As it turns out, our ears are sensitive to air
pressure, not air velocity (or displacement), so the
sound NULLS are actually equivalent to the spots on
the string with MAXIMUM displacement, and the sound
PEAKS are where the motion NULLS are on the string.
In other words, for the second harmonic, the motion
at the ends and at the middle of the string, so the
equivalent sound peaks would be at the walls and in
the middle of the room.
The sound peak locations
coincide with the best woofer locations for optimum
resonance excitation, for example at the walls.
Bohdan Raczynski presented some very nice charts in
his recent article in audioXpress that will help you
see what a standing wave room resonance looks like.
Interestingly, the resonance between two walls in a
typical room supports not just a single frequency
for each harmonic, but a band of frequencies,
usually about one third octave wide. Also of interest,
at higher harmonics, and higher frequencies, the peaks
and nulls will be spaced closer and closer together.
Other factors come into play as well, such as
tangential and oblique angle resonances.
This is explained by F. Alton Everest
in a very easy to understand way and his
writings on acoustics are highly recommended.
I would like to point out that while Everest uses
linear frequency response charts to explain room
resonances, logarithmic charts would better
indicate the closer resonance spacing at higher
If loud boomy bass is what you are after, then the
standing wave resonances are just what the doctor
ordered, as the spatial reinforcement greatly
increases bass volume at the peak locations,
and you can maximize the bass peaks by placing
the subwoofer in the corner. Of course this also
requires careful placement of your listening
chair to avoid as many null spots as possible.
However, if you are a certifiable audiophile
and you find uneven bass response unacceptable,
then read on.
The Standing Wave Paradox
Placing a subwoofer in the corner of a shoe box
shaped room excites the 3 fundamental standing
wave room resonances, boosting the bass at those
3 frequencies, as well as the higher harmonics,
at least at certain locations across the room.
Each resonance has a bandwidth of about one third
octave, so if they are closely spaced, as the higher
harmonics are, then they will overlap, considerably
smoothing out the peaks. However, the first 3 resonances
are usually too close together, or too far apart, and
that, along with the inevitable drop off below the
lowest resonance, produces a very uneven low frequency
The uneven low frequency response is due not only to
the empty frequencies between widely spaced resonances
and the compounding of closely spaced resonances,
but also because of the null spots (as described above)
inherent in standing
waves. Nevertheless, since all speakers roll off the
low frequencies, the room resonances reinforce at least
some of those frequencies, producing what is perceived
as better bass (hence the paradox).
Surprisingly, the uneven response is difficult to hear
because if some bass notes are loud and others are soft,
one assumes that the musician played them that way.
The Bose Wave radio is astounding to most people because
bass frequencies around 80 Hz are reproduced quite
loudly, but what they don't know is that there is a
precipitous drop-off in bass response below 80 Hz.
They simply don't notice the absense of very low notes.
Also, the human ear is less sensitive to variations in
the level of low frequencies versus higher frequencies.
Another factor to consider is frequency shifting during
reverberant decay caused by the room resonances. As
stated before, the room resonance actually supports
a band of frequencies about one third octave wide. This
can be thought of as the Q of the resonance and the
bandwidth is affected by acoustical absorption. If a
note is played at a frequency 1 Hz greater than the
peak room resonance frequency, it will still be
by the room resonance, but as soon as the note stops
playing, the sound field decays via reverberation and
the frequency is pulled 1 Hz lower by the room
resonance. Thus the reverberant decay shifts, or
de-tunes, musical notes.
The Near Field
Now if the room resonances could somehow be eliminated,
then we could compensate for the weakened bass by using
large woofers and large amplifiers! Alas, the room
resonances are part of the laws of physics and cannot
be completely eliminated (not in this universe).
Many people have the mistaken impression that splaying
the walls will eliminate room resonances. Not so! That
will only change the Q, which results in a wider
resonance bandwidth, albeit with a lower central peak.
Some suggest that bass traps are the answer, but they
have no effect on the null spots inherent in standing
waves, and, since absorption is proportional to surface
area, a bass trap would have to be quite large to
significantly reduce the peaks. However, we might be
able to overwhelm the room resonances with brute
force by listening in the near field of the woofer.
Many sound engineers have tried the obvious solution of
placing the subwoofer very close to the listener's head,
(within the near field). This works but is not aesthetically
pleasing and not very practical. Our collective spouses
I am sure would furrow their brows in disgust here as they
picture large subwoofers hung from the ceiling in the
middle of their family rooms.
A better solution is to place the subwoofer very close to
the listener's body (and down low) in a coffee table!
After all, the lowest frequencies are more felt than heard.
I am not at all sure that I can hear 20 cycles per second,
but I can sure feel the vibrations and I can see my pants
leg flapping when I stand in front of a massive subwoofer.
Because the coffee table is typically in the center of the
room, the 2 lowest room resonances are not excited by a woofer
placed at this location (right in the nulls of the length
and width of the room) while the floor/ceiling resonance
would still be excited (as the woofer is close to the floor).
Unfortunately this position will effectively raise the
inevitable low frequency roll off inherent in all woofer
systems by not exciting the two lowest room resonances,
and the accompanying bass reinforcement. Nonetheless, here
is our chance to compensate with large woofers and large
amplifiers (you knew I was wanting to do that anyway).
So the subwoofer will need a large bass boost to compensate at
the lowest frequencies, and while we are at it, we could even
go lower, below 20 Hz, down into the nether reaches, which
may not be heard, but they can be felt. This requires a high
output subwoofer that can handle a lot of power down ultra low,
which could cause problems with vented subwoofers. Although
the subject of sealed versus vented woofer boxes is quite
controversial, I thought I might put my own two cents in
and stir the pot a bit anyway.
The Cheater Tube
Most commercially available subwoofers
use vented enclosures with port tubes, what
I call "cheater tubes". The sole reason for
venting a speaker enclosure is to boost a small
portion of its low bass response. From a physics
standpoint, the boost is a resonant peak.
Vented enclosures are nothing but Helmholtz
resonators. Of course, Helmholtz resonators can
be musical, as evidenced by the acoustic guitar,
but they may not be accurate. You may lose
something in the trade off for the extra boost,
and that is the ability to punch out fast transient
Martin Colloms disagrees, saying that de-tuned,
over-damped bass reflex alignments sound as quick
and agile as you could wish for. I must admit, it
is difficult to hear any real difference between
well engineered sealed and vented boxes. And Collums
makes a valid point, that "Unless price is no object,
every designer must fix on a realistic target for an
affordable bass driver...". So if you can match the
system bass Q with your room by utilizing a tuned
(vented) enclosure, thus producing a flat
low frequency response, then why not? Ah, but you
could also opt for a more expensive driver in a
sealed box, along with equalization, which would
achieve similar results without the driver unloading
below the box cut off.
Bass guitar players in general do not always agree
that sealed boxes are best, but if you watch some
music videos you might see that the most popular
bass amplifier for professionals is an Ampeg with
eight 10" drivers in a sealed enclosure.
Think of a bass drum: a large membrane moving
outward as the drum beater hits it. This
produces a sharp transient pressure pulse.
Can you see a Helmholtz resonator reproducing
a bass drum accurately? It seems to do a pretty
good job, but I am not convinced, and I must
recommend sealed boxes.
Central room placement of subwoofers can help
minimize the problems with standing waves,
although it will not completely eliminate them.
For practicality, the woofer can be mounted in a
coffee table, an end table, or a raised platform
under the seating. For multiple listeners, use
several woofers. If everyone is within three or
four feet of a woofer, the near field may not
dominate, but it will certainly mitigate the
room resonances and help smooth things out.
To sum up my recipe for cafe' latte with bottom
1. Drag that coffee table sitting in your family
room out to the workshop.
2. Mount a sealed subwoofer box underneath it.
3. Put one or, even better, two woofers in it.
4. Then drag it back into the family room.
5. Hook it up to a powerful amp with an
equalizer used for low frequency boosting.
Sit down and plop your legs onto the coffee table
(maybe with a cafe' latte), and prepare for the
most beautiful, tight, punchy bass you have ever
heard, and get the added thrill of the table
vibrations on your legs!
References and related reading
1. Everest, F. Alton, "The Master Handbook of Acoustics",
Second Edition, Tab Books, 1989
2. Sherwin, James S., "Certified Bass for the Certifiable",
Audio magazine, January, 1990
3. Greiner, R. A., "The Lowdown on Subwoofers",
Audio magazine, August, 1993
4. Raczynski, Bohdan, "Subwoofer Placement in
Nonrectangular Rooms", audioXpress magazine,
5. Colloms, Martin, "Bass and the Room",
audioXpress magazine, October, 2002