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James Lehman wrote:
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James Lehman wrote:
I have measured the woofers grouped in
iso sets

What is an "iso set?"

4 woofers combined into a set of 2 isobaric coupled pairs,
with no cabinet behind them.

So, why not call them that, instead of inventing some nonsense
term?

and the figures that I get would indicate that they should be able
to put out a max SPL of about 117dB at 1 meter,

At what frequency? Since these things are most assuredly
excursion limited, as the vast majority of woofers are at
low frequencies, and since excursion goes essentially
as the inverse square root of frequency, a max SPL with
a frequency limit is pretty meaningless.

Max dispersion freq is where the cone moves the easiest
to produces the greatest volume in the room. At 23Hz, at
Xmax, for all the woofers together, you can expect to use
the least power to produce the most sound. It has to
do with the output of the port combined with the output of
the cone.

Several points:

First, it is noted how you have failed to answer the question.

Second, the term "dispersion frequency", given your
explanation, is simply nonsense. "Dispersion" in this
realm, already has well understood meanings, and your
misuse of the term is also noted.

In looking through a wide variety of references to the
term, there is not a single instance found in ANY of
them that uses the term "dispersion" in the manner
you do. There are simply none that even come close.
In the context of loudspeakers, the term has two
meanings:

1. The separation of a complex signal into its constituent
frequencies or wavelengths, e.g., dispersion due to
non-uniform group delay or,

2. The distribution of an acoustic signal across an angle
or an area, e.g., the measure of the directivity of an
acoustic source.

Third, there is already a measure for "the least power to
produce the most sound." It's called efficiency, and it is
the ratio of the acoustic power output to the electrical
power input. It has nothing to do with XMax. do you
know what Xmax means and why it is independent of
frequency?

Fourth, Your description of what is happening at the
box tuning frequency is basically at odds with the well-
known and well-understood behavior of vented loud-
speaker systems at the enclosure resonance. Contrary
to your statement:

"It has to do with the output of the port combined
with the output of the cone."

the VAST majority of the total system volume velocity
at Fb (the enclosure resonant frequency) comes from
the port, and very little comes from the cone. To quote
Small:

"Over the frequency range near Fb where the
passive radiator (or vent) contronutes most
usefully to the system output, it does so
through reducing and replacing, rather than
supplementing (as so often implied) the motion
of the driver."
JAES, vol 22, no 11, 1974 Nov.

Examine also the expression for displacement vs
frequency Small presents (Eq. 71 and 73, JAES,
vol 20, no 10, 1973 Oct), which clearly illustrates
Xd(w) showing a minimum at Fb. That also
corresponds to a minimum in the electrical
impedance at the same frequency.

Given these facts, it's thus obvious that two of your
assertions:

1. That the output of the port is combined with the
output of the woofers at Fb to increase the total
output of the system, and

2. The system efficiency, what you call "the least
power to produce the most sound," is maximum
at Fb,

are wrong.