(This is an attempt to rejoin a discussion thread from this past
February. I hope that this new message will "attach itself" to the
original thread.)

Bob Cain wrote:

The problem I see is in the low frequency polar diagram,
and in the dual frequency plots (0 degrees and 180 degrees)
that some makers show which maintains that there is good
rear rejection all the way down.

Theory tells me that is not possible. A pressure gradient
response falls off at 6 dB/octave below the critical frequency,
Ft, which is determined by the distance between the points
involved in measuring the gradient.

Bob's post concerned me because I translate and help edit most of
Schoeps' English-language publications. And I agreed with Bob's
viewpoint. But I had simply failed to notice that the polar graphs
in Schoeps' product literature were being shown with no specific
curves for frequencies below 1 or 2 kHz, and that disturbed me.

So I wrote to the person at Schoeps with whom I work the most closely
on publications, and asked him why we publish such misleading graphs
(as I assumed them to be). His reply surprised me: He sent evidence
in the form of response graphs showing that single-diaphragm cardioids
really can, and do, maintain their directionality down to the lowest
audio frequencies. In other words, what we publish isn't misleading
at all. Single-diaphragm cardioids such as any of the Schoeps or
certain of their competitors (e.g. the Neumann KM 140/KM 184) can
really still be cardioid at 50 Hz and even lower.

Thus the problem of widening response in the cardioid setting seems to
be a special characteristic of dual-diaphragm microphones, not one of
cardioids generally. How this squares with the notion of cardioids as
a blend of omni with figure-8 response--and with the figure-8 rolling
off at the lowest audio frequencies, leaving an ever-broader "cardioid"
response--I simply don't know yet.

When I think it through, however, it does seem right that a delay chamber
("acoustic labyrinth") behind the diaphragm of a pressure-gradient capsule
would work on the basis of the absolute path length difference (i.e. the
transit time difference), not the phase difference, between front- and
rear-incident sound waves--so that at any audio frequency low enough to
avoid being shadowed by the capsule, the rear-incident sound waves would
"meet up with themselves" on both sides the diaphragm simultaneously and
cancel each other out.

--best regards