Loudspeakes and Rooms fo Multichannel Audio Repoduction by Floyd E. Toole Vice Pesident Acoustical Engineeing Haman Intenational Pat 3 Getting the Bass Right Choosing the numbe and locations of subwoofes, and detemining whee to sit, ae fundamental to good bass. Multichannel audio should be shaed, so we ty to get good bass at seveal locations. Acoustical knowledge is essential, but EQ can help. The Rules fo Good Sound in Rooms At middle and high fequencies: Stat with a loudspeake that was designed to function well in a vaiety of diffeent ooms. Use geomety, eflection, diffusion, and absoption to achieve good imaging and ambiance. At low fequencies: Maximize the output fom the subwoofe(s). Achieve a unifom pefomance ove the listening aea. Equalize to achieve good pefomance. 123 So, we think that we know how to pick a good loudspeake, and with some simple acoustical devices o smat design, we can avoid destuctive eflections in a oom. Now, what about low fequencies, the ones whee the oom is the dominant facto? The fist task is to locate the subwoofe whee it adiates most effectively. Closed box o eflex (poted) woofes ae pessue souces. It mattes not which way the diaphagm faces because all such loudspeakes ae omni-diectional at low fequencies. Obviously, thee needs to be beathing space if we choose to face the diaphagm against a wall. And, if thee is a pot, don t plug it! Solid Angle VLF Gains 4π steadians = full sphee = ef. level = suspended in fee space 2π steadians = 1/2 sphee = +6dB SPL = on floo π steadians = 1/4 sphee = +12dB SPL = on floo against wall π/2 steadians = 1/8 sphee = +18dB SPL = on floo in cone 124 Howeve, whee we place the woofe with espect to the adjacent oom boundaies does matte. The least effective location is in the middle of a oom. It gets bette on the floo, still bette on the floo against a wall, and best in a cone. This is best in the sense of maximizing the quantity of bass adiated into the oom. 31 Januay, 2002 1
Measuements in a Patial Room 30 20 db 10 4p p * p/2 * THE SUBWOOFER REGION 0 * INFLEXIBLE SURFACES -10 20 50 100 500 1K 5K 10K 20K FREQUENCY (Hz) 125 In theoy we should be able to get huge gains fom cone placement, and the test shown in the slide indicates that, if conditions ae ight, the gains ae thee. In eal houses, the gains ae a lot less, because of flexible oom boundaies, open achways, etc. Still, even a 3 db gain doubles the acoustical powe into the oom, and that is equivalent to adding a second woofe. Not bad, and it's fee. A Subwoofe in a Cone Poduces the maximum possible LF output. This is good Enegizes all of the oom modes This can be good o bad, depending on the oom, and how it is aanged. CONCLUSION: Stat with the sub in a cone, and move it only if necessay. Howeve, as they say, thee is no fee lunch. Cone locations excite evey esonance in the oom. This may o may not be bad. You will lean how to know the diffeence befoe we ae though. If it is good fo a paticula oom, then leave it alone and move on to the next poblem. If not, find a bette location. Howeve, a cone is a logical stating location. Fo many simple installations, an unequalized single woofe in a cone can wok vey well indeed. In fact, I am listening ight now to just such a system in my office/den. 126 The Rules fo Good Sound in Rooms At middle and high fequencies: Stat with a loudspeake that was designed to function well in a vaiety of diffeent ooms. Use geomety, eflection, diffusion, and absoption to achieve good imaging and ambiance. At low fequencies: Maximize the output fom the subwoofe(s). Achieve a unifom pefomance ove the listening aea. Equalize to achieve good pefomance. 127 A multichannel audio system is intended to be a social expeience, shaed among seveal listenes. It is not like steeo, an antisocial expeience, if it is to be head popely. We need to ty to ceate a situation in which as many listenes as possible hea essentially the same sound. The poblem hee is Standing Waves, Room Resonances, Room Modes, Eigentones, etc. These ae all the same phenomenon. Most ooms boom. They have thei own bass pesonalities. It is simply not possible to listen to the tue bass output fom a loudspeake unless it is done in an anechoic space, and at vey low fequencies, that means outdoos. What we hea indoos, also includes the oom, and the positional factos within it. 128 Classes of Room Modes AXIAL: occuing between opposite paallel sufaces LENGTH WIDTH HEIGHT Sound eflects back and foth between two paallel sufaces. At cetain fequencies the incident and eflected sounds conspie to fom standing waves in which those fequencies can be amplified, and what we hea at those fequencies depends on whee we and the speakes ae located. These ae axial modes, since they exist along the majo axes of the oom. 129 31 Januay, 2002 2
Classes of Room Modes TANGENTIAL: occuing among fou sufaces, avoiding two that ae paallel The cyclical eflected pattens can include two, fou o moe sufaces. If fou ae involved, we call them tangential modes. Since some sound is absobed at each eflection, geneally the tangential modes ae less poweful than the axial modes, which include only two eflections pe cycle. 130 Classes of Room Modes OBLIQUE: occuing among any and all sufaces Oblique modes can involve any and all sufaces. They tend, theefoe, to be the least impotant. 131 In Tems of Causing Audible Poblems: AXIAL MODES ae the dominant facto! TANGENTIAL MODES can be significant in ooms with vey stiff/massive boundaies OBLIQUE MODES ae aely, if eve, elevant 132 What is a Standing Wave? Total + Pessue - Time = 0 Distance = 1/2 wavelength = 1/2l 133 The simplest of the standing waves, the axial modes, exist between two paallel eflecting sufaces. In this slide shown hee, imagine that the two vetical lines epesent walls in a oom. Imagine a woofe against the left-hand one, adiating a pue tone a sine wave as shown. If the ight wall wee not pesent, the sine wave would simply popagate away. With the wall in place, the potion of the sine wave that would have moved on to the ight is eflected back towads the souce. The walls hee ae sepaated by exactly one-half wavelength, so the eflected sound wave is identical to the incident wave they ovelap pefectly. When added they make the total sound wave shown. Remembe, this is a stop action view. Standing Waves Total + - P Hee is the same instant in time expanded in scale. D = 1/2 wavelength = 1/2l Time = 0 134 31 Januay, 2002 3
Standing Waves Total + - P Hee, we have done a vey, vey quick play and pause, stopping the action one-eighth of a wavelength late. Now the incident and eflected waves have diffeent shapes, but the total is much the same, only a bit lowe in amplitude. Inteestingly it still cosses zeo pessue half way between the walls. Time = + 1/8l 135 Standing Waves Total + - P This is anothe 1/8 wavelength late, o ¼ wavelength fom whee we stated. The instantaneous sound pessue is zeo eveywhee. Time = + 1/4l 136 Standing Waves Total + - P Moving on yet anothe 1/8 wavelength, we note that the total wavefom has flipped polaity, like a see-saw pivoting at the halfway point acoss the oom. Still no sound at the mid point. Time = + 3/8l 137 Standing Waves Total + - Time = + 1/2l P 138 At the half-wave stop-action view, we ae pecisely in a situation that mios whee we began. If we continued fo the emaining half wave, we would end up whee we stated. So, fo the fequency at which the oom dimension is pecisely onehalf wavelength, thee will be a esonance, and a standing wave in which the sound pessue is always zeo at the mid point between the eflecting sufaces. On eithe side the sound gets loude as one moves towads the walls. Note, that the instantaneous polaity of the pessue change is opposite on opposite sides of the pessue minimum, o null. This is impotant. Remembe it. Axial Standing Waves Total + - P Hee we see a supeimposition of the stop-action total wavefoms fo one complete wavelength. 139 31 Januay, 2002 4
What you hea at diffeent locations Thee is minimal sound at the mid point, and the sound gets loude as we move towads the walls. 140 Odes of Axial Standing Waves 2 x F Fequency = F 1 st Ode 2 nd Ode Fo a given distance between eflecting sufaces, the fist esonance will be at the fequency having a wavelength equal to twice the sepaation. If the distance is halved, the fequency is doubled. Thee is also a second-ode esonance, o standing wave, at exactly double the fist fequency, and this standing wave has two nulls. Thee will also be thid, fouth, and so on. 4 x F 2 x F 141 Visualizing Standing Waves Sound Level To visualize the standing waves, let us just plot the sound pessue as a function of dis tance, and emembe that the polaity changes each time we coss a null. + - + - + 142 Calculating the Fequencies of Modes f = c 2 n x 2 n y 2 n z 2 L x L y L z This fomula allows us to calculate all of the possible esonances in a ectangula oom. It is a bit fightening. WHERE: c is the speed of sound: 1130 ft/sec. n x, n y,n z ae integes fom 0 to, say, 5 and L x, L y, and L z ae the length, width and height of the oom in feet. 143 A Simple Way to Calculate the Axial Modes e.g. the fist length mode of a oom 20 feet long can be calculated as follows: speed of sound in ft/s 1130 f 1,0,0 = = = 28.25 Hz 2 x length in feet 40 othe length modes ae simple multiples of this: 2 x 28 = 56 Hz, 3 x 28 = 84 Hz, 4 x 28 = 112 Hz, and so on. Then do the same fo the width and height modes. 144 Fo the majoity of situations, it may be sufficient to calculate only the axial modes. If so, it is vey simple. Measue the oom dimensions. Multiply the length by two, and divide it into 1130 (fo dimensions in feet) o 345 (fo dimensions in metes). This gives this fist-ode esonance along that dimension. Multiply that fequency by 2 fo the second-ode esonance, by 3 fo the thid-ode, and so on. Usually it is necessay only to look at the fist thee o fou odes. Now, epeat that fo each of the othe two dimensions. 31 Januay, 2002 5
All Oblique Axial+Tan. Tangential All Axial Height Width Length An Even Simple Way to Calculate ALL of the Modes...and to Visualize Them. If you have a compute, it is all even easie. Just type in the dimensions, and the wok is done fo you. This is a little speadsheet pogam that uns in Micosoft Excel fo PC s that is available fo download fom www.haman.com in the section white papes. It shows, in an easy to undestand fom, all of the modes in a ectangula oom. 145 It has long been believed that, to be good, a oom must have a unifom distibution of modes in the fequency domain. This is cetainly tue fo evebeation chambes, whee the notion oiginated. But, is it tue fo listening spaces??? But what about the ideal oom? 146 The distibution of modes in the fequency domain is detemined by the RATIO of the oom dimensions: Height:Width:Length e.g. 1:1.5:2 = 8 x 12 x 16 feet 147 Is Thee an Ideal Room Shape? LENGTH Ove the yeas seveal acoustical luminaies have lent thei names to oom dimensions that pupot to have advantages. Do I have a favoite too? WIDTH 148 31 Januay, 2002 6
Let s Calculate Some Modes A cube with half-height ceiling Eveyone knows that a cube is the wost possible shape. Such a oom is eally impactical in any event, because the ceiling would be vey high. Let s compomise, and make the ceiling height half of the othe two dimensions. It can be seen that the oom esonant fequencies all line up like little soldies on paade, with big gaps between them. The suggestion is that some fequencies will be ovely accentuated, and othes not adequately epesented. A oom should be bette if it had a moe unifom distibution of esonant fequencies. L:W:H = 1:2:2 = 11.5 x 23 x 23 ft. 149 Let s Calculate Some Modes A cube with half-height ceiling with 6% mode sepaation (Bonello intepetation) It has been suggested that adjusting the oom dimensions to poduce a slight sepaation of the esonant fequencies should help. Hee, a ecommendation of 6% sepaation of fequencies has been followed, and it is seen that while the high fequencies appea to be impoved, the low fequency esonances ae still in closely-spaced goups with lage gaps. L:W:H = 1:2.1:2.2 = 11 x 23.15 x 24.5 ft. 150 Let s Calculate Some Modes Simple multiples A oom with dimensions that ae simple multiples of each othe poduces a mixed situation. Some of the modes seem to be well sepaated, but othes line up at cetain fequencies. L:W:H = 1:2:3 = 8 x 16 x 24 ft. 151 31 Januay, 2002 7
Let s Calculate Some Modes Not-so-simple multiples Just depating fom simple multiples seems to do wondes. Hee the modes all seem to be quite well distibuted. If this appoach to oom design has any meit, this oom should have some audible advantages. Does it? L:W:H = 1:1.8:2.3 = 9 x 16 x 21 ft. 152 This all makes a vey nice stoy, but does it eally matte? Maybe... Somewhat... It all depends... Oh, all ight, No! 153 Why not? The calculations assume that all of the modes ae equally enegized by the loudspeakes they ae not. The calculations assume that all of the modes ae equally head by the listene(s) they ae not. The only modes that matte, ae those that ae involved in the tansfe of sound enegy fom the loudspeakes to the listene(s). So, how do we detemine that? The simplifying assumptions undelying these pedictions make them simple, but also simply invalidate them! 154 Impotant Facts About Woofes, Listenes and Standing Waves. Conventional woofes ae sound pessue geneatos. They will couple to the oom modes when they ae located in high pessue egions of the standing waves. Eas espond to sound pessue, theefoe, oom modes will be most audible when ou heads ae located in the high pessue egions of the standing waves. 155 31 Januay, 2002 8
How To Expeience the Modes in an Ideal Room In ode to hea the benefits of a oom with ideal popotions, this is how it would need to be aanged. The ideal popotions wee detemined by looking at the distibution of all the esonances, so we need to enegize them all. A woofe on the floo in one cone excites all of the oom esonances. Likewise, the listene must sit with his head stuck in anothe cone, in ode to hea all of the modes. This sounds silly, but it is tue. 156 A pactical listening location does not couple to all of the modes. Of couse, in pactice, we don t do this. We sit whee we want to. 157 A pactical loudspeake location changes things even moe. And we place ou loudspeakes whee they need to go fo good imaging. 158 Two loudspeakes add moe complications. And we listen in steeo. 159 And with five loudspeakes we have seious complications. If not in a multichannel fomat. All of those neat calculations don t mean a thing in a situation like this! They ae just an academic execise, moe window dessing. 160 31 Januay, 2002 9
The classic monitoing aangement in a 20 x 24 oom Hee is how some pofessionals listen, with five full ange loudspeakes located accoding to the new Euopean standad: cente, +/- 30 and +/- 110. 161 We have five vey diffeent bass sounds, one fo each channel! 10 db 40 db The lage vaiations ae At low fequencies When a full-ange signal is panned to each of the loudspeakes in tun, and measuements ae made at the listening position, we find hugely diffeent bass esponses fo each of the loudspeakes. The diffeences ae a lage as 40dB in this oom, and the biggest ones ae all at low fequencies. The eason, the woofes each have vey diffeent acoustical coupling to the oom esonances because they ae in diffeent locations. This will be diffeent fo evey diffeent oom. Again, efeing back to the cicle of confusion the bass that was head in the contol oom will not be the same as that head at home. It cannot be. 162 Signal Panned to Speake Pais 10 db Diffeent, but not bette Attempting to impove the situation by panning the bass to pais of loudspeakes changes things, but does not emove the poblem. Anybody think that an ideal oom can help this? An anechoic oom would, but none of us would wish to live in one. 163 This is why we use bass management and subwoofes. The same bass sound fo all channels. 164 And this is why bass management and subwoofes make sense. Now we can place the woofes whee they pefom optimally fo a specific oom with a specific listening position. We can place the satellites (a tem that seems inappopiate fo some of the lage capable loudspeakes that we use in the high-passed channels) whee they need to be fo diectional and imaging effects. In othe wods, we design the low-fequency potion of the system sepaately because ooms foce us to do so. This is the only way that we can get good bass in any oom, and have any hope of having similaly good bass in diffeent ooms. Remembe about peseving the at? 31 Januay, 2002 10
How many subwoofes? Whee do we put them? Whee do we sit? Moe than one subwoofe may be needed fo high sound levels in lage listening spaces. It s physics. One huge box might be difficult to hide, while a numbe of smalle ones might be less conspicuous. But thee ae othe consideations which become obvious as soon as we stat looking in detail at oom esonances. 165 Fast and 'Slow Woofes. A digession hee about the speed of woofes. I keep on heaing stoies that small woofes ae faste than big ones. Well, thee is tuth in the agument if you conside the highest fequencies they ae capable of epoducing. Howeve, if we ae cossing them ove at 80 Hz, fo example, to use them as subwoofes, we have limited that highest fequency to be the same fo all. They ae then all equally fast. Woofes ae minimum-phase devices (see Pat 2). Thei time-domain behavio speed, punch, dive, pace and hythm - can be anticipated fom thei fequency esponses. We will soon see that ooms eally mess this up and detemine what we hea. As fo moving mass, we use bigge motos on lage, heavie, diaphagms. It s a hosepowe thing. A Standing Wave Calculato Undestanding what happens in ooms at low fequencies equies knowledge of what the standing waves, o esonances, ae doing to us. Pat of the Excel pogam mentioned ealie is a geat help. It shows the pessue distibutions fo the fist few axial modes along each of the oom dimensions. It is available fo download fom www.haman.com unde white papes. 166 Woofe Location Decides How Much Enegy Each Mode Receives. Hee I show a woofe placed against a wall, whee it excites all of the modes along the length of the oom. Why? Because it is in a highpessue egion fo all of the modes. What happens if we move the woofe fowad, to the location of the fist pessue minimum? A woofe on the floo, against a wall, enegizes all modes along that axis. What happens if we move it fowad, say, to the fist null? 167 Woofe Location Decides How Much Enegy Each Mode Receives. That paticula mode is not enegized by the woofe, and it disappeas. What then happens if it is moved futhe ahead to the next null? A pessue souce located at a pessue null, o minimum, does not enegize that mode. What happens if we move it fowad to the second null? 168 31 Januay, 2002 11
Woofe Location Decides How Much Enegy Each Mode Receives. A pessue souce located at a pessue null, o minimum, does not enegize that mode. Note that it is the woofe diaphagm that is the pessue souce, not the whole enclosue. 169 That mode ceases to be activated, but the othe one etuns. Woofe location detemines which of the oom esonances is activated, and which is not. Similaly, the Listene Location Detemines Which Modes Will Be Head. Just as a woofe against a wall enegizes all of the standing waves in that dimension, a listene with his head close to the opposite wall heas all of the modes. Just as a woofe against a wall enjoys a gain in output because of the adjacent bounday, so the eas enjoy a simila low-fequency gain. Thee will be too much bass!! A woofe on the floo, against a wall, enegizes all modes along that axis. A listene against the opposite wall, heas all modes along that axis. Thee may be too much bass. 170 Similaly, the Listene Location Detemines Which Modes Will Be Head. Moving the listene fowad povokes the same poblem we had when moving the loudspeake fowad. If the head is at a null, no sound will be head fom that mode. Fo this listene, the bass is in bette oveall balance, but he wondes what happened to one of the bass notes. 171 Similaly, the Listene Location Detemines Which Modes Will Be Head. Diffeent positions mean that diffeent fequencies will be head with sometimes vey diffeent loudness. And hee, it is a diffeent note that has disappeaed. 172 Similaly, the Listene Location Detemines Which Modes Will Be Head. And hee, two of the best eally low fequencies have gone away. 173 31 Januay, 2002 12
Similaly, the Listene Location Detemines Which Modes Will Be Head. Howeve, thee ae locations that might wok easonably well. But, thee ae seveal locations whee happiness might be possible. 174 Similaly, the Listene Location Detemines Which Modes Will Be Head. And this is tue fo woofes as well as listenes. These ae also suitable locations fo loudspeakes, but not all ae pactical, just as not all listene locations ae pactical. 175 31 Januay, 2002 13
2' 4' The Science of Audio - a seies of lectues by Floyd E. Toole, Ph.D. Vice Pesident Acoustical Engineeing Selective Mode Cancellation 0 ft. WIDTH 20 ft -5 in + One subwoofe enegizes all width modes. 0 ft. WIDTH 20 ft -5 in - + + + - - + + Two subs cancel the odd- ode modes. 0 ft. WIDTH 20 ft -5 in Leaving only one active width mode. 0 ft. WIDTH 20 ft -5 in + + Does this leave none?? 177 Hee we get a bit fancy. Remembe the standing wave diagams showing the see saw behavio of the wavefom pivoting on a null. It means that at any instant in time, the sound pessues on opposite sides of a null in a standing wave ae in opposite polaity. If one side is inceasing, the othe will be deceasing. None of this mattes if we have only one souce of low fequency enegy in a oom. Howeve, if we have two o moe, things get complicated. The top pictue shows all of the width modes in a oom being excited by a single subwoofe. If we place anothe in a symmetical position on the othe side of the oom, the woofes, which eceive exactly the same signal, ae opeating in phase (the same polaity) with each othe. The fist- and thid- ode modes, howeve, exhibit opposite polaities at the subwoofe locations see the opposite polaity signs. What happens? The subwoofes couple in a destuctive manne with the odd-ode modes, and those modes ae simply not enegized. They do not exist. This leaves only one mode acoss the width of the oom. If we get even moe cleve, and move the subwoofes to the null locations fo that mode. They ae still in opposite polaity egions fo the odd-ode modes, and the esult is that all of the width modes ae significantly attenuated, if not eliminated. Magic, no. Science, yes. So, why would we want to do this? Aha! Would it not be a good idea fo eveybody in each ow of a home theate to hea the same bass sounds? Would it not be a good idea fo a ecoding enginee to be able to move fom one end of the console to the othe without expeiencing huge changes in bass? Well, this is how it can be accomplished. We ae not saying, yet, that it is good sound, meely that it is the same sound. Once things ae equalized in the sense of getting eveybody heaing moe o less the same sound, we then may need to equalize in the sense of changing the fequency esponse of the system. 3'8 8'8 3'8 A Pactical Example: 8 x 16 x 24 1:2:3 In theoy, this is a bad oom. 24'3 2'3 Just to pove a point, let us take a eal example: a oom that, by most advice should be a bad oom. It is not an unusual situation. Thee is a living/dining oom, with a ea pojection television at one end, seats in the middle aea, and a dining aea behind the chais. 178 2'8 13'4 31 Januay, 2002 14
It looks nomal, and could happen in a detached dwelling o in an apatment. 179 Room Mode Calculato by: Allan Devantie The modal distibution shows that thee could be a poblem with thee modes stacking up at 70 Hz. dimensions length width height Cubic Volume metes 7.32 4.88 2.44 cubic cubic feet 24 16 8 metes feet inches 0 0 0 86.99 3072.00 all 8 oblique 7 tan & axial 6 tangential 5 This looks bad! axial 4 height 3 width 2 length 1 10 100 1000 Fequency (Hz) 180 Along the Length of the Room 0 ft. LENGTH 24 ft -0 in 3 4 8 9 12 15 16 21 Fotunately, we have some help fom the locations of loudspeakes and listenes. The loudspeakes ae lined up with the font of the RPTV, and that puts them in the null of the fouth-ode mode. The listenes ae seated at the mid point, and they ae in the nulls of the fist- and thid-ode modes. In theoy 181 Along the Length of the Room 0 ft. LENGTH 24 ft -0 in That leaves only the second-ode length mode to cause poblems. In pactice 182 31 Januay, 2002 15
Acoss the Width of the Room 0 ft. WIDTH 16 ft -0 in In theoy thee ae a bunch of modes at play. 2 2 3/4 51/4 6 8 10 103/4 14 In theoy 184 Acoss the Width of the Room 0 ft. WIDTH 16 ft -0 in + - + - + + In pactice, we have selected locations fo the loudspeakes and listenes that avoid them all. 2 2 3/4 51/4 6 8 10 103/4 14 In pactice the loudspeakes, which opeate in phase at low fequencies, destuctively dive the 1 st and 3 d ode modes (they ae not enegized), and they ae located at the nulls of the 2 nd ode mode (it is not enegized). The 4 th ode width mode is constuctively diven. 185 Acoss the Width of the Room 0 ft. WIDTH 16 ft -0 in But, the listenes ae located at nulls of the 4 th ode mode and it is not head. 186 Acoss the Width of the Room 0 ft. WIDTH 16 ft -0 in So, in pactice, thee ae no active width modes in the listening path. 187 Room Mode Calculato by: Allan Devantie dimensions length width height Cubic Volume metes 7.32 4.88 2.44 cubic cubic feet 24 16 8 metes feet inches 0 0 0 86.99 3072.00 all 8 oblique 7 6 tan & axial 5 tangential 4 axial 3 height width 2 length 1 10 100 1000 Fequency (Hz) The modal distibution looks a lot less clutteed afte we coss off all of the modes that ae not involved with communicating between the woofes and the listenes in those chais. Remembe, things will be diffeent elsewhee in the oom. 188 31 Januay, 2002 16
And, finally, the height dimension In pactice: the eas ae close to the nulls fo the 1 st and 3 d ode modes. They ae not eliminated, but ae seiously attenuated. 189 Room Mode Calculato by: Allan Devantie all oblique tan & axial tangential axial height width 8 7 6 5 4 3 2 length 1 dimensions length width height Cubic Volume metes 7.32 4.88 2.44 cubic cubic feet 24 16 8 metes feet inches 0 0 0 86.99 3072.00 What poblem? 10 100 1000 Fequency (Hz) When we ae though, thee is only one solitay oom esonance that is actively involved in the acoustical link fom the loudspeakes to the listenes. Amazing! Let s measue it and see what we have. This one might be a poblem because it is so lonely. 47 Hz, let s have a look. 190 And guess what we found? 3 coincident nulls 80 Hz cossove Supise, supise. Thee is a esonance at 47 Hz, the fequency of the emaining second-ode length mode. And, guess what, thee is a shap dip at 70 Hz, just whee we successfully canceled those poblematic modes. To get id of the dip, all we need to do is to be less successful at canceling some of those modes. In othe wods, move a chai o a loudspeake a few inches. 47 Hz! 191 A simple fix BEFORE and AFTER one band of paametic EQ 192 And, what about the esonant peak? When we listened, it was clealy audible, making kick dums boom, and all bass inaticulate and floppy. All bass tended to be one note bass, the tunes in the bass guita wee all but gone. We could have blamed the woofes, accusing them of being slow, uncontolled, and tuneless. But we know bette. The solution? Because the oom esonance is a minimum-phase phenomenon, we designed a paametic filte to attenuate the peak, and the system is instantly tansfomed. The bass was tight, the guitas played tunes at low fequencies, explosions no longe had a pitch. The oom sounded geat. The Poblem and Solution in the Time Domain BEFORE and AFTER one band of paametic EQ The long inging of the oiginal oom is tansfomed into a well damped, tight, tansient esponse. It woks. The woofes wee fast all along. We just couldn t hea it. 193 31 Januay, 2002 17
So, accoding to dimensional atio theoy, this was supposed to be a bad oom. In this pactical example, it ended up having only one poblem esonance and, afte equalization, it yielded tuly supeb sound! Good Sound in a Bad Room! O.K. So this is showing off. Howeve, it does pove a point. If you undestand basic oom acoustics, have some decent analytical tools at you disposal, including measuements, most ooms can be unde contol. 194 Not all stoies have such a happy ending, but happy endings ae unlikely unless the loudspeake and listene locations ae evaluated in conjunction with the standing wave pattens. 195 REMEMBER: The only modes that matte ae those that paticipate in the communication of sound fom the loudspeake to the listene! and Thee is NO ideal oom! So, back to the issue of ideal oom dimensional atios. Pesonally I have no favoites. I have yet to encounte a oom that could not be made to sound at least good, if not excellent. 196 So, what happens if we stat with a oom that is good to begin with? SUB L C R SUB LS RS LR RR In this example we will eally make use of acoustical measuements. It will be seen that high-esolution (bette than 1/3 octave) measuements allow us to confim which esonances ae active in which pats of the oom. They will allow us to expeiment, intelligently, with subwoofe and listene locations. In shot, good measuements put us in contol. We may o may not achieve ou fantasy pefomance, but we cetainly can get close than would be possible by tial and eo. 197 198 31 Januay, 2002 18
Not a Bad Modal Distibution all 8 Room Mode Calculato by: Allan Devantie length width height dimensions Cubic Volume metes 7.32 6.22 2.74 cubic cubic feet 24 20 9 metes feet inches 0 5 0 124.88 4410.00 Accoding to common belief, this oom should have some advantages, because of the favoable distibution of modes. oblique 7 tan & axial 6 tangential 5 axial 4 height 3 width 2 length 1 10 100 1000 Howeve, taking nothing fo ganted, let s actually measue what is happening at diffeent listening locations, when we employ one o two subwoofes. Fequency (Hz) 199 Let s measue the vaiations along the seating axes fo one sub, and then fo two subs. SUB L C R SUB $$ LS RS LR RR 201 It is obviously impotant to keep the custome and the family o close fiends happy, so pay attention to the font ow. I think it is natual to expect the best of eveything in the font ow. Measuements ae made at 18-inch intevals acoss the font ow, and fom each of the seats to the ea. Note, fist of all, in the slide below, that it is possible to identify many of the axial modes calculated fo this oom. The fequencies don t always line up exactly, and this will be explained late. axial height width 4 3 2 length 1 10 100 1000 16 db!! At 36 Hz CENTER SIDE vaiations in font ow one font sub. Length and height modes ae constant along this measuement axis. 202 31 Januay, 2002 19
The above gaph shows, in detail, what happens at 18-inch intevals acoss the font ow. Because the oom is symmetical, what we ae eally looking at is what happens fom the cente seat to the side seats. It can be seen that thee is a 16 db diffeence aound 36 Hz between the cente and the side seats. This is huge, and this is a vey impotant pat of the fequency ange. It could be that the host, sitting in the cente, exclaims to his buddy, to whom he is showing off the system, listen to that fantastic bass!. The buddy, sitting beside him, could be justifiably undewhelmed if the bass fequencies fall into this ange. axial 4 height 3 width 2 13 db!! At 27 Hz length 1 10 100 1000 SIDE CENTER Late in the same movie, thee is a thunde stom, and the almostsubsonic umble is peceived by the guest to be just stunning, but the host thinks it is just O.K. vaiations in font ow one font sub. Length and height modes ae constant along this measuement axis. 203 axial height width 4 3 2 length 1 10 100 1000 SIDE SEAT LOSES 13 db SIDE SEAT GAINS 16 db vaiations in font ow two font subs. The odd-ode width modes ae now cancelled. 204 This is whee mode canceling can be useful. Using a pai of subwoofes, the poblematic width modes ae cancelled, and the bass is endeed unifom acoss the font ow up to about 55 Hz. Thee is a tade-off. We sacifice some of the deepest sounds in the side seats, but we pick up 16 db of the moe impotant fequencies highe up, aound 36 Hz. The ecommendation is, theefoe, to use two subwoofes located opposite each othe acoss the font of the oom. The bass esponse is still uneven, but we have managed to make it moe unifom acoss the allimpotant font ow of seats. The pai of subs will not only deal with the font ow, but will also make pefomance acoss the back ow moe unifom. Howeve, as it is set up, the font and back ows will hea diffeent bass sounds. A decision must be made of how to equalize, if that oute is chosen. Nomally, pioity is given to the font ow 31 Januay, 2002 20
axial 4 height 3 width USE 2 TWO SUB LOCATIONS, ONE IN EACH CORNER. length 1 RECOMMENDATION: KEEP THE FRONT ROW HAPPY! USE THE CENTER SEATING LOCATION e.g. THREE OR FIVE SEATS ACROSS THE FRONT 10 100 1000 The thee font ow seats Two font subwoofes, one in each cone So, how did it all end? 210 axial 4 height 3 width 2 length 1 SADLY, THE BACK ROW HAS TO TAKE WHAT IT GETS 10 100 1000 The thee back ow seats Two font subwoofes, one in each cone 211 Now, let us look at a smalle oom 24 x 16 x 9, with 2 x 6 studs, and two layes of 5/8 gypsum boad. i.e. heavy, stiff walls. As stated ealie, heavy, stiff walls absob little enegy at low fequencies. This helps to keep the bass enegy inside the oom, and the pooly-damped standing waves will exhibit stong high-q peaks and dips, and ing enegetically. Also, the educed absoption at each eflection means that tangential modes may join the axial modes as being factos to deal with. 215 31 Januay, 2002 21
6 tangential 5 axial 4 height width 3 2 length 1 19 db!! At 33 Hz 10 100 1000 SIDE CENTER Fequency (Hz) In this oom, it is clea that the tangential modes ae vey active. Note that it is possible to identify almost all of the axial and tangential modes in the visible peaks at low fequencies. Moving acoss the font ow poduces a athe lage 19 db vaiation fom cente to side seats ove a vey impotant pat of the bass fequency ange. It would be nice to educe this. vaiations in font ow one font sub. 217 6 tangential 5 axial 4 height 3 width 2 length 1 10 100 1000 SIDE SEAT LOSES 12 db Fequency (Hz) Employing the tactic used in the pevious example, two subs, one in each font cone, we cetainly get consistent pefomance acoss the font ow, but we have sacificed a lot of good bass in the pocess. BUT, FRONT ROW VARIATIONS BELOW 65 Hz ARE GONE! vaiations in font ow two font subs. 218 tangential axial height width 6 5 4 3 2 length 1 19 db!! At 33 Hz 10 100 1000 SIDE CENTER RECOMMENDATION: USE ONE SUB LOCATION, AND DO NOT USE THE Fequency (Hz) CENTER SEATING LOCATION e.g. FOUR SEATS ACROSS THE FRONT A 9 db CHANGE IN SOUND LEVEL OVER THE NEXT 4.5 FEET! A 10 db CHANGE IN SOUND LEVEL FOR AN 18 INCH SHIFT OFF CENTER! vaiations in font ow one font sub. 219 Looking close, we notice that 10 of the 19 db change occus in the fist 18 inches away fom the cente location. This is a high-q null. The emaining 9 db accumulate ove the next 4.5 feet. Taking advantage of this knowledge, we decide to go back to one subwoofe location we may in fact use two subs stacked at that location, to get enough powe into the oom. We avoid the cente seating location, choosing to aange the chais symmetically aound the oom cente line. None of this would be obvious without measuements good measuements, and enough of them to help design the best listening expeience fo the cicumstances. 31 Januay, 2002 22
Some Obsevations You cannot escape fom oom modes! ONLY high esolution measuements can help you undestand what is happening. 1/3 octave not enough. Mode contol with multiple subs is vey position dependent, but it can wok IN CERTAIN ROOMS. Massive, igid walls make the situation much moe complicated by activating tangential modes. Spatial aveaging of measuements is essential to addess the needs of an audience. You will neve satisfy eveybody in the audience. 220 But, You Have Head That Non- Paallel Walls Solve all of These Poblems. 221 What About Non-Paallel Walls? The modes ae not eliminated The stength of the modes is much the same as in a ectangula oom Because of the complexity of the standing waves, pedictions of pessue distibutions ae not easy, and may not be pactical. Why bothe? 222 A Room With Only One Pai of Paallel Sufaces 30 2,0,0 20 3,0,0 db 1,0,0 4,0,0 10 14 db! 0-10 20 50 100 500 1K 5K 10K 20K FREQUENCY (Hz) 223 Hee is an example of a oom that had only one pai of paallel walls. The high ceiling was shaply angled, about 40 degees. The side walls had seveal lage openings, ecesses, and a lage staiwell. Thee was hadly any paallel suface left that was at a fixed spacing fom one acoss the oom. Taking a simple look at the oom, it should have some advantages. But, the bass in that oom was awful. It boomed hoendously. I know, because it was in my last house. When measued, it evealed a set of vey clea esonances, all of them associated with the emaining pai of paallel walls. With no competition fom any othe modes, these ones sang thei little heats out. Sound Absoption educes the enegy in the modes. This is called DAMPING. By emoving enegy fom the modes using damping at the eflecting sufaces, it is possible to attenuate the high-pessue egions of standing waves, and to elevate the low-pessue egions. Doing this makes the sound field less vaiable ove the oom. In my opinion, this is whee we should stat, pefeably when the oom is being built. 224 31 Januay, 2002 23
The Damping of Room Modes P MASSIVE, RIGID, REFLECTIVE, ROOM BOUNDARIES Less vaiation means moe happy listenes. FLEXIBLE, ABSORBING, ROOM BOUNDARIES P 225 Acoustical Damping of a Mode: (a) using esistive absobes, e.g. fibeglass, acoustic foam, dapes + - +? X SOUND PRESSURE PARTICLE VELOCITY 218 Sound absoption can be achieved with esistive absobing mateials, like fibeglass, acoustic foam, heavy dapes, etc. Howeve, to be effective these mateials must be in the egions of high paticle velocity. This does not happen immediately at the oom bounday, because, by definition, thee can be no paticle movement when the molecules ae had against a igid suface. Maximum paticle motion occus in egions of minimum pessue at the nulls in the standing wave patten, one-quate wavelength fom the eflecting suface. So, one eithe needs thicke mateial, o some ai space behind the mateial. Thicke mateial woks bette, but is costly. Eithe way we face using a lot of space. Resistive absobes ae most effective when positioned in the high velocity egions of the standing wave Dopped ceilings, the T-ba systems with lay-in panels actually wok well at low fequencies because of the lage space above them. The panels themselves, if placed on a had suface, ae no bette than the equivalent thickness of igid fibeglass boad puchased fom a building supplie. Be caeful not to let such ceiling systems buzz o attle, though. 227 Resistive Absobes ae not Pactical at Low Fequencies 1/4 wavelength at 100 Hz = 2.8 ft. 1/4 wavelength at 50 Hz = 5.7 ft. 1/4 wavelength at 30 Hz = 9.4 ft. 228 Bass Taps ae a favoite topic in po audio. The name conjues an image of a device that seeks out and sucks up bass, neve to spit it out. Well, eality is much less omantic, and eal bass absobes ae only as effective as space and the budget pemit. If we ty to damp eally low fequency esonances with esistive absobing mateials, success is possible only if seious amounts of eal estate ae devoted to the task! Want to Build a Bass Tap with Fibeglass? Be my guest! This should be a eal stimulus to the building industy, if evey home theate had to be about 20% lage in evey dimension. Remembe, to absob enegy in the modes in all diections, one of these appendages must be built on the ceiling, and anothe on a side wall. Cost conscious customes might wonde if thee is a bette way. Thee is. 229 31 Januay, 2002 24
ABSORPTION Howeve, Resistive Absobes Wok Supebly at Mid & High Fequencies. 100% 50% 0 5 3 2 1 thick fibeglass boad 125 250 500 1K 2K 4K Hz 230 Howeve, at highe fequencies, whee wavelengths ae shote, such mateials wok just fine, and ae highly ecommended. Just don t cove them with a non-poous mateial, because such mateials need to beathe. Resistive absobes do thei wok by making it difficult fo the ai molecules to move aound within the fibous tangle. A good low-cost coveing, available in a wide ange of colos, is polyeste double-knit, often used fo speake gilles. If the coveing needs to be fie ated, look elsewhee, and pay much moe. Acoustical Damping of a Mode: (a) using membane absobes, e.g. walls, floo, ceiling, custom units. + - + SOUND PRESSURE PARTICLE VELOCITY 231 At vey low fequencies, we need anothe technique. It is membane, o diaphagmatic, absoption. In this, the fluctuating sound pessue of sound causes a suface to move, and in doing so, tansfes enegy to the moving suface. So, when you feel the bass in you feet, o feel vibations in the walls, you ae expeiencing membane absoption. Obviously, the best location fo a membane absobe is in a highpessue egion fo the poblem mode. If the oom is constucted with bass absoption in mind, the poblem is diminished fom the outset. Let the boundaies move could become a manta fo enlightened oom design. Membane (mechanically esonant) absobes ae most effective when located in the high pessue egions of the standing wave patten. The oom boundaies do it natually. 224 Mechanically Resonant Membane Absobes The esonant fequency is detemined by the moving mass of the exposed panel, and the compliance of the ai inside the enclosue (the volume/depth). A heavie panel, o a deepe box, educes the fequency. Damping is achieved by mechanical losses in the panel mateial, and by acoustical losses in the fibeglass. Lossy, soft panels have low -Q, i.e. absoption ove a wide fequency ange. Heavy vinyl has been used successfully. 225 Commecial membane absobes ae available. Most ae flat, and fit against the oom boundaies. Othes ae designed to fit in cones, o to stand feely. Be sue to check that they exhibit high absoption coefficients at the fequencies you wish to damp. Some of them wok well at lowe mid fequencies, but lose it in the deep bass egion. Ionically, a single laye of wallboad on standad studs does a decent job. Things get poblematic when a second laye of wallboad is added, o bigge studs ae used, o the wall is filled with sand, etc. A somewhat compliant inne suface to a oom is a geneally good idea. Let the boundaies move. Mind you, a wall o ceiling that attles and buzzes is not welcome. So pay attention to how it is constucted. Acoustically Resonant Helmholtz Absobes M C In a classic esonato the esonant fequency is detemined by the mass of the ai in the neck, and the compliance of the ai in the chambe (volume). This is the soda bottle esonance. This can be expanded into a suface, with the esonant fequency being detemined by the mass of the ai in the slots between the bas, and the compliance of the ai in the cavity behind. Some fibeglass in the cavity povides damping. 226 A second kind of low-fequency absobe involves a tuned acoustical esonance. Usually these utilize slats with spaces between, and a damped volume behind. 31 Januay, 2002 25
Amplitude (db) The Walls Absob Low Fequencies Diffeent Amounts at Diffeent Fequencies SOLID WALL 6 4 2 0-2 -4-6 -8-10 -12 Low Q vs. High Q modes 0 2 4 6 8 10 12 14 16 18 20 22 24 9 db 14 db Distance (feet) WALL WITH DOOR WALLS: TWO LAYERS OF 5/8 GYPSUM BOARD ON 2 X 6 STUDS 233 Seies1 Seies2 If a oom suface absobs sound, it will do so diffeently at diffeent fequencies. It is the natue of such sufaces to slightly alte the timing of the eflected sounds (phase shift) depending on the fequency of the sound elative to the pefeed fequency fo the absobing suface. A eal wold example of this is shown hee. It was noted that one wall of a oom was vibating quite actively. The wall had a doo in it, and it appeaed that this educed the stuctual stiffness, allowing much moe movement than the othe walls. Out of inteest, we measued the pessue distibution acoss the oom fo the fist two modes. The fist ode mode had moe damping than the second. Amplitude (db) The Walls Absob Low Fequencies Diffeent Amounts at Diffeent Fequencies 6 4 2 0-2 -4-6 -8-10 -12 Low Q vs. High Q modes 0 2 4 6 8 10 12 14 16 18 20 22 24 Distance (feet)? Since membane absobes ae eactive devices, thee can be significant phase shift in the eflected sounds, causing the peaks and nulls to be moved fom thei pedicted locations. 234 Seies1 Seies2 This is seen as a lowe maximum-to-minimum pessue vaiation 9 db fo the fist-ode mode vs. 14 db fo the second. Also appaent was a positional shift of the high and low pessue points. They wee not exactly at the locations simple mathematics would pedict. The null of the fist ode mode was substantially off cente, towads the wall with the doo. Amplitude (db) The Walls Absob Low Fequencies Diffeent Amounts at Diffeent Fequencies 6 4 2 0-2 -4-6 -8-10 -12 Low Q vs. High Q modes 0 2 4 6 8 10 12 14 16 18 20 22 24 Distance (feet) ACOUSTICAL WALL @ 21 Hz PHYSICAL WALL 13.5 FT 13.5 FT Since membane absobes ae eactive devices, thee can be significant phase shift in the eflected sounds, causing the peaks and nulls to be moved fom thei pedicted locations. 235 Seies1 Seies2 3 FT I made the simple assumption that most of the absoption was occuing in the wall with the doo, and speculated that the phase shift in the absobing wall was making it look (acoustically) as though it was fathe away. On this basis, I took the distance fom the solid wall to the null to be the tue ¼ wavelength, and pojected the same distance towads the wall with the doo. This put the acoustical wall thee feet away fom the eal one! Acoustically, at this fequency, the oom was behaving as if it wee thee feet longe than the physical length. axial 4 height 3 PHYSICAL WALL width 2 length 1 10 100 1000 If this is tue, then the fequency of the fist-ode esonance must not be at the fequency pedicted by a measuement of the oom length, but at a fequency appopiate fo a oom thee feet longe. ACOUSTICAL WALL 236 This gaph shows that this is so. At the fequency calculated fo this mode based on the oom dimensions, thee is no esonant peak. Howeve, at a fequency appopiate to a oom thee feet longe, thee is a healthy esonant peak. This explains why, vey often, it will be found that the measued esonances do not exactly coespond with the calculated ones. This is also why oom acoustical modeling pogams do not always give the ight answes. In ooms it is essential to make high-esolution, accuate, measuements in the oom afte it is built. 31 Januay, 2002 26
Room Walls Pefom Two Key Tasks Povide tansmission loss to pevent inside sounds fom leaking into the est of the house, and outside sounds fom leaking into the listening space. Povide absoption to damp the lowfequency oom esonances. Conclusion: we need two kinds of wall in one. 237 Sound tansmission loss in a wa ll is a measue of how well it pevents sound fom taveling though it. Absoption coefficient is a measue of what popotion of the sound falling on a suface is absobed, and not eflected back into the oom. They ae two vey diffeent things, and they ae often confused. Most studies of tansmission loss wee concened with pivacy, and focused on speech fequencies, not paying much attention to low bass fequencies. With today s poweful woofes and subwoofes, we need new and highe standads. Fo Example: Concete o Masony Wall One laye of gypsum wallboad on wooden studs, with fibeglass. Hee the massive, stiff, concete is poviding the bulk of the sound isolation. The standad stud wall povides some attenuation, as well as some sound absoption. Its vibations ae isolated fom the concete wall by an ai space and, at low fequencies, the lage the bette. Some fibeglass in the cavity adds to the effectiveness by damping evebeation in the space between the walls, not by actually peventing sound fom passing though it. 238 Outside Inside O... FIBERGLASS BATT 239 Hee is anothe dual-pupose wall, with multiple layes of gypsum boad substituted fo the concete. Again a lage pat of the isolation is due to the mechanical sepaation between the inne micophone wall and the oute loudspeake wall. If the walls ae connected, the micophone talks diectly to the loudspeake and thee is almost no sound attenuation. Theefoe, these walls must not be mechanically connected at any point no conduits, no wate pipes, nothing to link the inne and oute walls. HVAC penetations must be flexible, and be equipped with special acoustical absobes on each side of the wall to pevent sound leakage though the duct itself. O... Fabicated o puchased membane absobes 240 If acoustical isolation is absolutely paamount, then thee is little choice but to go fo boke. Build a eally massive double wall, and then add membane absobes on the inne suface. Always emembe that low-fequency isolation can be defeated by even quite small ai leaks. Keep an eye on the builde, and be sue that all joints ae caulked, and that no penetations o mechanical shot cicuits have cept in. O... Concete o Masony Wall Fabicated o puchased membane absobes A membane absobe can be consideed a mechanically esonant panel absobe. Anothe type of low-fequency absobe is the acoustically esonant absobe, also known as the Helmholtz absobe. In these devices, one o a few lage openings, o many small openings, esonate with a volume of ai at the appopiate fequency. These equie caeful design, and caeful constuction, but can wok vey well. 241 31 Januay, 2002 27
The MOST PROBLEMATIC ooms I have eve encounteed ae those that have been constucted with massive, stiff walls. They have: 1. High Q esonances that ing 2. Poo bass unifomity ove the listening aea. It is tuly sad when someone has spent good money building a oom of solid walls, based on the belief that it keeps the bass in. Yup, it sue does, but it ma kes that bass unpleasant to listen to. To those who suggest that thumping a wall with a fist is a useful test of a wall, I will say that it is about as useful as the knuckle test is of a loudspeake enclosue. Both ae highly uneliable because sound waves enegize oom walls and loudspeake enclosues vey diffeently than fists o knuckles. 242 The Rules fo Good Sound in Rooms At middle and high fequencies: Stat with a loudspeake that was designed to function well in a vaiety of diffeent ooms. Use geomety, eflection, diffusion, and absoption to achieve good imaging and ambiance. At low fequencies: Maximize the output fom the subwoofe(s). Achieve a unifom pefomance ove the listening aea. Equalize to achieve good pefomance. 244 So, we have done what we can to achieve unifom sound quality ove the listening aea. Now we will attempt to make it sound good by using equalization. Equalization! You thought that it didn t eally wok. That equalizes added phase shift and othe ugly stuff. Histoically, equalization has not lived up to its pomise. Howeve, we have leaned what it can and cannot do. We now undestand why, the way it has been taditionally done, equalization we doomed to disappoint. The key to intelligent oom equalization is in knowing what can and cannot be coected with filtes. Remembe oom esonances, those things that cause boom, hangove, inging, coloation, and that mask ou ability to follow bass melodies. They behave as minimum-phase phenomena, and they can be equalized if the measuements have enough esolution to show the details of what is happening, and if they esonances ae addessed with caefully matched paametic equalizes. 245 30 20 db 10 0 Paametic equalization fixes the fequency esponse Oiginal Condition Afte Paametic Equalization: One Filte Only Hee is a oom with a eally big boom. I am familia with this one, as it was in my last house. It was whee I began expeimenting with selective paametic equalization, as an altenative to moving the funitue aound o engaging in massive econstuction. -10 20 50 100 500 1K 5K 10K 20K FREQUENCY (Hz) 246 And the tansient esponse is also fixed! BEFORE AFTER And it eally woks. Kick dums that peviously boomed elentlessly, became quick and tight, and bass guitaists could actually be head playing hamonies. Ogan pedal notes wee all thee in pope popotions. An amazing tansfomation. It doesn t wok eveywhee in the oom, but nothing does. Those pesky standing waves ae still thee. They will not go away. 247 31 Januay, 2002 28