EXPERIMENTS
WITH TAPERED PIPES
BY DAVID B.
WEEMS
Speaker
Builder 2/87
If
you run into trouble, use the line as a dog house and design either a closed box
or reflex enclosure for your woofer. For champions of transmission lines who are
disturbed by those frivolous words, here is a peace pipe. Or, to be more
specific, a tapered pipe, like the labyrinth, the tapered pipe makes use of
quarter-wave loading. Unlike the labyrinth, the driver is placed some distance
from the end of the pipe.
Tapered
pipes were popular in Britain years ago, but except for a small amount of
damping material behind the driver, they were bare-walled. In fact, the
de-signer of one 1960s pipe enclosure said damping material in the pipe would
spoil the performance?
The
stuffed tapered pipe is an alter-native to those designs. Voigt was the first to
use the "stopped" pipe, which is similar in action to an organ pipe.
In 1949, Ralph West developed the Decca comer speaker. Both systems had relatively
small drivers.
THEORY.
The principle behind the pipe is
shown in 
.
The sketch in Fig. la shows relative pressure and velocity in a closed pipe at
resonance. Pres-sure points occur at nodes, high velocity points at loops. If
you mount a speaker at the closed end of the pipe 
,
it will be loaded by the high pressure at that end, greatly increasing
efficiency. Two problems hinder this arrangement. First, the pipe's fundamental
frequency is so strongly favored, low frequency performance can sound like
one-note bass. Another disadvantage is odd harmonics production. The first
harmonic is the most serious, occurring at three times the fundamental's
frequency 
.
To connect it, place the driver at one-third the distance from the pipe's
stopped end 
.
At that point, the pressure will become somewhat lower than at the closed end,
but still high enough to provide good loading at the fundamental. At the first
harmonic frequency, the drive point occurs at a loop instead of a node, and
output will be reduced.
Voigt
tapered the pipe to reduce the one-note effect and to spread the resonance over
a band of frequencies 
.
In later versions, the throat area was reduced to zero for smoother response and
the driver installed at the midpoint of the line 
.
More about that later,
The
English builders of a generation ago designed their pipes for a single-cone
8" driver. Total cost of a driver and enclosure for one popular model was
about L5, or at the rate of exchange in those days, about $14. The speaker fired
upward at the rear wall so the highs dispersed around the room at a subdued
level. In an attempt to restore the lost Overtones, listeners applied treble
boost. Some thought the arrangement's high frequency reproduction was inadequate.
One asked, "Who put the blanket over the cymbals?'' The problem of highs
lost in the reflection process was com-pounded by the voice coil inductance in
the single-cone speaker.
British
builders almost always used 3/8" plywood to construct their pipes. Thick
walls were unnecessary, they said, be-cause their enclosures were stiffest at
the point of greatest pressure. Some suggested using a slight degree of wall
flexure because it would increase acoustic coupling near the fundamental
frequency and damp air column resonances. Such statements, however, made pipe
design seem more like magic or luck than science. Everyone seemed to agree on
the necessity for tight joints. One author said a 1/14" gap in the driver
mounting would reduce the output at 35Hz by a factor of four.
About
five years ago, after having ignored pipes because of their resemblance to the
infamous "air coupler" of early US hi-fi days, I built a pipe for a
dual cone 6" x 9" car driver featuring a 10 oz. magnet and foam
suspension. The $7 speaker had an amazing bass response in the pipe, but it also
had some obvious peaks, the worst of which occurred at 95Hz and 220 Hz. The
220Hz peak was probably caused by the second harmonic, which arises at five
times the pipe's fundamental frequency. A driver with a heavier magnet gave much
smoother response in the 95Hz region, but showed no improvement in the higher
resonance. I considered attacking the 220Hz problem with a Helmholtz resonator
designed to absorb energy at that frequency, but other endeavors interrupted my
plan.
Recently,
while digging through abandoned projects in my shop, I discovered the old pipes
and wondered how the principle would work with better drivers and with damping
material in the line. To save time and material, I decided to make a miniature
pipe for a 4" woofer, the Radio Shack #40-1022. I knew 1 could later apply
my experience to larger systems, but first, I had to design the enclosure.
PIPE
DESIGN. To design a
tapered pipe system, you must choose appropriate dimensions for pipe length,
throat and mouth area, and drive point. The fundamental frequency is almost
totally set by one parameter—the total line length. The formula given for a
labyrinth or pipe length is:
where
l is the length of
pipe, Ñ
is the speed of sound in air, f
is the pipe's fundamental frequency, and r
is the pipe's radius or equivalent radius. This formula, however, produces a
longer than necessary pipe length. Opposing factors are at work here because
tapering the pipe tends to raise the fundamental frequency, but folding and
choking the mouth at the port lowers it. A bare pipe will usually perform as
though it were about 30% longer than its measured length, and when you add
damping material, it can seem even longer. As a rough estimate, expect the
required length to be about 65% of the calculated length. The pipe's cross
sectional area will very from near zero to zero, to a maximum of about 2.5 times
that of the driver's effective piston area. The pipe area should be about equal
to the cone's 'area at the drive point, but ±20% is acceptable. The port area
is typically equal to the cone area, or about 0.4 that of the maximum area.
Taper
rate is one aspect of the tapered pipe that varies with driver size. A 4"
woofer requires less than a third of the pipe area needed by a 9" driver.
If a pipe for a 4" woofer WAS designed to have the same taper rate as that
for the larger speaker, its total length would be 20". Even if it "acted"
like a 30" pipe, the fundamental frequency would be about 100Hz. That is
too high, even for a 4" woofer. You can neglect taper rate as a design
factor for small drivers, but a low taper rate may demand more stuffing. If you
wish to experiment with bare pipes, use an 8" driver.
I
made a quick guess at the proper length by setting the enclosure height at 3',
which placed the drivers close to ear level. Unlike the British designs, I
decided to mount the drivers in the conventional way, on the enclosure's front.
Tî
complement the Radio Shack woofer, I used a Radio Shack 3/4" tweeter (#40-1376).
The crossover for this simple sys-tem is nothing more than the high-pass
capacitor that comes with the tweeter, An L-pad adjusted the tweeter level to
match the woofer's rather inefficient level, Unlike conventional systems,
how-ever, I placed the tweeter below the woofer, a move which made more of an
effect that I expected.
After
drawing a rough design sketch, I noticed the drive point would be some-what
short of the mid-point from the throat to the mouth. You can only estimate the
pipe length; the true acoustical length may be different from that estimate. The
formula for optimum drive point distance from the throat is:
where
d
is the drive point distance from the throat,
l
is the pipe length,
At
is the throat's cross-sectional area, and
Am
is the mouth's cross-sectional area.
The
mouth is defined as the port area. The maximum area is that of the section just
before the port. As you can see from the above formula, d can vary from
one-third where the area of the throat is equal to that of the mouth, to
one-half where the pipe tapers to zero throat area. Again, unless you use a
straight pipe, you can only estimate the drive point's optimum location.
After
doing some arithmetic, I found that by starting the throat at a point 6"
above the mouth and using an initial area of 2" the pipe would approximate
the formula for the drive point. The maximum area would be 24", 2 which
would be choked to 9.25"2 at the mouth 
.
My
final decision concerned the building material's type and thickness. For such a
small pipe, Vi" plywood seemed adequate. But, because 1 had a supply of Óç"
material and because using 1/4" plywood seemed like heresy, I opted for the
thicker walls. If you wish to try a pipe system without damping material, try a
thinner material. Here is a quick summary of my construction methods, should you
choose to follow them:
1.Cut
out the parts and prepare to attach the partition to the sides with glue and
nails.
2.To
place the partition precisely, first set it in place on the inner surface of
each side and mark an outline around it. Then, drill guide holes for
nails down the center line of that outline.
3.After
reversing the side, drive a nail into the partition through a hole at each end
of the line of holes, just far enough to temporarily hold the partition.
4.Remove
the side and spread glue on the matching surfaces. When you do the final nailing,
the pre-nailed holes will ensure the parts don't slip out of place as you drive
down the other nails.
5.After
the glue sets, caulk the joints and install the front and back panels with
silicone rubber sealer and nails. The sealer prevents air leaks on the joints
you can't reach during internal caulking.
6.To
make the top and bottom removable, install cleats inside the pipe to receive
screws.
7.Gasket
any removable parts with foam weather stripping or other sealer.
TEST
RESULTS.
In 
,
the impedance curve of the 4" woofer in a bare pipe looks similar to the
same model woofer in a reflex. As 1 discovered later, the woofers behaved
significantly differently in some tests. Some writers call the impedance peaks
in tapered pipes "resonances," but Bal dock claims the term resonance
isn't appropriate because a reactive component is present. When I ran an
oscilloscope test on bare pipes, the ellipse closed to a straight line at the
peaks and valleys of the impedance curves. After I added damping material, the
ellipses remained open. The lower peak was likely produced by cone loading from
the air in the pipe, while the upper one was likely caused by enclosed air
stiffness behind the cone.
If
you analyze the curves for the woofer in free air and in the pipe, you'll see
the lower peak in the pipe occurs at about 37.5Hz, whereas in free air, the
single peak is at 53Hz or 1.41 times that of the pipe. This ratio tells you the
air load mass in the pipe is approximately equal to the mass of the cone itself.
On
listening tests, the bare pipe produced a hollow, ringing sound, particularly on
male voices. When 1 conducted a rough frequency test, significant peaks and
valleys occurred in the region below 500Hz. So, I lined the pipe area behind the
woofer with a 1" layer of acoustical fiberglass on the sides, back, and
under the top of the enclosure. I then noticed some improvement in the listening
tests, and a considerable difference in the 200-500 Hz frequency response test.
I
added loose wads of polyester batting to the pipe, placing 1/4 oz. in the throat,
filling the space behind the woofer, and then gradually increasing the amount in
the large section of the pipe. With each addition, I monitored the progress with
impedance and listening tests.
You
can stuff the pipe until the impedance curve shows a single peak, like that of a
closed box speaker. The peak frequency, however, will be lower in the pipe than
in a closed box. In my case, the single peak occurred at 60Hz. After stuffing
and restuffing, I arrived at what seemed to be a good compromise between under
and overstuffing: a total of 3 1/2 oz. of batting. My pipes internal volume is
0.5 ft, not including the volume occupied by drivers, partitions and cleats.
Therefore, the rate of fill is probably about 8 oz. per cubic foot. The
impedance curve for that condition is shown in 
,
After the final stuffing.. I compared the pipe speaker performance with drivers
of the same model in a closed box and a reflex enclosure. The closed box was
clearly superior to the other two in one respect. With a total volume of only
140 in? it occupied the least amount of room space. The reflex had a volume of
334 in3 and was tuned to 60Hz.
I
then conducted near field microphone tests, which showed the three systems
performed similarly in the 80-100 Íã range. Listening trials, however, told me a different story about bass
range perception. The closed box speaker was clearly more limited in low
frequency response. (Near field technique doesn't register the output of ports
removed some distance from the woofer.)When listeners compared the reflex with
the pipe, most initially thought the reflex had a bit more bass than the pipe.
After longer and more careful listening, however, their conviction waned
be-cause the pipe speaker performed better on the lowest frequencies. Frequency
response tests confirmed this conclusion. The reflex had slightly more output in
the 70-100Hz range, while the pipe was clearly superior below 60Hz.
An
interesting way to compare speaker performance is to feed a 20Hz square wave to
the speakers and observe the patterns produced on an oscilloscope. This simple
test setup is shown in 
.
The
pattern will alter according to the resonance frequency of your speaker and its
degree of damping. The lower the resonance frequency, the fewer the number of
oscillations that will show on the trace. The oscillations' amplitude, however,
will also vary. I used this method to test four identical woofer models: one in
free air, then again in free air with a blob of modeling clay [whose mass was
equal to the cone's mass) stuck to the cone; and three other woofers in the
three types of enclosures I mentioned earlier, Before you examine my various
pat-tern photographs, be aware my oscilloscope exhibits considerable droop when
it is fed a 20Hz square wave. That droop may be caused by a too small coupling
capacitor, but whatever the reason, it is constant. If your instrument's
controls are unchanged during the tests of various speakers, consider the
comparisons valid.
The
pattern in 
and 
indicate, as expected, the driver cone moves farther in free air than when
installed in an enclosure. Little change occurred in the two free air tests,
except for the lower resonance frequency in the one 1 con-ducted after 1 added
mass to the cone. The trace for the closed box woofer 
shows decreasing oscillation amplitude, but the reflex's trace 
indicates little amplitude change. The pipe speaker 
shows a single pulse movement, about half a sine wave, then very little hangover.
I took
after I added damping material to the pipe, but the woofer in the bare pipe's
trace was almost identical except for a small deflection at tail's end.
To
test the woofers in the three kinds of enclosures, I fed each a 55Hz sine wave
signal from an audio generator through a tone burst generator and an amplifier 
.
In fairness to the reflex speaker, it had no more over-shoot than the pipe
speaker at frequencies above 80Hz, and only slightly more at 70Hz. The pipe
speaker was at least equal to the others at all frequencies, except at 180Hz
where it showed a bit more hangover.
After
reviewing the experiments with the A" woofer, I decided the tapered pipe
system deserved further testing with a larger woofer. With that in mind, I began
to work on a pipe designed around the Peerless TP165F.
SECOND
DESIGN.
Peerless lists the TP165F's effective piston area at 12.45 x 10-3 square meters,
or about 20 in. I made the internal dimensions 6 1/2" x 8", putting
the pipe's theoretical maximum area at 52 in. By using 1/2" material, the
minimums outside dimensions are 7 1/2" x 9." Because pipes are so
compact, they occupy very little floor space and yet do not require stands. On
most floor surfaces, however, you may wish to enlarge the bottom board to add
stability to the tower. Extend the board beyond the en-closure's front to
counter gravity's pull on the front-mounted drivers.
For
easy pipe construction, place the tweeter below the woofer, as shown in
.
Ironically, a tall enclosure, with the tweeter at car level, should have the
tweeter above the woofer. When I planned my design, I overlooked one effect of
placing the tweeter below the woofer. Although, as you will see, I later solved
the problem to my satisfaction, consider placing the tweeter outside the pipe,
on top of the tower. This decision will depend on your personal preferences as
you weigh performance against appearance and construction ease.
I
increased the larger pipe's length in an attempt to extend the bass range.
Except for loading the driver to a lower frequency, however, I doubt whether it
made much improvement. Again, I had to do some arithmetic to estimate the
optimum drive point. My figures indicated I should begin the throat about
6" above the mouth, with an initial area of slightly under 5 in. You can do
this by gluing à
3/4" strip across the front of the partition, at the point where it will
make con-tact with the rear of the front panel. I ran the usual tests with
various amounts of damping material and settled on a lighter optimum packing
density than I had used on the smaller pipe. The final amount was a square foot
of 1" fiberglass on the surfaces behind the woofer, an ounce of polyester
batting in the throat, and 5 oz. in the remainder of the pipe. Although the
density was lower than for the smaller pipe, the impedance curve was similar 
.The
larger system's bass performance was promising from the start, but something
about the sound wasn't right. At first, I was tempted to blame the tweeter, a
German-made MBM25S I obtained from McGee Radio, but later tests proved me wrong.
As it turned out, I had several problems, some of which involved the crossover
network.
EVOLUTION
OF A CROSSOVER. My first
crossover network choice was a second-order APC (all-pass crossover) described
by Bullock/ My enclosure design had placed the woofer-tweeter center-to-center
distance at 5 1/4", so I planned to put the crossover frequency below the
point where that distance was equal to a wavelength, or under 2.6kHz. With that
in mind, I chose a crossover frequency of 2.2kHz.
At
first, the system sounded loud—an ominous symptom. The problem turned out to
be a rise in output between 800Hz-1.8kHz, so I made a filter to smooth the
woofer's response in that range. The filter transformed the sound, helping the
speaker to wear well in long listening sessions. But one abnormality remained:
the vertical response was not uniform when I stood in the sound field and then
sat down. Even people who liked the anomaly mentioned it. ''It sounds sweeter
when you sit down," one person remarked.
When
I checked the frequency response at various elevations, I found a null in the
2.6kHz region at ear level while listening from across the room. I realized that
when I placed the tweeter below the woofer, it tipped the axis up-ward 
.
At standing ear level, the null was replaced by a smooth response. Surely, the
crossover network was involved, but the problem was caused by a combination of
factors that made the woofer's realized roll off rate different than that
predicted by the second-order filter.
I
measured each driver's response, substituting a resistor in the crossover
network for the muted driver, In the 2-3kHz band, the woofer's and tweeter's
output were equal.
I
had several solutions to choose from. An obvious one was to use a higher order
crossover. Having already made up a set of crossover networks, I tried to
salvage them with notch filters, tuned to 3kHz, in the woofer circuit. The first
filter, made with a 0.25mH coil and an 11mF capacitor, did not provide enough
cut. So, I made up another set, using 1mH coils and 3mF capacitors. They solved
the problem, but I wondered whether a simpler method could give me an acceptable
performance.
Throughout
the tests, I tried nearly every option, including reversed driver polarities.
Finally, a single, larger-than-normal inductance in the woofer circuit offered
promise. So, I reduced the crossover frequency to 2kHz and made up a third-order
filter for the tweeter. When you. consider the woofer's impedance with the Zobel
in its circuit is about 6
Om,
the calculated value for a single inductance is about 0.48mH. Instead of
deriving the value from calculations, I set up the speaker outdoors on a quiet
day and ran microphone tests with various values of inductance. The one that
produced the flattest curve turned out to be l mH, more than twice the indicated
value, This, however, is not a rare conclusion.
RESONANT PEAK
FILTERS. The MBM25S gave a
good performance, but I found it had one peculiar trait. Even with a third-order
network, a consider-able output from the tweeter occurred at 1.1kHz—its
resonance frequency. The obvious fix seemed to be a resonant peak filter. The
Loudspeaker Design Cookbook (LDC) lists the following formula for resonant peak
filters;
Ñ
= 1/15.2 f
L =
1/39.48 f2C
R
= approximate rated driver impedance.
Filters
produced by this formula are effective in removing the peak, but they can also
effect a lower than desired impedance in the octave above resonance. In those
cases, you need a higher Q. A formula that usually works well is:
Ñ
= l/50f
You
can compute the other values from the LDC formulas. If possible, choose the
final values by experimenting. I used the formula above to make up the RPFs (resonant
peak filters) suggested in the crossover diagram 
.
You will need a different RFF 
for the MCD25M, the more expensive titanium tweeter made by the MBM25S's German
manufacturer. For either tweeter model, the combined impedance of the RPF,
L-pad and tweeter is about 6 Om,
so the same crossover values will work on both. While the wiring diagram shows
re-versed polarities for the drivers, putting the drivers in phase will make for
a slightly more uniform response at crossover. Unfortunately, it also raises the
level a bit at 1.8kHz. Going back to the re-versed condition will shift the
boost up-ward on the axis, leaving a slight dip at crossover at ear level when
you're listening while sitting. Unlike the earlier problem, however, the dip is
too shallow to be noticed by most listeners. Another solution is to move the
tweeter to a position on top of the enclosure. A small baffle here should give
you improved horizontal distribution.
The
tapered pipe, with its low cost and construction ease, should be a contender in
the enclosure race. It does require a bit more tinkering with damping material
than a simple box, but challenge is part of the game.
The
damped pipe has several advantages over the bare pipe, including one that might
not be obvious. In 1963, Alan Lovell, news editor of the British magazine The
Tape Recorder, heard unusual noises coming from one of his tapered pipe
enclosures. After analyzing the sound, he found his cat had crawled in-to the
pipe and was stuck. He called and called, the cat howled and howled, but it
didn't move. Mr. Lovell had to take his enclosure apart to get the cat out.
Another builder reported the first time his cat saw a tapered pipe, it went
right into it.
As
a result of these incidents, warnings were issued for builders to place screens
over their pipes' ports. So, if you run into trouble, don't expect to use the
discarded pipe as a cat residence. But, if you know anyone who has a pet snake...
