In article ,
Pat wrote:

I was away for a while, so this thread is new to me today. Your
comments above make sense, but bring up a question I have had for many
years. I own a pair of ESS AMT Monitor speakers that I purchased new
back in the 80's. Each has a pair of 12" woofers - one active (ie, a
normal speaker) and the other passive. I would think that when the
active one is compressing the air in the cabinet, the passive one
would be pushed out thereby appearing to be out of phase to a
listener. That doesn't appear to be the case because these speaker
have a great low end sound. Can you explain why they work? (I am
just picking you because you seem to know something about the subject,
but others are welcome to explain my misunderstanding as well.)

You have to analyze these "passive radiator" systems as resonant
systems to see how they work.

At very low frequencies (below their cutoff) they do work in the way
you think... the driver and passive-radiator outputs are out of phase
(by angles approaching 180 degrees as you approach DC) and cancel out,
and the acoustic output of the system drops off sharply.

At higher frequencies, the phase offset between the two diaphragms is
different. The driver moves, and compresses the air inside the
cabinet; the air presses on the passive radiator and accelerates it,
and the passive radiator moves. Each of these "presses on" and
"accelerates" steps takes time, and introduces some time delay and
thus some phase delay... and this phase delay adds up, and has the
effect of cancelling out part or all of the 180 degrees of phase shift
between the two drivers.

So, at higher frequencies (above cutoff, but still down in the bass),
the acoustic output of the driver and passive radiator are either in
phase, or close to it... and their outputs reinforce.

The same thing occurs in a common "bass reflex" or "ported" speaker
cabinet. At very low frequencies, the output of the port/vent is
out of phase with that of the driver and there's no useful output from
the system, while at higher frequencies, phase delay in the "back of
the driver, through the air in the cabinet and port, to the port
output" brings the driver and port outputs into phase, and they
reinforce and you get stronger bass.

Both ported, and passive-radiator systems (and sealed "acoustic
suspension" as well) can be modeled as electrical circuits. The
compliance / springiness of the air and the driver surrounds "looks
like" a capacitor, the mass/momentum of the driver and radiator and
air "looks like" an inductor, and frictional and other losses "look
like" a resistor. A speaker system ends up "looking like" an LCR
high-pass filter, and the math for designing and tuning such filters
can be applied to the physics of the speaker driver(s) and enclosure.

The development of this sort of electrical-equivalent modeling some
decades ago was quite an innovation, and it's what enabled the
development of predictable commercial ported speaker enclosures (as
opposed to those which were worked out by trial and error, "by guess
and by God", and tuned through listening tests until they sounded good
to their creators).