The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

harman / kardon
Loudspeakers andRooms forMultichannel Audio
Reproduction
byFloyd E. Toole
Vice President Acoustical Engineering
Harman International

Part 3 – Getting the Bass Right
Choosing the number and locations ofsubwoofers, and determining where to sit, arefundamental to good bass. Multichannel
audio should be shared, so we try to get goodbass at several locations. Acousticalknowledge is essential, but EQ can help.
The Rules for Good Sound inRooms
At middle and high frequencies:ü Start with a loudspeaker that was designed tofunction well in a variety of different rooms.
ü Use geometry, reflection, diffusion, and absorption toachieve good imaging and ambiance.
At low frequencies:
Ø Maximize the output from the subwoofer(s).
Ø Achieve a uniform performance over the listeningarea.
Ø Equalize to achieve good performance.
123

Solid Angle VLF Gains
4π steradians
2π steradians
π steradians
π/2 steradians

So, we think that we know how to pick a good loudspeaker, and withsome simple acoustical devices or smart design, we can avoid
destructive reflections in a room. Now, what about low frequencies,
the ones where the room is the dominant factor?
The first task is to locate the subwoofer where it radiates mosteffectively. Closed box or reflex (ported) woofers are pressuresources. It matters not which way the diaphragm faces because allsuch loudspeakers are omni-directional at low frequencies.
Obviously, there needs to be ‘breathing’ space if we choose to face
the diaphragm against a wall. And, if there is a port, don’t plug it!

However, where we place the woofer with respect to the adjacentroom boundaries does matter. The least effective location is in the
middle of a room. It gets better on the floor, still better on the floor
against a wall, and best in a corner. This is “best” in the sense of
maximizing the quantity of bass radiated into the room.

= full sphere = ref. level= suspended in free space= 1/2 sphere = +6dB SPL= on floor= 1/4 sphere = +12dB SPL= on floor against wall
= 1/8 sphere = +18dB SPL= on floor in corner124

31 January, 2002

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The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

Measurements in a “Partial” Room
30

π*

4π

In theory we should be able to get huge gains from corner placement,
and the test shown in the slide indicates that, if conditions are right,
the gains are there. In real houses, the gains are a lot less, because offlexible room boundaries, open archways, etc. Still, even a 3 dB gain
doubles the acoustical power into the room, and that is equivalent toadding a second woofer. Not bad, and it's free.

π/2 *

20
dB
10

THE SUBWOOFER REGION

0-10* INFLEXIBLE SURFACES

20

50 100500 1K
5K
FREQUENCY (Hz)10K 20K
125

A Subwoofer in a Corner• Produces the maximum possible LF output.
– This is good

• Energizes all of the room modes– This can be good or bad, depending on theroom, and how it is arranged.

CONCLUSION: Start with the sub in acorner, and move it only if necessary.

However, as they say, there is no free lunch. Corner locations excite
every resonance in the room. This may or may not be bad. You willlearn how to know the difference before we are through. If it is goodfor a particular room, then leave it alone and move on to the next
problem. If not, find a better location. However, a corner is a logicalstarting location. For many simple installations, an unequalized
single woofer in a corner can work very well indeed. In fact, I am
listening right now to just such a system in my office/den.

126

The Rules for Good Sound inRooms
At middle and high frequencies:ü Start with a loudspeaker that was designed tofunction well in a variety of different rooms.
ü Use geometry, reflection, diffusion, and absorption toachieve good imaging and ambiance.
At low frequencies:
ü Maximize the output from the subwoofer(s).
Ø Achieve a uniform performance over the listeningarea.
Ø Equalize to achieve good performance.

A multichannel audio system is intended to be a social experience,shared among several listeners. It is not like stereo, an antisocial
experience, if it is to be heard properly.
We need to try to create a situation in which as many listeners as
possible hear essentially the same sound.

127

Most rooms “boom”. They have their own bass personalities. It issimply not possible to listen to the true bass output from aloudspeaker unless it is done in an anechoic space, and at very low
frequencies, that means outdoors. What we hear indoors, also
includes the room, and the positional factors within it.

The problem here is Standing Waves,
Room Resonances, Room Modes,
Eigentones, etc.

These are all the same phenomenon.

128

Classes of Room Modes• AXIAL: occurring between opposite
parallel surfaces

LENGTHWIDTHSound reflects back and forth between two parallel surfaces. At
certain frequencies the incident and reflected sounds conspire to form
“standing waves” in which those frequencies can be amplified, andwhat we hear at those frequencies depends on where we and the
speakers are located. These are axial modes, since they exist along
the major axes of the room.

HEIGHT129

31 January, 2002

2

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

Classes of Room Modes

818 895 5761

ftoole@harman.com

The cyclical reflected patterns can include two, four or more surfaces.
If four are involved, we call them tangential modes. Since somesound is absorbed at each reflection, generally the tangential modes
are less powerful than the axial modes, which include only two
reflections per cycle.

• TANGENTIAL: occurring among four
surfaces, avoiding two that are parallel

130

Classes of Room Modes• OBLIQUE: occurring among any and all
surfaces

Oblique modes can involve any and all surfaces. They tend,
therefore, to be the least important.

131

In Terms of Causing Audible
Problems:
AXIAL MODES are the dominant factor!
TANGENTIAL MODES can be significant in rooms withvery stiff/massive boundaries
OBLIQUE MODES are rarely, if ever, relevant

132

What is a Standing Wave?
Total+

Pressure
Time = 0
Distance = 1/2 wavelength = 1/2λ
133

The simplest of the standing waves, the axial modes, exist between
two parallel reflecting surfaces. In this slide shown here, imagine thatthe two vertical lines represent walls in a room. Imagine a woofer
against the left-hand one, radiating a pure tone – a sine wave – asshown. If the right wall were not present, the sine wave would
simply propagate away. With the wall in place, the portion of thesine wave that would have moved on to the right is reflected backtowards the source. The walls here are separated by exactly one-halfwavelength, so the reflected sound wave is identical to the incident
wave – they overlap perfectly. When added they make the “total”
sound wave shown. Remember, this is a “stop action” view.

Standing Waves
Total+

Here is the same instant in time expanded in scale.

PTime = 0
D = 1/2 wavelength = 1/2λ

31 January, 2002

134

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The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

Standing Waves
Total
+

P
-

Here, we have done a very, very quick “play” and “pause”, stopping
the action one-eighth of a wavelength later. Now the incident andreflected waves have different shapes, but the “total” is much thesame, only a bit lower in amplitude. Interestingly it still crosses zeropressure half way between the walls.

Time = + 1/8λ
135Standing Waves
Total
+

P

This is another 1/8 wavelength later, or ¼ wavelength from where we
started. The instantaneous sound pressure is zero everywhere.

Time = + 1/4λ136Standing Waves
Total
+

P
-

Moving on yet another 1/8 wavelength, we note that the total
waveform has “flipped” polarity, like a see-saw pivoting at the halfway point across the room. Still no sound at the mid point.

Time = + 3/8λ137Standing Waves
Total
+

P
Time = + 1/2λAt the half-wave stop-action view, we are precisely in a situation thatmirrors where we began. If we continued for the remaining halfwave, we would end up where we started.
So, for the frequency at which the room dimension is precisely onehalf wavelength, there will be a resonance, and a standing wave inwhich the sound pressure is always zero at the mid point between thereflecting surfaces. On either side the sound gets louder as one
moves towards the walls. Note, that the instantaneous polarity of thepressure change is opposite on opposite sides of the pressure
minimum, or null. This is important. Remember it.

138

Axial Standing Waves
Total
+

P

Here we see a superimposition of the stop-action “total” waveforms
for one complete wavelength.

-

139

31 January, 2002

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The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

What you hear atdifferent locations

There is minimal sound at the mid point, and the sound gets louder as
we move towards the walls.

140

Orders of Axial Standing Waves
1 st
Order
2xF

Frequency = F
2 nd
Order

For a given distance between reflecting surfaces, the first resonancewill be at the frequency having a wavelength equal to twice theseparation. If the distance is halved, the frequency is doubled.
There is also a second-order resonance, or standing wave, at exactly
double the first frequency, and this standing wave has two nulls.
There will also be third, fourth, and so on.

2xF

4xF

141

Visualizing Standing Waves
To visualize the standing waves, let us just plot the sound pressure asa function of dis tance, and remember that the polarity changes eachtime we cross a null.

Sound Level

+

-

+

+
142

Calculating the Frequencies of Modes

f=

c
2

nx 2

ny 2

nz 2

Lx

Ly

Lz

This formula allows us to calculate all of the possible resonances in arectangular room. It is a bit frightening.

WHERE: c is the speed of sound: 1130 ft/sec.
nx , ny ,nz are integers from 0 to, say, 5
and Lx , Ly , and Lz are the length, width and height of theroom in feet.
143

A Simple Way to
Calculate the Axial Modes
e.g. the first length mode of a room 20 feet longcan be calculated as follows:
f1,0,0=speed of sound in ft/s=
2 x length in feet1130
= 28.25 Hz
40other length modes are 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 for the width and height modes.

For the majority of situations, it may be sufficient to calculate only
the axial modes. If so, it is very simple. Measure the room
dimensions. Multiply the length by two, and divide it into 1130 (fordimensions in feet) or 345 (for dimensions in meters). This gives thisfirst-order resonance along that dimension. Multiply that frequency
by 2 for the second-order resonance, by 3 for the third-order, and soon. Usually it is necessary only to look at the first three or fourorders. Now, repeat that for each of the other two dimensions.

144

31 January, 2002

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The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

An Even Simpler Way to
Calculate ALL of the Modes .
. .and to Visualize Them.

All
Oblique
Axial+Tan.
Tangential
All Axial
HeightWidth
Length818 895 5761

ftoole@harman.com

If you have a computer, it is all even easier. Just type in thedimensions, and the work is done for you. This is a little spreadsheet
program that runs in Microsoft Excel for PC’s that is available fordownload from www.harman.com in the section “white papers”. It
shows, in an easy to understand form, all of the modes in arectangular room.

145

It has long been believed that, tobe good, a room must have auniform distribution of modes in
the frequency domain.
This is certainly true forreverberation chambers, where
the notion originated. But, is ittrue for listening spaces???

But what about the “ideal” room?

146

The distribution of modes in thefrequency domain is determinedby the RATIO of the room
dimensions:
Height:Width:Lengthe.g. 1:1.5:2 = 8 x 12 x 16 feet
147

Is There an “Ideal” Room Shape?
Over the years several acoustical luminaries have lent their names toroom dimensions that purport to have advantages. Do I have afavorite too?

LENGTH

8
4
8
WIDTH

31 January, 2002

148

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The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

Let’s Calculate Some Modes

Everyone knows that a cube is the worst possible
shape. Such a room is really impractical in any
event, because the ceiling would be very high.
Let’s compromise, and make the ceiling height halfof the other two dimensions. It can be seen that theroom resonant frequencies all line up like little
soldiers on parade, with big gaps between them.
The suggestion is that some frequencies will beoverly accentuated, and others not adequately
represented. A room should be better if it had amore uniform distribution of resonant frequencies.

A cube withhalf-heightceiling

L:W:H = 1:2:2 = 11.5 x 23 x 23 ft.

ftoole@harman.com

149

Let’s Calculate Some Modes
It has been suggested that adjusting the room
dimensions to produce a slight separation of theresonant frequencies should help. Here, arecommendation of 6% separation of frequencies
has been followed, and it is seen that while the highfrequencies appear to be improved, the low
frequency resonances are still in closely-spaced
groups with large gaps.

A cube withhalf-heightceiling with
6% mode separation (Bonello interpretation)

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 room with dimensions that are simple multiples
of each other produces a mixed situation. Some of
the modes seem to be well separated, but others line
up at certain frequencies.

L:W:H = 1:2:3 = 8 x 16 x 24 ft.

31 January, 2002

151

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The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

Let’s Calculate Some Modes
Just departing from simple multiples seems to do
wonders. Here the modes all seem to be quite welldistributed. If this approach to room design has any
merit, this room should have some audible
advantages. Does it?

Not-so-simple
multiples

L:W:H = 1:1.8:2.3 = 9 x 16 x 21 ft.

152This all makes a very nice story,
but does it really matter?
Maybe . . . Somewhat . . . It all
depends . . .
Oh, all right,

No!
153

Why not?
• The calculations assume that all of the modes areequally energized by the loudspeakers –they are not.
• The calculations assume that all of the modes areequally heard by the listener(s) – they are not.
• The only modes that matter, are those that are
involved in the transfer of sound energy from theloudspeakers to the listener(s).

The simplifying assumptions underlying these predictions make themsimpler, but also simply invalidate them!

So, how do we determine that?
154

Important Facts About Woofers,
Listeners and Standing Waves.
• Conventional woofers are sound pressure
generators. They will “couple” to the roommodes when they are located in highpressure regions of the standing waves.
• Ears respond to sound pressure, therefore,
room modes will be most audible when ourheads are located in the high pressure
regions of the standing waves.
155

31 January, 2002

8

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

How To Experience the Modes inan “Ideal” Room818 895 5761

ftoole@harman.com

In order to hear the benefits of a room with “ideal” proportions, this is
how it would need to be arranged. The ideal proportions were
determined by looking at the distribution of all the resonances, so weneed to energize them all. A woofer on the floor in one corner excites
all of the room resonances. Likewise, the listener must sit with hishead stuck in another corner, in order to hear all of the modes.
This sounds silly, but it is true.

156

A practical listening location does
not couple to all of the modes.

Of course, in practice, we don’t do this. We sit where we want to.

157

A practical loudspeaker location
changes things even more.
And we place our loudspeakers where they need to go for good
imaging.

158

Two loudspeakers add more
complications.

And we listen in stereo.

159

And with five loudspeakers wehave serious complications.
If not in a multichannel format. All of those neat calculations don’tmean a thing in a situation like this! They are just an academic
exercise, more window dressing.

160

31 January, 2002

9

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

The “classic” monitoringarrangement in a 20’ x 24’ room
Here is how some professionals listen, with five full range
loudspeakers located according to the new European standard: center,+/- 30° and +/- 110°.

161

We have five very different bass
sounds, one for each channel!
10 dB

40 dB

The large variations are
At low frequencies

When a full-range signal is panned to each of theloudspeakers in turn, and measurements are made at
the listening position, we find hugely different bass
responses for each of the loudspeakers. The
differences are a large as 40dB in this room, and thebiggest ones are all at low frequencies. The reason,
the woofers each have very different acoustical“coupling” to the room resonances because they are
in different locations. This will be different forevery different room. Again, referring back to the“circle of confusion” the bass that was heard in thecontrol room will not be the same as that heard at
home. It cannot be.

162

Signal Panned to Speaker Pairs

Attempting to improve the situation by panning thebass to pairs of loudspeakers changes things, butdoes not remove the problem.

10 dB

Anybody think that an “ideal” room can help this?
An anechoic room would, but none of us would
wish to live in one.

Different, but not better

163

This is why we use bass management
and subwoofers.
The same bass sound for all channels.

164

31 January, 2002

And this is why bass management and subwoofers make sense. Now
we can place the woofers where they perform optimally for a specificroom with a specific listening position. We can place the satellites (aterm that seems inappropriate for some of the large capable
loudspeakers that we use in the high-passed channels) where theyneed to be for directional and imaging effects.
In other words, we design the low-frequency portion of the systemseparately because rooms force us to do so. This is the only way that
we can get good bass in any room, and have any hope of having
similarly good bass in different rooms. Remember about preserving
the art?
10

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

How many subwoofers?
Where do we put them?

818 895 5761

ftoole@harman.com

More than one subwoofer may be needed for high sound levels inlarge listening spaces. It’s physics. One huge box might be difficult
to hide, while a number of smaller ones might be less conspicuous.
But there are other considerations which become obvious as soon as
we start looking in detail at room resonances.

Where do we sit?

165

‘Fast’ and 'Slow’ Woofers.

A Standing
Wave
Calculator

A digression here about the “speed” of woofers. I keep on hearing stories
that small woofers are “faster” than big ones. Well, there is truth in theargument if you consider the highest frequencies they are capable ofreproducing. However, if we are crossing them over at 80 Hz, for example,
to use them as subwoofers, we have limited that highest frequency to be thesame for all. They are then all equally “fast”. Woofers are minimum-phasedevices (see Part 2). Their time-domain behavior – speed, punch, drive, paceand rhythm - can be anticipated from their frequency responses. We willsoon see that rooms really mess this up and determine what we hear.
As for moving mass, we use bigger motors on larger, heavier, diaphragms.
It’s a “horsepower thing”.

Understanding what happens in rooms at low frequencies requires
knowledge of what the standing waves, or resonances, are doing to
us. Part of the Excel program mentioned earlier is a great help. It
shows the pressure distributions for the first few axial modes alongeach of the room dimensions. It is available for download fromwww.harman.comunder “white papers”.

166

Woofer Location Decides How
Much Energy Each Mode Receives.
Here I show a woofer placed against a wall, where it excites all of themodes along the length of the room. Why? Because it is in a highpressure region for all of the mo des. What happens if we move thewoofer forward, to the location of the first pressure minimum?
A woofer on the floor, against a wall, energizes allmodes along that axis.
What happens if we move it forward, say, to the first
null?

167

Woofer Location Decides How
Much Energy Each Mode Receives.
That particular mode is not energized by the woofer, and it
disappears. What then happens if it is moved further ahead to thenext null?
A pressure source located at a pressure null, or
minimum, does not energize that mode.
What happens if we move it forward to the second null?
168

31 January, 2002

11

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

Woofer Location Decides How
Much Energy Each Mode Receives.

That mode ceases to be activated, but the other one returns. Woofer
location determines which of the room resonances is activated, andwhich is not.
A pressure source located at a pressure null, or
minimum, does not energize that mode. Note that it is
the woofer diaphragm that is the pressure source, notthe whole enclosure.
169

Similarly, the Listener Location
Determines Which Modes Will Be
Heard.

Just as a woofer against a wall energizes all of the standing waves inthat dimension, a listener with his head close to the opposite wallhears all of the modes. Just as a woofer against a wall enjoys a gainin output because of the adjacent boundary, so the ears enjoy a similar
low-frequency gain. There will be too much bass!!

A woofer on the floor, against a wall, energizes allmodes along that axis.
A listener against the opposite wall, hears all modes
along that axis. There may be too much bass.
170

Similarly, the Listener Location
Determines Which Modes Will Be
Heard.
Moving the listener forward provokes the same problem we had whenmoving the loudspeaker forward. If the head is at a null, no soundwill be heard from that mode.

For this listener, the bass is in better overall balance, but
he wonders what happened to one of the bass notes.
171

Similarly, the Listener Location
Determines Which Modes Will Be
Heard.
Different positions mean that different frequencies will be heard withsometimes very different loudness.

And here, it is a different note that has disappeared.
172

Similarly, the Listener Location
Determines Which Modes Will Be
Heard.

And here, two of the best really low frequencies have gone away.
173

31 January, 2002

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The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

Similarly, the Listener Location
Determines Which Modes Will Be
Heard.
However, there are locations that might work reasonably well.

But, there are several locations where happiness might bepossible.

174

Similarly, the Listener Location
Determines Which Modes Will Be
Heard.
And this is true for woofers as well as listeners.

These are also suitable locations for loudspeakers, but not all
are practical, just as not all listener locations are practical.

175

31 January, 2002

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The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

Selective Mode Cancellation
0 ft.

WIDTH

20 ft -5 in

+
0 ft.

WIDTH

-

20 ft -5 in

-

+

+

+ +

-

0 ft.

WIDTH

20 ft -5 in

0 ft.

WIDTH

20 ft -5 in

+

+

+

One subwoofer
energizes all
width modes.
Two subs cancel
the odd- ordermodes.
Leaving only one
active width
mode.
Does this leavenone??
177

Here we get a bit fancy. Remember the standing wave diagrams showing the “see saw” behavior of the waveform
pivoting on a null. It means that at any instant in time, the sound pressures on opposite sides of a null in a standing
wave are in opposite polarity. If one side is increasing, the other will be decreasing. None of this matters if wehave only one source of low frequency energy in a room. However, if we have two or more, things get
complicated. The top picture shows all of the width modes in a room being excited by a single subwoofer. If weplace another in a symmetrical position on the other side of the room, the woofers, which receive exactly the same
signal, are operating in phase (the same polarity) with each other. The first- and third- order modes, however,exhibit opposite polarities at the subwoofer locations – see the opposite polarity signs. What happens? The
subwoofers couple in a destructive manner with the odd-order modes, and those modes are simply not energized.
They do not exist. This leaves only one mode across the width of the room. If we get even more clever, and movethe subwoofers to the null locations for that mode. They are still in opposite polarity regions for the odd-ordermodes, and the result is that all of the width modes are 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 for everybody in each row of a hometheater to hear the same bass sounds? Would it not be a good idea for a recording engineer to be able to movefrom one end of the console to the other without experiencing huge changes in bass? Well, this is how it can beaccomplished. We are not saying, yet, that it is good sound, merely that it is the same sound. Once things areequalized in the sense of getting everybody hearing more or less the same sound, we then may need to equalize inthe sense of changing the frequency response of the system.
3'8

8'8

3'8

A Practical Example:
8’ x 16’ x 24’ – 1:2:3
In theory, this is abad room.
24'3

4'

2'

2'3

Just to prove a point, let us take a real example: a room that, by mostadvice should be a bad room. It is not an unusual situation. There isa living/dining room, with a rear projection television at one end,seats in the middle area, and a dining area behind the chairs.

178

2'8

31 January, 2002

13'4

14

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

It looks normal, and could happen in a detached dwelling or in anapartment.

179

The modal distribution shows that there
could be a problem with three modes
stacking up at 70 Hz.

Room Mode Calculator
by: Allan Devantierdimensions
metersfeet
incheslength
7.32
24
0

width
4.88
16
0

height2.44
80

Cubic Volume
cubic
cubic
metersfeet
86.99
3072.00

all 8
oblique

7

tan & axial 6This looks bad!

tangential 5
axial 4height 3
width 2length

1
10

100

1000

Frequency (Hz)180

Along the Length of the Room
0 ft.

LENGTH

3

4

8

9

12

Fortunately, we have some help from the locations of loudspeakers
and listeners. The loudspeakers are lined up with the front of the
RPTV, and that puts them in the null of the fourth-order mode. The
listeners are seated at the mid point, and they are in the nulls of thefirst- and third-order modes.

24 ft -0 in

15

16

21

In “theory”

181

Along the Length of the Room
0 ft.

LENGTH24 ft -0 in

That leaves only the second-order length mode to cause problems.

In practice182

31 January, 2002

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The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
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Across the Width of the Room
0 ft.

WIDTH

16ft -0in

In theory there are a bunch of modes at play.
2

2 3/4 51/4

6

8

10

103/4

14

In “theory”

184

Across the Width of the Room
0 ft.

WIDTH

16ft -0in+
2

2 3/4 51/4

In practice, we have selected locations for the loudspeakers andlisteners that avoid them all.

-

+
+

+
6

8

10

103/4

14

In practice – the loudspeakers, which operate ‘in phase’ at low
frequencies, “destructively” drive the 1st and 3rd order modes(they are not energized), and they are located at the nulls of the 2 ndorder mode (it is not energized). The 4 th order width mode is“constructively” driven.
185

Across the Width of the Room
0 ft.

WIDTH

16ft -0in

But, the listeners are located at nulls of the 4t h order mode
and it is not heard.
186

Across the Width of the Room
0 ft.

WIDTH

16ft -0in

So, in practice, there are no active width modes in the listening path.

187

Room Mode Calculator
by: Allan Devantierdimensions
metersfeet
incheslength
7.32
24
0

width
4.88
16
0

height2.44
80

Cubic Volume
cubic
cubic
metersfeet
86.99
3072.00

The modal distribution looks a lot less cluttered after we cross off allof the modes that are not involved with communicating between thewoofers and the listeners in those chairs. Remember, things will bedifferent elsewhere in the room.

all 8
oblique 7
tan & axial 6
tangential 5
axial 4height 3
width 2length 1
10

r

r

r r r
r r
100

1000

Frequency (Hz)188

31 January, 2002

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The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

And, finally, the height dimension

In practice: the ears are close to the nulls for the 1 st and 3 rd ordermodes. They are not eliminated, but are seriously attenuated.
189

Room Mode Calculator
by: Allan Devantierdimensions
metersfeet
incheslength
7.32
24
0

width
4.88
16
0

height2.44
80

Cubic Volume
cubic
cubic
metersfeet
86.99
3072.00

When we are through, there is only one solitary room resonance thatis actively involved in the acoustical link from the loudspeakers to thelisteners. Amazing!

all 8
oblique 7
tan & axial 6

What problem?

tangential 5
axial 4height 3
width 2length 1
10

r

r

r
r r r
r r
100

r

Let’s measure it and see what we have.
1000

Frequency (Hz)This one might be a problem
because it is so lonely. 47 Hz, let’s have a look.
190

And guess what we found?

Surprise, surprise. There is a resonance at 47 Hz, the frequency of
the remaining second-order length mode. And, guess what, there is a
sharp dip at 70 Hz, just where we successfully canceled those
problematic modes. To get rid of the dip, all we need to do is to beless successful at canceling some of those modes. In other words,
move a chair or a loudspeaker a few inches.

80 Hz crossover

3 coincident nulls

47 Hz!
191

A simple fix
BEFORE and
AFTER one bandof parametric EQ

192

And, what about the resonant peak? When we listened, it was clearly
audible, making kick drums “boom”, and all bass inarticulate andfloppy. All bass tended to be “one note bass”, the “tunes” in the bass
guitar were all but gone. We could have blamed the woofers,
accusing them of being slow, uncontrolled, and tuneless. But weknow better.
The solution? Because the room resonance is a minimum-phase
phenomenon, we designed a parametric filter to attenuate the peak,
and the system is instantly transformed. The bass was tight, theguitars played tunes at low frequencies, explosions no longer had apitch. The room sounded great.

The Problem and Solution
in the Time Domain
BEFORE and
AFTER one bandof parametric EQ

The long ringing of the original room is transformed into a welldamped, tight, transient response. It works. The woofers were ‘fast’
all along. We just couldn’t hear it.

193

31 January, 2002

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The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

So, according to dimensional ratio
theory, this was supposed to be a badroom. In this practical example, it
ended up having only one problem
resonance and, after equalization, it
yielded truly superb sound!

818 895 5761

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O.K. So this is showing off. However, it does prove a point. If you
understand basic room acoustics, have some decent analytical tools at
your disposal, including measurements, most rooms can be undercontrol.

Good Sound in a “Bad” Room!
194

Not all stories have such a happy
ending, but happy endings areunlikely unless the loudspeakerand listener locations areevaluated in conjunction with thestanding wave patterns.
195

REMEMBER:
The only modes that matter are
those that participate in thecommunication of sound fromthe loudspeaker to the listener!
and
There is NO ‘ideal’ room!

So, back to the issue of “ideal” room dimensional ratios. Personally I
have no favorites. I have yet to encounter a room that could not bemade to sound at least good, if not excellent.

196

So, what
happens if westart with aroom that is“good” tobegin with?

SUB

LS

LR

L

C

R

SUB

RS

RR

In this example we will really make use of acoustical measurements.
It will be seen that high-resolution (better than 1/3 octave)
measurements allow us to confirm which resonances are active inwhich parts of the room. They will allow us to experiment,
intelligently, with subwoofer and listener locations. In short, goodmeasurements put us in control. We may or may not achieve ourfantasy performance, but we certainly can get closer than would bepossible by trial and error.

197

198

31 January, 2002

18

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

Not a Bad Modal Distribution
Room Mode Calculator

According to common belief, this room shouldhave some advantages, because of the favorable
distribution of modes.

by: Allan Devantierall8oblique7dimensions
meterslength
7.32

width
6.22

height2.74

feet
inches

24
0

20
5

9
0

C u b i c Volume
cubic
cubic
meters124.88feet
4410.00

However, taking nothing for granted, let’s actually
measure what is happening at different listening
locations, when we employ one or two
subwoofers.

tan & axial 6
tangential 5
axial 4height

3

width

2

length

1
10

100

1000

Frequency (Hz)

199

Let’s
measure thevariations
along theseating axes
for one sub,and then for
two subs.

SUB

L

C

Y

$$

LS

R

SUB

It is obviously important to keep the customer and the family or closefriends happy, so pay attention to the front row. I think it is natural toexpect the best of everything in the front row.
Measurements are made at 18-inch intervals across the front row, andfrom each of the seats to the rear.
Note, first of all, in the slide below, that it is possible to identify manyof the axial modes calculated for this room. The frequencies don’t
always line up exactly, and this will be explained later.

Y
RS

LR

RR

201

axial 4rheight 3
width

2

length

1

r

10

r

r r
100

1000

CENTER

16 dB!!
At 36 Hz
SIDE

variations in front row – one front sub.
Length and height modes are constantalong this measurement axis.

31 January, 2002

202

19

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

The above graph shows, in detail, what happens at 18-inch intervals across the front row. Because the room issymmetrical, what we are really looking at is what happens from the center seat to the side seats. It can be seenthat there is a 16 dB difference around 36 Hz between the center and the side seats. This is huge, and this is avery important part of the frequency range. It could be that the host, sitting in the center, 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 underwhelmed if the bass frequencies fall into this range.

axial

4

height

3

width

2

length

1

r
r

10

r r
100

r

1000

Later in the same movie, there is athunder storm, and the almostsubsonic rumble is perceived by theguest to be just stunning, but the hostthinks it is just O.K.

SIDE

13 dB!!
At 27 HzCENTER

variations in front row – one front sub.
Length and height modes are constantalong this measurement axis.

axial

4

height

3

width

2

length

1

203

r
r
r

10

r

r
r r
100

1000

SIDE SEATLOSES 13 dB

SIDE SEATGAINS 16 dB

variations in front row – two front subs.
The odd-order width modes are now
cancelled.

204

This is where mode canceling can be
useful. Using a pair of subwoofers,
the problematic width modes arecancelled, and the bass is rendered
uniform across the front row up to
about 55 Hz. There is a trade-off.
We sacrifice some of the deepest
sounds in the side seats, but we pickup 16 dB of the more important
frequencies higher up, around 36 Hz.
The recommendation is, therefore, to
use two subwoofers located opposite
each other across the front of theroom. The bass response is still
uneven, but we have managed tomake it mo re uniform across the allimportant front row of seats.

The pair of subs will not only deal with the front row, but will also make performance across the back row more
uniform. However, as it is set up, the front and back rows will hear different bass sounds. A decision must be
made of how to equalize, if that route is chosen. Normally, priority is given to the front row

31 January, 2002

20

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

axial 4

RECOMMENDATION: KEEP THE FRONT ROW HAPPY!
USE TWO SUB LOCATIONS, ONE IN EACH CORNER.
l e n g t h USE
1
THE CENTER SEATING LOCATION –10100
e.g. THREE OR FIVE SEATS ACROSS THE FRONT
height 3
width 2

1000

The three front row seats
Two front subwoofers,
one in each cornerSo, how did it all end?

210

axial 4height 3
width 2SADLY,THE BACK ROW HAS1 0 0TO TAKE WHAT IT GETS
10length 1

1000

The three back row seats
Two front subwoofers,
one in each corner211

Now, let us look at a smaller
room – 24 x 16 x 9,
with 2” x 6” studs,
and two layers of
5/8” gypsum board.
i.e. heavy, stiff walls.

As stated earlier, heavy, stiff walls absorb little energy at low
frequencies. This helps to keep the bass energy inside the room, andthe poorly-damped standing waves will exhibit strong high-Q peaks
and dips, and ring energetically. Also, the reduced absorption at eachreflection means that tangential modes may join the axial modes as
being factors to deal with.
215

31 January, 2002

21

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

6
tangential 5
axial 4height 3
width 2length

1
10

100

1000

Frequency (Hz)SIDE

19 dB!!
At 33 HzCENTER

variations in front row – one front sub.

In this room, it is clear that the tangential
modes are very active. Note that it ispossible to identify almost all of theaxial and tangential modes in the visible
peaks at low frequencies. Moving
across the front row produces a rather
large 19 dB variation from center to sideseats over a very important part of thebass frequency range. It would be niceto reduce this.

217

6
tangential 5
axial 4height 3
width 2length1
10100

SIDE SEATLOSES 12 dB

1000

Frequency (Hz)

Employing the tactic used in theprevious example, two subs, one in eachfront corner, we certainly get consistent
performance across the front row, but wehave sacrificed a lot of good bass in theprocess.

BUT, FRONT ROW VARIATIONS BELOW 65 Hz ARE GONE!

variations in front row – two front subs.

218

6
tangential 5
axial 4height 3
width 2lengthRECOMMENDATION: USE ONE SUB
100
LOCATION,ANDDO NOT USE THE
Frequency (Hz)CENTER SEATING LOCATION –e.g. FOUR SEATS ACROSS THE FRONT

1
10

SIDE

19 dB!!
At 33 HzCENTERA 9 dB CHANGE IN SOUND LEVELOVER THE NEXT 4.5 FEET!
A 10 dB CHANGE IN SOUND LEVELFOR AN 18 INCH SHIFT OFF CENTER!

variations in front row – one front sub.

31 January, 2002

1000

219

Looking closer, we notice that 10 of the
19 dB change occurs in the first 18
inches away from the center location.
This is a high-Q null. The remaining 9dB accumulate over the next 4.5 feet.
Taking advantage of this knowledge, we
decide to go back to one subwoofer
location – we may in fact use two subs
stacked at that location, to get enoughpower into the room. We avoid thecenter seating location, choosing toarrange the chairs symmetrically aroundthe room center line.
None of this would be obvious without
measurements – good measurements,and enough of them to help design thebest listening experience for thecircumstances.

22

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

Some Observations• You cannot escape from room modes!
• ONLY high resolution measurements can help you
understand what is happening. 1/3 octave not enough.
• Mode control with multiple subs is very position
dependent, but it can work IN CERTAIN ROOMS.
• Massive, rigid walls make the situation much more
complicated by activating tangential modes.
• Spatial averaging of measurements is essential toaddress the needs of an audience.
• You will never satisfy everybody in the audience.

220

But, You Have Heard That NonParallel Walls Solve all of These
Problems.

221

What About Non-Parallel Walls?
• The modes are not eliminated• The strength of the modes is much the sameas in a rectangular room
• Because of the complexity of the standing
waves, predictions of pressure distributions
are not easy, and may not be practical.
• Why bother?
222

A Room With Only One Pair of Parallel Surfaces
30

2,0,0

20
dB

3,0,0
1,0,0

4,0,0

14 dB!

10
0
-10

20

50 100500 1K
5K
FREQUENCY (Hz)10K 20K
223

Here is an example of a room that had only one pair of parallel walls.
The high ceiling was sharply angled, about 40 degrees. The sidewalls had several large openings, recesses, and a large stairwell.
There was hardly any parallel surface left that was at a fixed spacingfrom one across the room. Taking a simple look at the room, it
should have some advantages. But, the bass in that room was awful.
It boomed horrendously. I know, because it was in my last house.
When measured, it revealed a set of very clear resonances, all of themassociated with the remaining pair of parallel walls. With nocompetition from any other modes, these ones sang their little heartsout.

By removing energy from the modes using damping at the reflecting
surfaces, it is possible to attenuate the high-pressure regions ofstanding waves, and to elevate the low-pressure regions. Doing thismakes the sound field less variable over the room. In my opinion,
this is where we should start, preferably when the room is being built.

Sound Absorption
reduces theenergy in the modes.
This is called DAMPING.

224

31 January, 2002

23

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

The Damping of Room Modes
MASSIVE, RIGID,
REFLECTIVE, ROOMBOUNDARIESLess variation means more happy listeners.

P

FLEXIBLE, ABSORBING,
ROOM BOUNDARIESP
225

Acoustical Damping of a Mode:(a) using resistive absorbers, e.g.
fiberglass, acoustic foam, drapes+-+

SOUND PRESSURE

PARTICLE VELOCITY

ü ü X
?
ü

218

Resistive absorbers are mosteffective when positioned in thehigh velocity regions of thestanding wave

Sound absorption can be achieved with resistive absorbing materials,
like fiberglass, acoustic foam, heavy drapes, etc. However, to beeffective these materials must be in the regions of high particle
velocity. This does not happen immediately at the room boundary,because, by definition, there can be no particle movement when themolecules are hard against a rigid surface. Maximum particle motion
occurs in regions of minimum pressure – at the nulls in the standing
wave pattern, one-quarter wavelength from the reflecting surface. So,
one either needs thicker material, or some air space behind thematerial. Thicker material works better, but is costly. Either way weface using a lot of space.

Dropped ceilings, the T-bar systems with lay-in panels actually work
well at low frequencies because of the large space above them. The
panels themselves, if placed on a hard surface, are no better than theequivalent thickness of rigid fiberglass board purchased from abuilding supplier. Be careful not to let such ceiling systems buzz or
rattle, though.

227

Resistive Absorbers are notPractical at Low Frequencies• 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.

“Bass Traps” are a favorite topic in pro audio. The name conjures animage of a device that seeks out and sucks up bass, never to spit itout. Well, reality is much less romantic, and real bass absorbers are
only as effective as space and the budget permit.

If we try to damp really low frequency resonances with resistive
absorbing materials, success is possible only if serious amounts ofreal estate are devoted to the task!

228

Want to Build a “Bass Trap” with
Fiberglass?

This should be a real stimulus to the building industry, if every hometheater had to be about 20% larger in every dimension. Remember,to absorb energy in the modes in all directions, one of theseappendages must be built on the ceiling, and another on a side wall.
Cost conscious customers might wonder if there is a better way.
There is.

Be my guest!
229

31 January, 2002

24

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

However, Resistive Absorbers Work
Superbly at Mid & High Frequencies.
ABSORPTION

100%

5”
3”
2”

50%

1” thick fiberglass board
0

125

250

500

1K

2K

4K Hz

818 895 5761

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However, at higher frequencies, where wavelengths are shorter, suchmaterials work just fine, and are highly recommended. Just don’t
cover them with a non-porous material, because such materials needto “breathe”. Resistive absorbers do their work by making it difficult
for the air molecules to move around within the “fibrous tangle”. A
good low-cost covering, available in a wide range of colors, ispolyester double-knit, often used for speaker grilles. If the coveringneeds to be fire rated, look elsewhere, and pay much more.

230

Acoustical Damping of a Mode:(a) using membrane absorbers, e.g.
walls, floor, ceiling, custom units.
+-+

SOUND PRESSURE

PARTICLE VELOCITY

231

At very low frequencies, we need another technique. It is membrane,or diaphragmatic, absorption. In this, the fluctuating sound pressureof sound causes a surface to move, and in doing so, transfers energy
to the moving surface. So, when you feel the bass in your feet, or feelvibrations in the walls, you are experiencing membrane absorption.
Obviously, the best location for a membrane absorber is in a highpressure region for the problem mode. If the room is constructedwith bass absorption in mind, the problem is diminished from theoutset. “Let the boundaries move” could become a mantra forenlightened room design.

Membrane (mechanicallyresonant) absorbers are mosteffective when located in the highpressure regions of the standing
wave pattern.
The room boundaries do it
naturally.
224

Mechanically Resonant
Membrane Absorbers

The resonant frequency is determined by the moving mass ofthe exposed panel, and the compliance of the air inside theenclosure (the volume/depth). A heavier panel, or a deeper box,
reduces the frequency. Damping is achieved by mechanicallosses in the panel material, and by acoustical losses in thefiberglass. Lossy, “soft” panels have low -Q, i.e. absorption overa wide frequency range. Heavy vinyl has been usedsuccessfully.
225

Commercial membrane absorbers are available. Most are flat, and fit
against the room boundaries. Others are designed to fit in corners, orto stand freely. Be sure to check that they exhibit high absorption
coefficients at the frequencies you wish to damp. Some of them work
well at lower mid frequencies, but lose it in the deep bass region.
Ironically, a single layer of wallboard on standard studs does a decent
job. Things get problematic when a second layer of wallboard isadded, or bigger studs are used, or the wall is filled with sand, etc. A
somewhat compliant inner surface to a room is a generally good idea.
“Let the boundaries move.” Mind you, a wall or ceiling that rattles
and buzzes is not welcome. So pay attention to how it is constructed.

Acoustically Resonant“Helmholtz ” Absorbers
M

A second kind of low-frequency absorber involves a tuned acousticalresonance. Usually these utilize slats with spaces between, and adamped volume behind.

C
In a “classic” resonator the
resonant frequency isdetermined by the mass of
the air in the neck, and thecompliance of the air in thechamber (volume). This is
the “soda bottle” resonance.

This can be expanded into a surface, withthe resonant frequency being determinedby the mass of the air in the slots
between the bars, and the compliance of
the air in the cavity behind. Somefiberglass in the cavity provides damping.

31 January, 2002

226

25

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

The Walls Absorb Low Frequencies
Different Amounts at Different Frequencies
SOLID WALL

WALL WITH DOOR

Low Q vs. High Q modes

6
4

Amplitude (dB)

2
0
-2 0

2

4

6

9 dB

-4

8

10

12

14

16

18

20

22

24

Series1

14 dB

Series2

-6
-8
-10
-12
Distance (feet)

WALLS: TWO LAYERS OF 5/8” GYPSUM BOARD ON 2” X 6” STUDS

233

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If a room surface absorbs sound, it will do so differently at different
frequencies. It is the nature of such surfaces to slightly alter thetiming of the reflected sounds (phase shift) depending on thefrequency of the sound relative to the preferred frequency for theabsorbing surface.
A real world example of this is shown here. It was noted that one
wall of a room was vibrating quite actively. The wall had a door in it,
and it appeared that this reduced the structural stiffness, allowing
much more movement than the other walls. Out of interest, wemeasured the pressure distribution across the room for the first twomodes. The first order mode had more damping than the second.

The Walls Absorb Low Frequencies
Different Amounts at Different Frequencies
Low Q vs. High Q modes
6
4

Amplitude (dB)

2
0
-2 0

2

4

6

8

10

12

14

16

18

20

22

24

Series1-4

Series2

-6
-8
-10
-12
Distance (feet)?

This is seen as a lower maximum-to-minimum pressure variation – 9
dB for the first-order mode vs. 14 dB for the second. Also apparent
was a positional shift of the high and low pressure points. They were
not exactly at the locations simple mathematics would predict. The
null of the first order mode was substantially off center, towards thewall with the door.

Since membrane absorbers are reactive devices, there can besignificant phase shift in the reflected sounds, causing thepeaks and nulls to be moved from their predicted locations.
234

The Walls Absorb Low Frequencies
Different Amounts at Different Frequencies“ACOUSTICAL” WALL @ 21 Hz
PHYSICAL WALL

Low Q vs. High Q modes
6
4

Amplitude (dB)

2
0
-2 0

2

4

6

8

10

12

14

16

18

20

22

24

Series1-4

Series2

-6
-8

3 FT

-10
-12
Distance (feet)

13.5 FT

13.5 FT

Since membrane absorbers are reactive devices, there can besignificant phase shift in the reflected sounds, causing thepeaks and nulls to be moved from their predicted locations.

I made the simple assumption that most of the absorption was
occurring in the wall with the door, and speculated that the phase shift
in the absorbing wall was making it look (acoustically) as though it
was farther away. On this basis, I took the distance from the “solid”
wall to the null to be the true ¼ wavelength, and projected the same
distance towards the wall with the door. This put the “acoustical”
wall three feet away from the real one! Acoustically, at thisfrequency, the room was behaving as if it were three feet longer thanthe physical length.

235

axial

4

height3

PHYSICAL
WALL
width 2length

1
10

r

r
r r r
100

1000

“ACOUSTICAL”
WALL

This graph shows that this is so. At thefrequency calculated for this mode basedon the room dimensions, there is noresonant peak. However, at a frequency
appropriate to a room three feet longer,
there is a healthy resonant peak.

236

31 January, 2002

If this is true, then the frequency of thefirst-order resonance must not be at thefrequency predicted by a measurement of
the room length, but at a frequency
appropriate for a room three feet longer.

This explains why, very often, it will befound that the measured resonances do notexactly correspond with the calculated
ones. This is also why room acousticalmodeling programs do not always give theright answers. In rooms it is essential to
make high-resolution, accurate,measurements in the room after it is built.

26

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

Room Walls Perform Two Key
Tasks• Provide transmission loss to prevent insidesounds from leaking into the rest of thehouse, and outside sounds from leaking into
the listening space.
• Provide absorption to damp the lowfrequency room resonances.
Conclusion: we need two kinds of wall in one.

818 895 5761

ftoole@harman.com

Sound transmission loss in a wall is a measure of how well it prevents
sound from traveling through it. Absorption coefficient is a measureof what proportion of the sound falling on a surface is absorbed, andnot reflected back into the room. They are two very different things,
and they are often confused. Most studies of transmission loss wereconcerned with privacy, and focused on speech frequencies, notpaying much attention to low bass frequencies. With today’s
powerful woofers and subwoofers, we need new and higher
standards.

237

For Example:

Here the massive, stiff, concrete is providing the bulk of the soundisolation. The standard stud wall provides some attenuation, as well
as some sound absorption. Its vibrations are isolated from theconcrete wall by an air space and, at low frequencies, the larger the
better. Some fiberglass in the cavity adds to the effectiveness bydamping reverberation in the space between the walls, not by actually
preventing sound from passing through it.

Concrete or Masonry Wall

One layer of gypsum wallboard on
wooden studs, with fiberglass.

238

Here is another dual-purpose wall, with multiple layers of gypsum
board substituted for the concrete. Again a large part of the isolationis due to the mechanical separation between the inner “microphone”
wall and the outer “loudspeaker” wall. If the walls are connected, the“microphone” talks directly to the “loudspeaker” and there is almost
no sound attenuation. Therefore, these walls must not bemechanically connected at any point – no conduits, no water pipes,
nothing to link the inner and outer walls. HVAC penetrations must
be flexible, and be equipped with special acoustical absorbers on eachside of the wall to prevent sound leakage through the duct itself.

Or . . .
OutsideFIBERGLASS BATT

Inside239

Or . . .

Fabricated or purchased membraneabsorbers

If acoustical isolation is absolutely paramount, then there is little
choice but to go for broke. Build a really massive double wall, andthen add membrane absorbers on the inner surface. Always
remember that low-frequency isolation can be defeated by even quite
small air leaks. Keep an eye on the builder, and be sure that all joints
are caulked, and that no penetrations or mechanical short circuits
have crept in.

240

Or . . .
Concrete or Masonry Wall

Fabricated or purchased membraneabsorbers

A membrane absorber can be considered a mechanically resonant
panel absorber. Another type of low-frequency absorber is theacoustically resonant absorber, also known as the Helmholtz
absorber. In these devices, one or a few large openings, or manysmall openings, resonate with a volume of air at the appropriate
frequency. These require careful design, and careful construction, but
can work very well.

241

31 January, 2002

27

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

The MOST PROBLEMATIC rooms
I have ever encountered
are those that have been
constructed with massive, stiff walls.
They have:
1. High Q resonances that ring
2. Poor bass uniformity over thelistening area.

818 895 5761

ftoole@harman.com

It is truly sad when someone has spent good money building a roomof “solid” walls, based on the belief that it keeps the bass in. Yup, it
sure does, but it makes that bass unpleasant to listen to. To those whosuggest 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 loudspeakerenclosure. Both are highly unreliable because sound waves energize
room walls and loudspeaker enclosures very differently than fists or
knuckles.

242

So, we have done what we can to achieve uniform sound quality overthe listening area. Now we will attempt to make it sound good byusing equalization.

The Rules for Good Sound inRooms
At middle and high frequencies:ü Start with a loudspeaker that was designed tofunction well in a variety of different rooms.
ü Use geometry, reflection, diffusion, and absorption toachieve good imaging and ambiance.
At low frequencies:
ü Maximize the output from the subwoofer(s).
ü Achieve a uniform performance over the listeningarea.
Ø Equalize to achieve good performance.
244

The key to “intelligent” room
equalization is in knowing what
can and cannot be corrected withfilters.

Equalization! You thought that it didn’t really work. That equalizers
added phase shift and other ugly stuff.
Historically, equalization has not lived up to its promise. However,
we have learned what it can and cannot do. We now understand why,
the way it has been traditionally done, equalization we doomed todisappoint.

Remember room resonances, those things that cause “boom” ,“hangover” , “ringing” , “coloration”, and that mask our ability tofollow bass melodies. They behave as minimum-phase phenomena,and they can be equalized if the measurements have enoughresolution to show the details of what is happening, and if they
resonances are addressed with carefully matched parametricequalizers.

245

Parametric equalization fixes thefrequency response
30•Original Condition•After ParametricEqualization: One
Filter Only

20
dB
10

Here is a room with a really big boom. I am familiar with this one, as
it was in my last house. It was where I began experimenting withselective parametric equalization, as an alternative to moving thefurniture around or engaging in massive reconstruction.

0
-10

20

50 100500 1K
5K
FREQUENCY (Hz)10K 20K
246

And the transient response is also
fixed!
BEFOREAFTER

And it really works. Kick drums that previously boomed relentlessly,
became “quick” and “tight”, and bass guitarists could actually beheard playing harmonies. Organ pedal notes were all there in proper
proportions. An amazing transformation.
It doesn’t work everywhere in the room, but nothing does. Thosepesky standing waves are still there. They will not go away.

247

31 January, 2002

28

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

A problem and solution:in the frequency domain
equalization can fix thisBEFORE and
AFTER one bandof parametric EQThis is one I showed earlier, pointing out what can and cannot be
equalized.

Equalization cannot fix this248

Dips are caused by acousticalcancellations• The problem is very position sensitive – it will bedifferent at different positions in the room. In factthat leads us to the solution: move the speaker, thelistener, or both. A few inches may be sufficient.
• Trying to fill the dip is foolish! A 10 dB boost
uses 10x more power! A 20 dB boost uses 100xmore power! You have just added a 10 or 20 dB
resonance that will be clearly audible at most
locations other than the one at issue.

And this is why.

249

A problem and solution:in the time domain
BEFORE and
AFTER one bandof parametric EQ

Just to confirm that our ears weren’t lying to us, the time-domain
measurement shows that the extended ringing of the original room istamed.

250

So, equalization can work!
• If you have high resolution measurements• If you try to fix the right things• If you have a parametric filter that you cantune to match the problem.

But, what happens if you don’t?
251

This is the problem situation,
seen in high resolution.

252

31 January, 2002

29

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

This what a 1/3-octave analyzer
sees. Some things are missing!

It is amazing that so much information could just slip away so easily.

253

Oh well, let’s do something withthe 1/3-octave graphic equalizer.
However, we do have a “graphic” equalizer, so we had better dosomething with it. [A “graphic” equalizer is the one with a large
collection of fixed-bandwidth filters, adjusted using a collection ofsliders on the front panel].

254

This is what we really did, as
seen in high resolution.
When it was done, the customer complained that the bass level was
lower, and it still was boomy. This is why. When we look at things
with the clarity of high-resolution measurements we see what
happened. The crude measurement did not show the true situation,and the crude equalizer could not address it even if we could see it.
255

Less bass, and the ringing is still
there!
And, yes, the time domain was still corrupted, because the frequency
domain was still corrupted.

256

It is no wonder that equalization
has acquired a bad reputation.
It deserves it!

257

31 January, 2002

30

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

Bass Equalization can work!
• If it is based on accurate high resolution
measurements - i.e. not simplistic 1/3octave real-time analyzer data.
• If the equalization addresses the room
resonance problems with accurately
matched parametric filters - not thesimplistic 1/3-octave multifilter devices.
• If you do not try to fill dips caused byacoustical cancellations. It is impossible.

To see what is happening at low frequencies, analyzers must haveresolution of 1/10 octave or better.

258

The Dream Psychoacoustically-Optimized Active Control

One day we will be able to have all of this done automatically and‘perceptually correct”. The holdup is partly cost, and partly thedevelopment of the measurement and equalization methodology thatis smart enough to know what is wrong and what it should and should
not try to fix. It has to be foolproof.
Sadly, equalization cannot fix everything. Some problems willremain stubbornly in the acoustical domain, so there will be acontinuing role for people who understand room acoustics, and who
provide the all-important final link to the customers’ satisfaction.

DSP

259

Some relevant scientific publications by staff of the Harman International
R&D Group (F.E. Toole, S.E. Olive)
1.

F.E. Toole, “Listening Tests, Turning Opinion Into Fact”, J. Audio Eng. Soc., vol. 30, pp. 431445 (1982 June).

2.

F.E. Toole, “The Acoustics and Psychoacoustics of Headphones”, 2nd International
Conference, Audio Eng. Soc. , preprint C1006 (1984 May).
F.E. Toole, “Subjective Measurements of Loudspeaker Sound Quality and Listener
Performance”, J. Audio Eng. Soc., vol 33, pp. 2-32 (1985 January/February)**F.E. Toole, “Loudspeaker Measurements and Their Relationship to Listener Preferences”,
J. Audio Eng, Soc., vol. 34, pt.1 pp.227-235 (1986 April), pt. 2, pp. 323-348 (1986 May).

3.
4.
5.
6.
7.

**F.E. Toole and S.E. Olive, “The Modification of Timbre by Resonances: Perception andMeasurement”, J. Audio Eng, Soc., vol. 36, pp. 122-142 (1988 March).
F.E. Toole, “Principles of Sound and Hearing”, in K.B. Benson, ed. “Audio Engineering
Handbook”, chap. 1 (McGraw-Hill, New York, 1988).
S.E. Olive and F.E. Toole, “The Detection of Reflections in Typical Rooms”, J. Audio Eng,
Soc., vol. 37, pp. 539-553 (1989 July/August).

8.

S.E. Olive and F.E. Toole, “The Evaluation of Microphones - Part1: Measurements”, 87th
Convention, Audio Eng, Soc., preprint no. 2837 (1989 October).
9. F.E. Toole, “Listening Tests - Identifying and Controlling the Variables”, Proceedings of the
8th International Conference, Audio Eng, Soc. (1990 May).
10. F.E. Toole, “Loudspeakers and Rooms for Stereophonic Sound Reproduction”, Proceedingsof the 8th International Conference, Audio Eng, Soc. (1990 May).
11. S.E. Olive, “The Preservation of Timbre”, Proceedings of the 8th International Conference,
Audio Eng, Soc. (1990 May).
12. F.E. Toole, “Binaural Record/Reproduction Systems and Their Use in Psychoacoustic
Investigations”, 91st Convention, Audio Eng, Soc., preprint no. 3179. (1991 October).

31 January, 2002

31

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com

13. P. Schuck, S. Olive, E. Verreault, M. Bonneville, S. Sally “On the Use of ParametericSpectrum Analysis for High-Resolution, Low-Frequency, Free-Field Loudspeaker
Measurements”,11th Int. Conference, Audio Eng. Soc. (1992 May).
14. P. L. Schuck, S. Olive, J. Ryan, F. E. Toole, S Sally, M. Bonneville, E. Verreault, Kathy
Momtahan, "Perception of Reproduced Sound in Rooms: Some Results from the Athena
Project", pp.49-73, Proceedings of the 12th International Conference, Audio Eng. Soc. (1993
June).
15. F.E. Toole, “Subjective Evaluation”, in J. Borwick, ed. “Loudspeaker and Headphone
Handbook - Edition”, chap. 11 (Focal Press, London, 1994).
16. **S.E. Olive, P. Schuck, S. Sally, M. Bonneville, “The Effects of Loudspeaker Placement on
Listener Preference Ratings”, J. Audio Eng. Soc., Vol. 42, pp. 651-669 (1994 September).
17. F.E. Toole and S.E. Olive, "Hearing is Believing vs. Believing is Hearing: Blind vs. Sighted
Listening Tests and Other Interesting Things", 97th Convention, Audio Eng. Soc., Preprint
No. 3894 (1994 Nov.).
18. S. E. Olive, "A Method for Training of Listeners and Selecting Program Material for Listening
Tests", 97th Convention, Audio Eng. Soc., Preprint No. 3893 (1994 November).
19. S.E. Olive, ”Separating Fact From Fiction Through Listening Tests”, proceedings of the 1995
DSPx Technical Program, pp. 454-463, (1995 May).
20. F.E Toole and S.E. Olive, "Listening Test Methods for Computer Workstation Audio
Systems", 99th Convention, Audio Eng. Soc., No Preprint (1995).
21. S.E. Olive, P. Schuck, J. Ryan, S. Sally, M. Bonneville, “The Variability of LoudspeakerthSound Quality Among Four Domestic-Sized Rooms”, presented at the 99 AES Convention,
preprint 4092 K-1 (1995 October).
st

22. S. E. Olive, “A Method for Training Listeners: Part II –“, presented at the 101 Convention,
Audio Eng. Soc., (no preprint), abstract published in J. AES Vol. 44, No. 12 (1996 Dec.).
23. S.E. Olive, P. Schuck, J. Ryan, S. Sally, M. Bonneville, “The Detection Thresholds ofResonances at Low Frequencies”, J. AES Vol. 45, No. 3 (1997 March.).
24. F.E. Toole, “The Future of Stereo”, Part 1, Audio, Vol.81, No.5, pp. 126-142 (1997, May), Part2, Audio, Vol. 8, No. 6, pp. 34-39 (1997 June).
th

25. F.E. Toole, “The Acoustics and Psychoacoustics of Workstation Audio Systems”, 16thInternational Congress on Acoustics and 135 Meeting of the Acoustical Society of America,
Seattle, WA, Session 4pSP, (1998 June).
26. S.E. Olive, B. Castro and F.E. Toole, “ A New Laboratory For Evaluating MultichannelthSystems and Audio Components”, 105 Convention, Audio Eng. Soc., preprint no. 4842
(1998 Sept).
27. S.E. Olive, ”Subjective Evaluation of 3-D Sound Based on Two Loudspeakers”, Proceeding ofth
the 15 International Conference, Audio Eng. Soc. (1998 Oct.).
28. S.E. Olive, B. Castro and F.E. Toole, “A New Laboratory and Methodology for the Subjectiveth
Evaluation of Workstation Audio Systems” presented at the 106 Convention, Audio Eng.
Soc., Munich, (1999 May).
29. F.E.Toole, “The Acoustics and Psychoacoustics of Loudspeakers and Rooms – The Stereoth
Past and the Multichannel Future”, an invited paper at the 109 Convention, Audio Eng. Soc.,
Preprint no. 5201 (2000 Sept.).
th
30. S.E. Olive, “A New Listener Training Software Application”, 110 Convention, Audio Eng.
Soc., Preprint no. 5384 (2001 May).
31. S.E. Olive, “Evaluation of Five Commercial Stereo Enhancement 3D Audio Software Plugthins”, 110 Convention, Audio Eng. Soc., Preprint no. 5386 (2001 May).
32. F.E. Toole and S.E. Olive, “Subjective Evaluation”, in J. Borwick, ed. “Loudspeaker andHeadphone Handbook - Third Edition”, (Focal Press, London, 2001).
33. F.E. Toole, “Sound Reproducing Systems”, in McGraw-Hill Encyclopedia of Science andTechnology, ninth edition, in press.
31 January, 2002

32

The Science of Audio - a series of lectures by Floyd E. Toole, Ph.D. Vice President Acoustical Engineering
Harman International Industries, Inc.
8500 Balboa Boulevard, Northridge, CA 91329

818 895 5761

ftoole@harman.com** For these papers the authors received Audio Engineering Society Publications Awards
In 1996 Floyd Toole was awarded the AES Silver Medal “for significant developments inthe subjective and objective evaluation of audio devices”.

For some lighter reading: go to www.harman.com . Look under“white papers”.

Useful References:“The Master Handbook of Acoustics”, Fourth Edition, by F. Alton Everest
McGraw-Hill, 2001
This comprehensive, and readable text goes beyond the normal “handbook” formula, andtries to give the reader some understanding of why things happen. For those interested inlow- frequency absorbers, there are several helpful sections.
“Loudspeaker and Headphone Handbook”, Third Edition, edited by John Borwick.
Focal Press, 2001
Is there a definitive book on this subject? This may be it. Up to date and loaded withdetailed engineering level information.

31 January, 2002

33