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-a five-part article in Home Theater magazine, October 1993 - February 1994
Home Theater Acoustics
Volume Three
The proper placement of
subwoofers in your home
theater system is crucial
to the quality of the
desired sound. Placing
them in the correct
location creates a bass
sound level smooth with
frequency.

BY ARTHUR NOXON
T
he subwoofer generates
very low frequency sounds.
The size of these sound
waves compares to the size
of the listening room. If
the subwoofer is placed in the wrong
position in the room, we hear “room
booms” instead of the musical bass
scale. On the other hand, if we get
the subs into the proper location, the
bass sound level becomes smooth
with frequency. Subwoofer extension
into deep bass is achieved along with
significant punch capacity. In this
section of work, we will study both
the good and bad placement positions
for subwoofers located in smaller
sized listening rooms, the kind most
of us have. Bad speaker positions
are those that allow the speaker to
stimulate room resonance (modes).
Good speaker positions are those from
which the speaker cannot stimulate
such “room boom” effects. These
golden spots are called the anti-mode
speaker positions.
RESONANT MODES
To gain some understanding of mode
vs. anti-mode speaker positions, it
will be very helpful to consider a
one-dimensional acoustic space. In a
regular room, sound can travel in any
direction. If, however, the speaker was
located at the end of a long, narrow
pipe, the sound could only travel in
one direction, along the axis of the
pipe. A pipe is a one-dimensional
acoustic space. If we plug up both ends
of the long pipe, then the “boundary
conditions” of a one-dimensional room
are met. This is a similar idea to a
room having walls.
If the woofer is positioned at one
end of the big pipe and a frequency
sweep is delivered to it while a sound
meter is positioned at the opposite
end of the pipe, we will see evidence
of the modes. At first, in the very
low frequency (LF) range, there are
no special changes in the sound level
meter. Sooner or later, there will be
some frequency where the meter
needle gets pegged. The sound got
exceedingly loud at this opposite
end of the tube, marking the first or
“fundamental” resonant frequency and
mode.
As the frequency sweep continues
upwards, the meter level drops back
SEALED PIPE
SUBWOOFER
SOUND
METER
dB
f0
f1
f2
f3
SOUND LEVEL VS FREQUENCY IN A SEALED PIPE
to normal for a while, but finally peaks again. This next
frequency marks the second resonance mode and is called
the first partial or first harmonic. Curiously, the frequency
of this second resonance is exactly twice that of the first
resonance. We go up some more, only to find another
resonance, the third resonance or second partial which is
exactly three times the fundamental resonance frequency.
This harmonic. Series goes on and on with this same pattern.
Needless to say, if we moved the speaker to the opposite
end of the pipe, exactly the same harmonic series would
be developed. However, if the speaker were moved to the
exact middle of the pipe, the first resonance would not
SUBWOOFER
f1
The reason for harmonic selectivity is not
in magic numbers, or any other form of
audio voodoo. It’s more like simple physics,
otherwise known as the nature of things. A
play set swing can provide a good example for
this effect. As children, most of us learned to
“pump the swing” by coordinating our leg/
body action with the position, more accurately,
the phase of the swing’s position. It’s all in the
timing and it is pretty hard to explain, so we
teach by showing. Monkey see, monkey do. If we can get
the timing right, up we go, almost like magic.
The swing system is a resonant system and a pipe filled
with air is also a resonant system. Applying the right kind
of force at the right place and time can pump either up.
In a closed pipe, which has been stimulated into its first
resonance condition, we will find that the sound is very
loud at either end of the pipe and very quiet at the halfway
point, the middle. These loud areas are called sound
“pressure zones”; and, if the speaker is located in either of
these pressure zones, it efficiently couples to and can pump
up the resonant condition. Conversely, if it is
not so located, it can’t pump.
SOUND
METER
dB
f3
sound out. Nor would the third resonance, the fifth, and
so on. Odd numbered resonances cannot be stimulated in
a closed pipe when the speaker is located in the middle of
the pipe. From the middle of the pipe the speaker can only
stimulate half of the total number of resonances available
to the pipe, the even numbered resonances.
This position dependent selectivity does not stop with the
ends or middle of the pipe. Move the speaker to a position
one third from either end or, presto, only the
third, sixth, ninth, and so on harmonics can be
stimulated. Then we move to a position one
quarter of the pipe length from either end
and are not surprised to find only the fourth,
eighth, twelfth, and so on harmonics. And
next the fifth ... and so on.
The second harmonic of a closed pipe has
three pressure zones, one at either end and
one in the middle. If we located the speaker
in any three of these pressure zones, we can
stimulate the second harmonic. However, if
we locate the speaker in the middle pressure
zone, we cannot stimulate the first resonance
but we can still stimulate the second one. Once
the understanding of these variables has been
made clear, it becomes easy to expect what will
happen if a speaker is located in any particular
location.
It seems that no matter where a speaker might be located
in a closed pipe, one resonant harmonic series or another
will become stimulated. However, subwoofers are always
rolled off just below the beginning of the vocal range,
about 85 Hz. This means that the subwoofer cannot
stimulate resonances above the roll off frequency. Now, if
the first resonance is 25 Hz, the second will be 50 Hz, and
the third 75 Hz. The fourth resonance will be at 100 Hz.
100%
f0
+
-
0
100%
DISTANCE
distance
-
+
0
DISTANCE
f2
-
+
+
The concepts of subwoofer placement have by
now been well developed and now some practical
applications can be considered. Two things need to
be shown - the roll off frequency of the subwoofer
and the first resonance frequency of each pipe axis of
the room. Typical roll off is set at 85 Hz.
-
0
100%
No computer program is needed to properly position
the subwoofer in a room; a tape measure is your only
investment. Note also that the currently popular
“rule of thirds” placement formula is not consistent
with the understanding of an aresonant speaker
placement. This over publicized “rule of thirds” would
only be applicable if the subwoofer roll off was set so
that the speaker did not play the third harmonic.
f1
+
100%
non-resonant playback will be about one-quarter
of the ceiling height off the floor, one-quarter the
width of the room off the side walls, and one-quarter
the room length off the front or back wall. When
discussing speaker location, it is only the dimensions
to the center of the driver cone that count. The
location of the edge of the box really doesn’t matter.
DISTANCE
f1
+
-
+
-
0
Pressure zones for pipe resonances
The fourth resonance and all of those higher than it are
above the 85 Hz roll off frequency of the subwoofer. This
means that the speaker need only be positioned so that it
doesn’t stimulate the first, second, or third resonances. The
speaker has to be located somewhere, but not at either end,
not at the middle, and definitely not at the third waypoints.
+
The shortest dimension of a room is the floor to
ceiling distance. If this dimension is eight feet, the
first vertical resonance occurs at: 1130/2x8 = 70.6
Hz. The second at 141 Hz is well above roll off and
DISTANCE
f2
f0, f1, f2
100%
f1
f2
f0, f1, f2
f0
f1
f2
0
0
100%
0 35 50 67 100%
There is another factor that limits the remaining options
for speaker placement. The pressure zone is not a pinpointsized space; it spreads out. If the speaker is located near
enough to the center of the pressure zone, the resonance
can still be stimulated. A pressure zone effectively extends
about one quarter of the distance between adjacent pressure
zones and the speaker should not be located inside the
effective pressure zone space. For all practical purposes, the
speaker should be located 25 percent away from the end
of the pipe to best avoid stimulating any of its first three
harmonics. There is no location towards the middle of thepipe that suits a subwoofer position, as the pressure zones
there are overlapping.
A listening room can be approximated as if composed of
three intersecting pipes. These pipes would lie along the
three room axes -- front to back, side to side, and floor to
ceiling. This means that the subwoofer location for best,
Anti-mode speaker positions for combined 1st, 2nd and 3rd harmonic modes
f0, f1
f0, f1
f1
100%
+
0
0
100%
Anti-mode speaker positions for combined 1st and 2nd harmonic modes
f0
f0
100%
+
0
0
100%
Anti-mode speaker positions for only 1st harmonic mode resonance
can be ignored as well as any higher partials. The vertical
position range for aharmonic playback will be to locate the
subwoofer anywhere in the middle half of the room, keeping
it at least two feet away from either he floor or ceiling.
FREQUENCY (Hz)
200
150
d ft.
cancellation is being used a little more often these days,
particularly with industrial noise control applications.
Sound cancellation seems to possess a form of sci-fi lure
for some people. The idea of beaming “anti-sound” waves
to quiet freeway noise is one of the more popular of these
energy-out-of-water type schemes. To the literal
reader, words create reality. But to the engineer and
scientist, reality exists independently from words. Just
because someone can dream up a sentence that seems
to make sense doesn’t mean that it physically does
make sense.
Normally, sound cancellation applications remain
limited to the control of sound in pipes. For example,
100
if we take a closed pipe that contains a harmonic
condition and drill a hole into the pipe, we will get
f3 = 4f0
varied results, which depend on where the hole is
f2 = 3f0
located. For the first harmonic, with a pressure zone
f0 = 565 Hz
50
at either end and a cancel zone at the middle, we can
d
f1 = 2f0
drill a hole into the pressure zone at either end and
f0
kill the resonance. But, if we drill through the wall of
the cancel zone, there is absolutely no change in the
10
20
30
resonant condition. A hole in either pressure zone
Harmonic Series for Parallel Walls
allows pressure energy to leak out. But there is no
pressure energy in a cancel zone, so a hole that leaks
The next shortest distance in a room is the width, typically
pressure doesn’t affect anything.
about 15 feet. The first resonance for this is 1130/2x15 =
37.7 Hz. The second is twice that at 75.4 Hz and the third
This is not news -- the ancients knew about it. The flute
is three times that or 113.1 Hz. The second harmonic is
and clarinet type instruments use this open/closed hole
within the subwoofer range but not the third. The sub has
effect to select pipe resonances, heard by us as notes. Let’s
to be placed more than 25 percent away from the wall
consider what can happen if the closed pipe is engaged with
because of the first harmonic, but not in the central oneits second harmonic. There are three pressure zones and
eighth width of the room due to the second harmonic. The
two cancel zones. A hole could be drilled through the pipe
sub can be located anywhere between three-quarters and
wall at each cancel zone and not affect the existence of the
6-3/4 feet from the side wall. Lastly, the length of a room
resonance. Now we have made a closed pipe into an open
might easily be 21 feet long. The first resonance for this
pipe; and, if we blow air into one hole, it will come out the
would be 1130/2x21 = 26.9 Hz. The second is 53.8 Hz and
other hole. We have discovered a pathway to conduct air
the third is 80.7 Hz. The fourth at 107.6 Hz md above are
through a pipe filled with sound without having any of the
all well above the roll off frequency and can be ignored. For sound leak out.
the length of the room, the sub position should be onequarter of the room length or five feet off either end wall.
With industrial sound canceling, the tonal sounds of a
blower that moves air in a closed duct can be cancelled at
So, a room 8 feet by 15 feet by 20 feet will have the
an air outlet. One can use either this standing wave pipe
smoothest bass if the piston of the subwoofer is located two process or a speaker/microphone/computer system to create
to six feet off the floor, between 3-3/4 and 6-3/4 feet off
this same sound canceling effect at the opening of the pipe.
the side walls, and five feet off the end wall. This is true as
Although the sound at the opening can be cancelled, the
far as avoiding strong coupling of the speaker to the room
sound elsewhere in the pipe is very loud. If two forces are
modes, but there is more than modes to worry about as far
applied equal and opposite, there is no force imbalance,
as speaker smoothness is concerned.
hence no movement. That doesn’t, however, mean there is
no stress on the material. There is twice as much stress to
the material than if only one force was applied.
SOUND CANCELLATION
Incidentally, these silent areas located between the pressure
So it is with sound. If two sounds are applied equal and
zones deserve a little attention as well. They are “cancel
opposite, there is no sound at some point, but that doesn’t
zones” because sound is cancelled at these locations. Sound
FREQUENCY (Hz)
200
wall, sound from the speaker expands out from
the speaker, impacts the wall, and rebounds back
toward the speaker. At some certain frequency,
the timing of the rebound wave will be exactly
one-half a period of the tone.
d ft.
150
100
f1 = 85 Hz crossover
f3 = 4f0
f2 = 3f0
50
f1 = 2f0
f0
0
d ft.
10
8 ft
Room
Height
For 1st
Harmonic
Only
f0
0
2
For 1st
and 2nd
Harmonic
Only
f0 f1
Safe Region
4
Height
20
21 ft
Room
Length
15 ft
Room
Width
Safe
6
8
0
3 3/4 5
For 1st, 2nd
and 3rd
Harmonic
Only
f0 f1 f2
Safe
Safe
Width
10 11 1/415
30
0
5
Safe
Length
Anti-mode Subwoofer Positioning
mean there is no stress on the material. There is, in fact,
twice as much stress in the material than if only one
sound had been applied. If we move away from the point
where there is no sound, we’ll find twice as much sound
everywhere else. That’s the point. Sound cancellation doesn’t
mean sound energy cancellation. The energy is still there.
In fact, it has become twice as strong. Just because we can’t
hear it at one location only means we will hear it twice as
loud at another.
This brings to mind freeway noise cancellation and many
other sound cancellation schemes. The real rule for sound
cancellation engineering is that if we arrange to not hear
sound in one place, then to someone else it has become
twice as loud. We always have to watch out where that
loud zone has become located. If it is onto our neighbor’s
property, we might get sued. Sound is energy. We also know
that energy plus energy equals more energy, not less. We
can steer sound around somewhat by adding more sound,
but we can’t simply erase sound with “anti-sound” waves.
Except, of course, in the imaginations of those who read
and write sci-fi stories.
Under certain conditions, a speaker can cancel its own
sound. Consider what happens when a positive part of a
sound wave meets a negative part of the same sound wave.
We have sound cancellation. When a speaker is near a
16
The period of a wave is exactly the time it takes
for one cycle to occur. Middle C of the musical
scale has the frequency of 256 Hz. That means
the period takes 1/256 second to occur. A half
period for 256 Hz would be 1/512 second. If
sound could go from the speaker to a reflecting
surface and back to the speaker in 1/512 second,
the positive of the reflected wave would mix
with the half-period-later negative of the wave
at the speaker face and there would occur sound
cancellation. The round trip distance covered
would have to be 1130xl/512 =2.2 feet. A wall
located 1.1 feet away from the speaker could
reflect sound back to the speaker and create this
self-cancellation effect.
A single bounce is bad enough, sometimes
creating a three to four dB reduction speaker
21
output at and around the self- cancel frequency.
But to have two walls reflecting waves back to
the speaker at the same time is nearly intolerable.
Whenever we have a speaker near a corner,
there results three wall reflections, three corner reflections,
and one tricorner reflection. In order to keep the selfcance11ing effect to a minimum, every one of these round
trip distances should be as different from one another as
possible. The most obvious setup is to keep the distances the
three walls as different as possible.
ANTI-MODE, ANTI-CANCEL SUB SETUP
For our example room, the distance off the end wall had
to be five feet. The distance off the side wall could also
have been set up at five feet. We could have had two, tenfoot round trip waves impacting the speaker with a time
delay of 10/1130 = 1/113 second. This would create the
self-cancel effect to occur for a frequency whose period
is twice that time or 2 x 1/113 = 1/56 second. This would
be the frequency of 56 Hz which is well below the 85 Hz
roll off frequency of the subwoofer. A better choice for the
subwoofer position might be 2-1/5 feet up, 3-3/4 feet out
from the side wall, and five feet off the end wall.
A graph can be used to help with this latest decision
whenever there is a range of speaker positions available.
For any axis in which the third harmonic is engaged, the
speaker position is fixed at 25 percent. There is flexibility in
speaker position for any axis that only engages the first or
second harmonic. Outside of keeping the three dimensions
other, so the pair of values needs to stay away from the
“equal” line on the graph. There is another consideration.
Subwoofers sound weaker when played out in the open and
stronger when played near sound reflecting surfaces. This
wall or floor loading effect is a form of horn loading which
always makes low-frequency speakers more efficient. In
addition, we elected to keep the sub as close to the side wall
as possible, out of t, he middle of the room. The coordinates
of 2 to 2-1/2 foot height and 3-3/4 off the wall meets all of
our requirements.
Choose C to be the
longest dimension
A and B are less
Than C
12
11
=B
Li
ne
10
A
8
ARCs of C
12
3
11
2
10
1
9
1
2
3
4
5
6
7
8
RANGE OF A (ft)
9
10
11
12
Anti Self-Cancelling Subwoofer Position
as different, as far apart as possible, there is one other detail.
We need to keep the bicorner bounces from overlapping
the wall bounces. The only opportunity for trouble here
is if the distance to the corner formed by the two shorter
dimensions equals the third longer dimension.
To use the timing graph provided here, you darken the
arcs whose radius equals the fixed, third harmonic, 25
percent dimensions. Then you darken the straight lines that
correspond to the ranges available in speaker placement for
the other, lower harmonic axis.
For our example, the room length engaged the third
harmonic and the distance off the back wall became fixed
at five feet. An arc with a five-foot radius is darkened on
the graph. The width and height of the room were not long
enough to engage the third harmonic. The corresponding
ranges for speaker placement are plotted on the graph, one
axis for each graph axis. It doesn’t matter which room axis
goes on which graph axis. Here, the side wall was placed
on the vertical axis and the height range was placed on the
horizontal axis.
The result is a rectangle with an arc passing through the
lower corner. The distance off the floor and side wall can
take any pair of values inside the rectangle, except those
on or close to the arc. They also shouldn’t be equal to each
Li
4
=B
5
ne
Choose C to be the
longest dimension
A and B are less
Than C
6
A
7
RANGE OF B (ft)
RANGE OF B (ft)
9
8
7
ARCs of C
6
5
OK
4
AVOID DARKENED LINES
OK
3
2
1
1
2
3
4
5
6
7
8
RANGE OF A (ft)
9
10
11
12
C = 5 ft length
A = 2 to 4 ft height, choose 2 to 2-1/2 ft
B = 3-3/4 to 5 ft width, choose 3-3/4 ft
Combined Anti-Mode and Anti Self-Cancelling Subwoofer Position
Subwoofer setup is usually accomplished by listening to
music, inching the box around the room, and trying to find
the smoothest location. This sport is more like fishing than
anything else, to be specific, bass fishing. What we have
tried to do here is debunk some of the practices of audio
voodoo, reduce your dependency on the audio personality
or guru, limit your searching for magic numbers, and the
purchase of guru computer programs. We have tried to
replace them with simple graphs, the otherwise desperate
and often misdirected groping for that elusive, but real,
subwoofer sweet spot. 
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