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Excerpts
From the Bass List
Here
are some old posts from the Bass List that some might find
useful.
- The science
of box stuffing
Subject:
How Stuffing Increases Box Size: Adiabatic vs. Isothermal
[Was: F illed Box Effective Volume]
From: owner-bass <owner-bass@lunch.engr.sgi.com>
Date: Fri, 31 Mar 1995 04:56:00 -0500
To: bass <bass@lunch.engr.sgi.com>
From: Douglas Purl
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>>
How exactly does the filling "effectively" increase
the box volume? I
>> can imagine the filling increase the box's absorptive
losses, thereby
>> increasing the damping. But what exactly causes the
lower resonance
>> frequency of filled vs. unfilled? Does the filling
cause an
>> increased air load on the driver diaphragm and/or
add moving mass
>> itself? Perhaps I should break down and buy a copy
of Beranek? :-)
I will attempt
to answer this question so that no technical knowledge or
mathematical background is necessary to its comprehension.
Because I believe two formulas clarify the description, I
do include and refer to them.
A sealed
box, unless a vacuum has been created within it, contains
a gas in the form of air. The gas is composed of a number
of particles randomly distributed. If one or more walls of
the box contains a movable boundary in the form of a loudspeaker
diaphragm and motor, the means will be available to alter
the pressure within the box. When the diaphragm presses into
the box, pressure rises because the air particles are being
violently forced into one another and compelled to occupy
a smaller volume. (When the diaphragm moves outwards from
the box, a vacuum compared to the ambient pressure--ambient
pressure being zero, the neutral pressure of the box--is created
and all the reckoning above likewise applies, but with a negative
value.)
The air
inside a sealed enclosure behaves like a simple spring. This
spring is said to have a constant, which describes mathematically
the compression factor in the air. Now the interesting matter
that enters here is that there is a different result when
pressure rises from a rapid change in volume and when it rises
from a slow change in volume. Rapid changes are adiabatic
and slow changes are isothermal (we will define these shortly).
I will reproduce their representation here because the figures
instruct us:
Adiabatic:
Delta P = -1.4K Delta V
Isothermal: Delta P = -K Delta V
Where K
= the gas constant, P = pressure, V = Volume, Delta = change
in
Notice that
the pressure change is greater in adiabatic compression than
in isothermal. Why the difference?
An isothermal
compression is one that takes place at a constant temperature.
An adiabatic compression (or rarefaction, remember) is one
in which the temperature rises during compression and falls
during rarefaction.
During slow
compressions, there is time for the heat generated by the
compression of the air particles to be transferred to the
walls of the enclosure; during slow rarefaction, the heat
is transferred back into the air from the walls of the enclosure,
keeping the temperature of the gas constant (and hence isothermal).
[Note: "Slow" here does not refer to the rate of
change, but to the velocity of propagation of the particle
disturbance through the gas medium. The velocity is the same
across the audible sound-wave spectrum into both infra- and
ultra-sonic propagation.]
During fast
compressions and rarefactions, there is insufficient time
for the disturbed air particles to transfer their heat to
the enclosure surfaces; hence, the temperature of the gas
rises during compression and falls during rarefaction. In
fact, under such circumstances the instantaneous temperature
of the gas could be used to indicate the instantaneous pressure.
It so happens
that sound in air observes the laws of rapid-change gas variations.
Thus normal propagation-velocity sound in a sealed enclosure
behaves adiabatically.
Now if the
velocity of the air particles could be slowed, the adiabatic
compression could be converted into isothermal. The velocity
of gas molecules varies as the square root of the absolute
temperature of the gas. In the adiabatic process, the heat
of the gas rises and therefore the velocity of the gas molecules
increases. The gas particles collide with each other more
frequently and more violently, causing more momentum transfer
from particle to particle. In the adiabatic process, the gas
molecules get hotter, collide with each other and the box
walls more frequently as they heat, and having acquired greater
momentum, transfer more momentum to the walls.
Compared
to adiabatic, in the isothermal process the air molecules
are cooler, have less momentum, and collide with the enclosure
walls less often. In other words, the enclosure looks larger
to the confined gas.*
This is
the principle that Edgar Villchur patented (which he later
revoked rather than fight Jensen Loudspeakers over it--ironically,
Jensen International now owns the company Villchur founded,
Acoustic Research) in 1954 (or soon thereafter). Compared
to the (virtual) infinite baffle, an acoustic suspension reverses
the relation between the spring constants of the diaphragm
spider and surround on the one hand and the spring constant
of the entrapped air in the sealed enclosure on the other.
One great advantage is that the isothermal air mass has a
relatively linear compression behavior, whereas the mechanical
spider and annulus vary in their stiffness according to position
and temperature. The acoustic suspension principle necessarily
results in lower distortion than the sealed-box method it
displaced.
Isothermal
compression is achieved by critical box stuffing. Too much
and the enclosure walls are effectively constricted; just
right and the enclosure walls are expanded. Thus the impedance
contributed by critical stuffing in a sealed box converts
the displacement/volume equation into an isothermal process
and effectively couples the driver diaphragm to a larger enclosure.
*The matter
discussed above is the first topic considered by Leo Beranek
in *Acoustics*. I have the 1993 edition (revised in 1986)
published--inexpensively--by the Acoustical Society of America
(ISBN 0-88318-494-X) for $30 in hardback. Like every good
text book, it requires comprehension of preceding matters
before subsequent discussions can be understood. It is not
for browsers, nor for those allergic to math. Despite its
several revisions, it contains errors. For example, on p.
4 Beranek states that isothermal molecules will collide with
the container more often and on p. 5 he states that adiabatic
molecules will so collide more often. The ambiguity is the
product of an insufficiently rendered discussion of the mechanics
of alterations in gas pressures. Even so, the book is required
reading for those who wish to understand the physics of sound
and sound reproduction, and it is a steal at its subsidized
price (491 pp. in a quality hardbound).
Subject:
Stuffing Stuff
From: owner-bass <owner-bass@lunch.engr.sgi.com>
Date: Tue, 4 Apr 1995 03:41:00 -0500
To: Bass <bass@lunch.engr.sgi.com>
From: Ken Kantor
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In light of recent discussions, let me share some thoughts
regarding cabinet stuffing. I'll do this from a practical
point of view, partly because the physics side has been well
articulated by Doug. The other reason I'll stay away from
theory is that, in the matter of cabinet fill, theory has
proven over the years to be of only limited help in real-world
speaker design. I'll also confine most of my comments to issues
related to sealed systems. Vented systems do share a few of
these same issues, but really the goals and the physics of
stuffing a vented box are different.
Most professional
designers would agree that practical experience, combined
with trial and error, is best way to find the optimum stuffing
material, quantity and method for a given design. This is
why good designers routinely experiment with fill in the development
of a new system, ala Vance's data cited here. This particular
information is a valid data point, but it is important not
to over-generalize. If you are designing a system that differs
substantially in shape or volume or source impedance (passive
crossover) from a known you will need to iterate for best
performance.
In my practice,
adjusting the filling is the last step in getting the bass
right, and is used mostly to fine-tune the system Qtc and
resonance. As increasing amounts of polyester are added to
a sealed box, the resonance and Q gradually go down. This
can be shown mathematically to be due in roughly equal parts
to the effects of simple resistive damping and isothermal
conversion. At some point, a mimimum is reached, and further
material simply reverses the trend by taking up volume. During
the filling process the impedance curve is constantly monitored,
and convergence to optimum usually takes only a short time.
Filling also has the important effect of reducing internal
reflections, to reduce standing waves and comb filtering.
However, the amount of filling has comparitively little effect
on its efficacy in this regard.
[Side Note-
it is a common misconception, I believe, that professional
designers rely heavily on LEAP and SPICE and CALSOD to define
their designs a priori. On the contrary, professional designers
use these modeling tools mostly to guide and optimize revisions.
Unlike DIY designs, a typical commercial 2-way will go through
perhaps 3 revs of each driver, 2 to 4 box trials, and easily
a dozen+ crossover changes.]
Lining the
walls of a vented enclosure to reduce internal reflections,
or filling a transmission line to absorb the back wave, highly
absorptive wool or fiberglass are ideal. However, these materials
will not generally provide the desired results in a sealed
system. It is true that they will provide more reflection
absorption than polyester, but the later is quite good in
this regard in the critical midrange. In a sealed system you
don't want absorption at lower frequencies anyway; you want
damping and isothermal conversion. I have tried "all-out"
efforts using fiberglass lining and polyester fill to achieve
the best of both worlds. I found the results to offer little
practical benefit over polyester alone, but its worth looking
into.
All NHT
systems now use polyester fill, of one variety or another.
We used to use fiberglass in our vented designs, but found
a Danish polyester that mimicked the properties of fiberglass
very closely. I don't know if this kind of polyester is available
to hobbyists. Excluding this special poly, there are essentially
two kinds of fiber available: pillow stuffing, and audio-spec
polyester. The later type allegedly has hollow core fibers,
but I have been unable to verify this with my keen eyesight!
Sorry, but forget the pillow type. Sure, it's easy to get.
If you use enough, it will damp the midrange, and that's better
than an empty box (by alot). But it will have little effect
on the lower frequencies.
Well, that's
pretty much all I know about stuffing speakers. I'm anxious
to hear about the results of people here. Especially the one's
experimenting with the use of small animals and children to
fill subwoofers.....
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