honeyomb driver is approximately 3 db lower than the one displaement. This has some major onsequenes on the measurement of the equivalent radiation surfae S D (the aoustial measurement gives different results than the geometrial measurement). Selet the lower diagram on the tab Cross-setional View of the honeyomb.ksp and lik with the right-mouse button on the diagram to deativate Show urrent point. Selet the radio button Aeleration on Modeling Mode. Find the natural frequenies by moving the frequeny ursor in the lower diagram to the peaks in the aeleration level urve shown in red. QUESTION 7: Whih loudspeaker omponents ontribute signifiantly to the modal vibration at the natural frequenies 843 Hz and 6,14 khz? MC a: 843 Hz: both surround and honeyomb one; 6,14 khz; honeyomb one MC b: 843 Hz: surround; 6,14 khz: honeyomb one MC : 843 Hz: both surround and honeyomb one; 6.14 khz: both surround and honeyomb one; MC d: 843 Hz: surround; 6,14 khz surround MC e: 843 Hz: honeyomb one; 6,14 khz; honeyomb one QUESTION 8: Whih natural frequeny provides the largest AAL? Step 8: MC a: The largest mode is at 6.1 khz. MC b: The largest mode is at 5 khz. MC : The largest mode is at 2.5 khz. Use the ursor to read the 3 db bandwidth in the AAL response of the honeyomb.ksp at the natural frequeny 6.14 khz. QUESTION 9: Use the equation (7) to determine the modal loss fator at 6.14 khz. MC a: The modal loss fator η is 0,03 approximately. MC b: The modal loss fator η is 0,3 approximately. MC : The modal loss fator η is 0,003 approximately. QUESTION 10: Why is the modal loss fator η at 6.14 khz muh smaller than at 5 khz? MC a: Beause the vibration of the surround is muh smaller at 6.14 khz and the honeyomb material provides less damping than the surround. MC b: Beause the vibration of the surround is muh smaller at 6.14 khz and the honeyomb material provides more damping than the surround. QUESTION 11: How an the modal loss fator η at 6.14 khz be inreased? MC a: Using a different surround material providing more damping. MC b: Using a different spider material providing more damping. MC : Using a different honeyomb material providing more damping. QUESTION 12: What are the onsequenes of a low modal loss fator on the sound pressure output? MC a: Signifiant peaks in the SPL response whih orresponds with long ringing in the umulative deay spetrum (transient distortion). MC b: High exursion ausing nonlinear distortion in the sound pressure output. 13

MC : Low modal loss fator only affets the mehanial vibration but not the radiation of the sound and has no influene on the sound pressure output. 6.3 Axial Symmetrial Deomposition Step 9: Step 10: Open the file piston driver.ksp. Selet the tab Animation. Swith the Modelling Mode to Aeleration. Swith the Deomposition to Radial and selet Total Vibration. Press Animation button. Set the frequeny ursor in the lower diagram to 140 Hz. Compare the Radial and Cirular omponent with the Total Vibration by seleting the omponents in Deomposition. Adjust the Amplitude Enhanement to view eah omponent. QUESTION 13: Whih modes determine the vibration behavior at 140 Hz? Step 11: MC a: There is an axial symmetrial mode that dominates the total omponent. MC b: The irumferential omponent is more than 20 db below the AAL of the total vibration and an be negleted. MC : The irumferential mode affets the spider and the surround ausing a small tilting of the piston (roking mode). MC d: The irumferential and radial omponents have approximately the same AAL at this frequeny. MC e: There is no irumferential mode at this frequeny. Set the frequeny ursor in the lower diagram to the seond peak of the total AAL at 3.9 khz. Compare the Radial and Cirular omponent with the Total Vibration by seleting the omponents in Deomposition. Adjust the Amplitude Enhanement to view eah omponent properly. QUESTION 14: Whih modes determine the vibration behavior at 3.9 khz? MC a: There is an axial symmetrial mode whih dominates the total vibration (irumferential omponent is negligible). MC b: There is a dominant irumferential omponent whih dominates the total AAL (radial omponent is negligible). MC : The irumferential mode affets the spider and the surround ausing a tilting of the piston (roking mode). MC d: The irumferential and radial omponents have approximately the same AAL at this frequeny. 6.4 Sound Pressure Step 12: Open the file piston driver.ksp and selet the tab Animation. Selet in Modelling Mode Aeleration and in Deomposition SPL related and Total Vibration. Set the angles theta θ = 0 o and phi φ = 0 o to see the on-axis response and ompare the total AAL with total SPL response. QUESTION 15: Whih relationship exists between the SPL and AAL response? MC a: Below 800 Hz the SPL and AAL response are almost idential beause the radiator vibrates as a rigid body. MC b: Sharp peaks in the AAL response orrespond to high values in the SPL-response at the same frequeny. MC : Sharp dips in the SPL response orrespond to sharp peaks at the same frequeny in the AAL response. 6.5 Beam Pattern 14

Step 13: In the file piston driver.ksp view the tab Radiation Analysis. Selet the SPL under Modeling Mode and Total Vibration under SPL related Deomposition. Compare the polar pattern (dependeny of SPL on angle θ) shown in the upper left diagram by varying the angles φ (turning the ursor in the upper right diagram). QUESTION 16: How does the SPL hange versus angles φ and θ at 700 Hz, 1.1 khz and 1.5 khz? MC a: The SPL variation versus angles θ at both 700 Hz and 1.5 khz is very small (< 3 db) produing an almost omni-diretional radiation pattern. MC b: The SPL at 1.1 khz is on-axis (θ = 0 ) lower than off-axis (for example, θ > 50 o ). MC : The SPL pattern is almost independent of angles φ (turning the ursor in the upper right diagram) for all three frequenies. MC d: There is an omni-diretional radiation pattern (onstant SPL for any hoie of angle φ and θ) at all three frequenies. QUESTION 17: How does the beam pattern hange at the higher natural frequenies 11.2 khz, 12.5 khz and 14 khz? Step 14: MC a: MC b: At higher frequenies the loudspeaker produes an omni-diretional radiation pattern. At higher frequenies the loudspeaker produes more SPL on-axis (θ = 0 ) than off-axis (θ > 50 ). There is only minor variation versus angle φ. In Deomposition mode selet the radio button Radial and then Cirular to see the beam pattern of the irumferential modes on the tab Radiation Analysis. Change the angle φ (turning the ursor in the upper right diagram) and hange the frequeny ursor in the diagram below. QUESTION 18: What is the typial radiation harateristi of the irumferential (irular) modes? MC a: The beam pattern has a null on-axis (θ=0 ) for any angle φ and any frequeny beause irumferential modes generate a regular vibration pattern on the irumferene omprising an equal number of positive and negative sound soures having equal soure strength approximately and anelling eah other on- axis in the far field. MC b: At low frequenies the SPL raises with rising value of θ beause the anellation effet vanishes off-axis. MC : Cirumferential modes generate an omni-diretional radiation pattern. 6.6 Diretivity Index Step 15: In the file piston driver.ksp lik on Tools, selet Sound Power and press the button Start Calulation. Searh for frequenies where the diretivity index is negative. QUESTION 19: What means a negative Diretivity Index DI = -10 db? MC a: The on-axis SPL is 10 db smaller than the sound pressure generated by an omni-diretional soure radiating the same sound power. MC b: The on-axis SPL is 10 db higher than the sound pressure generated by an omni-diretional soure radiating the same sound power. MC : The SPL generated by the radiator in an infinite baffle at a distane 0.4 m on-axis is 10 db lower than the sound power level. MC d: The SPL generated by the radiator in an infinite baffle at a distane 0.4 m on-axis is 10 db higher than the sound power level. MC e: The loudspeaker is beaming on-axis. 6.7 Sound Pressure Deomposition 15

Step 16: In the analysis of the file piston driver.ksp selet SPL related under Deomposition. Set the angle (θ=0 ) to analyze the sound pressure on-axis. Selet the In-phase Component and view the vibration pattern at 843 Hz. QUESTION 20: Where is the sound generated at 843 Hz? Step 17: MC a: The enter of the piston ontributes onstrutively to the sound pressure output on-axis. MC b: The outer area of the piston and the surround ontributes onstrutively to the sound pressure output on-axis. MC : The omplete surround and one area ontributes to the sound pressure on-axis. Compare the vibration patterns of the Quadrature Component, Anti-phase Component and the In-phase Component measured at the same frequeny 843 Hz. Keep the angle (θ=0 ) to analyse the sound pressure on-axis. QUESTION 21: To whih omponents an a point r on the one ontribute at one partiular frequeny? (Tip: See Figure 10.) MC a: A point an ontribute to the quadrature omponent and either to the in-phase omponent or to anti-phase omponent. MC b: A point an ontribute both to the in-phase and to the anti-phase omponent. MC : A point an ontribute to all three omponents (quadrature, in-phase and anti-phase). Step 18: Press the Export Curve button to save the urves in a.kdbx file and open this file in db-lab. Open the operation CAL Sanner Results in the objet Piston Driver and inspet the result window Result Curve 1. Compare the In-Phase and the Anti-Phase responses. QUESTION 22: Are there any frequenies where the In-Phase and Anti-Phase omponent have the same SPL value? MC a: At the fundamental resonane frequeny of the transduer. MC b: At the frequenies where the total sound pressure response shows signifiant dips (anellation points). MC : At the frequenies 1.078 khz, 4.429 khz., MC d: At the natural frequenies of the higher order modes where the total AAL response shows loal maxima (resonane peaks). MC e: In-phase omponent is always larger than the anti-phase omponent. 6.8 Roking Mode Step 19: Return to the SCN Analysis Software and selet the tab Animation. Selet the Quadrature Component under Deomposition and keep the angle (θ=0 ) to analyse the AAL on-axis. Swith the Modeling mode to Aeleration. View the radiation pattern at loal peaks of the AAL response. Adjust the Amplitude Enhanement to make the vibration visible. QUESTION 23: At whih frequeny ours the roking mode? MC a: The roking mode ours at 140 Hz and is approximately 28 db below the AAL of the total omponent. Thus the roking mode is not ritial. MC b: The roking mode ours at 468 Hz and is approximately 17 db below the AAL of the total omponent. Thus the roking mode is not ritial. MC : The roking mode ours at 890 Hz and is approximately 12 db below the AAL of the total omponent. Thus the roking mode is not ritial. MC d: The roking mode ours at 2.5 khz and is approximately 4 db below the AAL of the total omponent. Thus the roking may be onsidered as ritial beause the differene is smaller than 10 db. 16

Step 20: Open the file headphone.ksp and follow the Step 19:. QUESTION 24: Where is the roking mode of the headphone transduer? MC a: The roking mode ours 1.8 khz and is approximately 3 db below the AAL of the total omponent and almost idential with the in-phase omponent. Thus the roking mode dominates the total vibration and is ritial. MC b: The roking mode ours 398 Hz and is approximately 2 db below the AAL of the total omponent and 3 db above the in-phase omponent. The roking mode dominates the total vibration and is ritial. MC : The roking mode ours 4.5 khz and is approximately 13 db below the AAL of the total omponent. Thus the roking mode is not ritial. MC d: The roking mode ours 8.3 khz and is approximately 6 db below the AAL of the total omponent. Thus the roking may be onsidered as ritial beause the differene is smaller than 10 db. 6.9 Effetive Radiation Area Step 21: In the file headphone.ksp lik on Tools and then SD Calulation on the menu bar. Set the blue ursor in the upper left diagram to r oil = 7.5 mm where the voie oil is loated. View the effetive radiation area S d (f) as a funtion of frequeny. QUESTION 25: Why the radiation area S d (f) rises at higher frequenies (>10 khz)? Step 22: MC a: Beause there is more movement of the voie oil but less vibration at other areas of the one at higher frequenies. MC b: Beause there is less movement of the voie oil at higher frequenies while other parts of the diaphragm (in the enter of the diaphragm) generate suffiient volume veloity. MC : The quadrature omponent is rising at higher frequenies dereasing the aoustial output at higher frequenies. Set the blue ursor in the upper left diagram to middle area of the surround (r=12 mm) and in the entre of the diaphragm (r=3 mm) and investigate the influene of the radius on the effetive radiation area S d. QUESTION 26: How does the speified radius r affet the S d value? MC a: If the speified radius r is larger than the oil radius r oil the mean veloity v oil of the voie oil is alulated in the surround area where the veloity dereases with radius r. Thus v oil is smaller than the true value and the effetive radiation area SD is larger than the true value. MC b: If the speified radius r is smaller than the oil radius r oil the mean veloity v oil of the voie oil is alulated in the enter of the one where the veloity is almost onstant. Thus v oil is orretly measured and the error in the alulation of the effetive radiation area S D is negligible. MC : The radius r has only a minor influene on the SD alulation. 17

7 Performing a Vibration San (Hardware required) If the sanning hardware is available it is reommended to perform a san on a transduer provided by the instrutor or the partiipants. The target of the optional experiment is to determine the influene sanning grid and the number of points determining the sanning time. 7.1 Information to the Sanner Hardware The demo movie Vibration and Radiation Behavior of Loudspeakers Membrane gives you some pratial tips how to use the sanner hardware and software. A detailed desription of the hardware setup is provided in the manual. 7.2 Performing a Short Profile San Step 23: Step 24: Step 25: Step 26: Step 27: Start the software Klippel Sanning System SCN. In the File menu selet Perform New San. The shortest san is the profile san whih uses an asymmetrial grid on one angle only. After the initialization steps a new sanning projet an be started. Create a Projet File and give it name profile san.ksp. Leave the San Setup with the default setup and proeed to the Measurement Grid Setup. In Grid hoose Profile Grid in Preset to measure a single ross-line and enter the Outer Radius of your driver. Clik on Save and Start. Step 28: Step 29: Step 30: Follow the San Preparation steps and start the sanning. After ompleting the sanning proess (after a few minutes) start the SCN Visualization Software. Selet the anti-phase omponent in SPL. Searh for the frequeny f break-up where the one break-up ours. This is the frequeny where the SPL of the anti-phase omponent rises rapidly and is 30dB below the total SPL. Step 31: Selet the total omponent in AAL. Searh for the natural frequenies where the AAL shows destint maxima. Determine the modal loss fator. Does the material provides optimal damping for the mode? View the mode of vibration. Whih omponent (surround, one, dust ap) ontibutes signifiantly to the total modal loss fator? 7.3 Performing a Normal Explore San Step 32: Step 33: Step 34: Step 35: Step 36: Step 37: Step 38: SPL( fbreakup) SPLanti( fbreakup) 30dB Repeat Step 23: - Step 26: give it name explore san.ksp Selet in Preset Manual Grid to ustomize the sanning grid. Choose the Cirular San Area, enter the Radius of your driver and adapt the regular spaing of Radius Steps and Angle Steps. Follow the San Preparation steps. After the sanning view the results of the measurement using the analysis software. Compare the SPL response on-axis in the measurement profile san.ksp with the orresponding SPL urve measured in the explore san.ksp. Explain the auses for the differenes. Investigate the influene of the grids on the measurement of the irumferential modes of the loudspeaker. 18

Selet the quadrature omponent in AAL. Searh for the frequeny f rok where the first maximum in AAL quadrature omponent indiates a roking mode. Is the differene AAL rok (f rok )=AAL quad - AAL in larger than - 5 db? Step 39: Step 40: Start the Sound Power Calulation under the menu TOOLs. View the diretivity index and searh for frequeny f 6dB where the DI equals 6 db. Start the SD Calulation under the menu TOOLs. Set the ursor at the voie oil position and read the the S D -value. 8 Further Literature User Manual for the KLIPPEL R&D SYSTEM SCN Vibrometer Speifiation C5 Sanning Vibrameter (SCN): http://www.klippel.de/fileadmin/klippel/bilder/our_produts/r-d_system/pdf/c5- Sanning_Vibrometer.pdf Poster Loudspeaker Cone Vibration: http://www.klippel.de/uploads/media/klippel_cone_vibration_poster_01.pdf Poster Loudspeaker Sound Radiation: http://www.klippel.de/uploads/media/klippel_sound_radiation_poster_01.pdf Appliation Note AN31 Cone Vibration and Radiation Diagnostis: http://www.klippel.de/uploads/media/an_31_cone_vibration_and_radiation_diagnostis.pdf Paper Distributed Mehanial Parameters Desribing Vibration and Sound Radiation of Loudspeaker Drive Units: http://www.klippel.de/uploads/media/klippel Shlehter Distributed_parameter.pdf Paper Visualization and Analysis of Loudspeaker Vibrations: http://www.klippel.de/uploads/media/visualization_and_analysis_of_loudspeaker_vibration_01.pdf 19