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.
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
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 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
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 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.
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. 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.
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There is another factor that limits the remaining
options for speaker placement. The pressure zone is not a
pinpoint-sized 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 the-pipe 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,
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.
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
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
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 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.
The next shortest distance in a room is the
width, typically 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 is three times that or 113.1 Hz. The second
harmonic is within the subwoofer range but not the third.
The sub has to be placed more than 25 percent away from the
wall because of the first harmonic, but not in the central
one-eighth width of the room due to the second harmonic. The
sub can be located anywhere between three-quarters and 6-3/4
feet from the side wall. Lastly, the length of a room might
easily be 21 feet long. The first resonance for this would
be 1130/2x21 = 26.9 Hz. The second is 53.8 Hz and the third
is 80.7 Hz. The fourth at 107.6 Hz md above are all well above
the roll off frequency and can be ignored. For the length
of the room, the sub position should be one-quarter of the
room length or five feet off either end wall.
So, a room 8 feet by 15 feet by 20 feet will
have the smoothest bass if the piston of the subwoofer is
located two to six feet off the floor, between 3-3/4 and 6-3/4
feet off the side walls, and five feet off the end wall. This
is true as far as avoiding strong coupling of the speaker
to the room modes, but there is more than modes to worry about
as far as speaker smoothness is concerned.
Incidentally, these silent areas located between
the pressure zones deserve a little attention as well. They
are "cancel zones" because sound is cancelled at
these locations. Sound 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, if
we take a closed pipe that contains a harmonic condition and
drill a hole into the pipe, we will get varied results, which
depend on where the hole is located. For the first harmonic,
with a pressure zone at either end and a cancel zone at the
middle, we can drill a hole into the pressure zone at either
end and kill the resonance. But, if we drill through the wall
of the cancel zone, there is absolutely no change in the resonant
condition. A hole in either pressure zone allows pressure
energy to leak out. But there is no pressure energy in a cancel
zone, so a hole that leaks pressure doesn't affect anything.
This is not news -- the ancients knew about
it. The flute and clarinet type instruments use this open/closed
hole effect to select pipe resonances, heard by us as notes.
Let's consider what can happen if the closed pipe is engaged
with its second harmonic. There are three pressure zones and
two cancel zones. A hole could be drilled through the pipe
wall at each cancel zone and not affect the existence of the
resonance. Now we have made a closed pipe into an open pipe;
and, if we blow air into one hole, it will come out the other
hole. We have discovered a pathway to conduct air through
a pipe filled with sound without having any of the sound leak
With industrial sound canceling, the tonal sounds
of a blower that moves air in a closed duct can be cancelled
at an air outlet. One can use either this standing wave pipe
process or a speaker/microphone/computer system to create
this same sound canceling effect at the opening of the pipe.
Although the sound at the opening can be cancelled, the sound
elsewhere in the pipe is very loud. If two forces are applied
equal and opposite, there is no force imbalance, 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.
So it is with sound. If two sounds are applied
equal and opposite, there is no sound at some point, but that
doesn't 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
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
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 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.
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 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 self-cance11ing 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
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,
ten-foot 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 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 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.
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.