Tech Design.....
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Dipole woofer on axis response in relation to listening distance.

Figure 2 shows the unequalized response of a
dipole with 1' separation between the sources at
distances of 4, 8, 16 feet and at infinity. We see
that only as r goes to infinity does the
6dB/octave roll off continue without change. The
vertical line indicates the frequency at which the
separation is 3 times the wave length and the
curves are valid below this frequency. At a radius
of 4' it is observed that the response begins
deviate from the 6dB/octave roll off and to level
out starting in the area of 100 Hz. As the
distance from the dipole is doubled this transition
point moves an octave lower in frequency. In the
shelving region, where the level is constant with
frequency, while the level of the response is
much below that of a monopole it is noted that
this level behaves as a monopole in that it drops
off at 6dB each time the distance is doubles,
regardless of frequency.

In Figure 3 the impact of this behavior on
equalization of the dipole response to a specific
on axis target is examined. The target response,
indicated by the black diamonds, is a 20 Hz,
Q=0.707 high pass function. The equalization is
a simple 6dB/octave low pass response plus gain
to bring the response to the zero dB level. In
Figure 3 the equalization has been applied to
have the response match the target based on
the unequalized response at infinity. Note the
effect this has on the response at the different
finite distances. Recall that these responses are
normalized to that of a monopole at the same
distance. As such they do not show the 6dB
overall increase in level in the flat region which
would otherwise be observed each time the
distance is halved. What is important is that
as the distance is reduced the response
develops a hump. At 4' the response peaks at
+5dB, or 8dB above the target.

Figure 4 shows a similar result when the
equalization is chosen to match the target
alignment at 16'. In this case the corner
frequency of the equalization function is 11 Hz.
The magnitude of the hump in the response at 4'
doesn't change relative to the response at
infinity, but compared to the 16' response it
is now only about 7dB. A minor but real
improvement.

The last figure, Figure 5, shows the result when
Fc of the equalization function is raised an
octave to 22 Hz. Note that the reduction in
distance by a factor of 2 requires raising the
equalization Fc by a factor 2 as well. The
maximum deviation between the 8' and 4'
response is now about 5dB. Still significant.  
Raising the Fc of the equalization to 44 hz would
match the target at 4'.

Concluding comments:

In the discussion above reference has been
made consistently to the hump in the response at
4' relative to the response at the equalization
distance. The reason for this is simple. If it is
assumed that the typical listening distance is
between 8 and 16 feet from the speaker, and
that the speakers are about 4 feet from the wall
behind them, then the response at 4 feet is
indicative of the response which would be
reflected off the rear wall. This is in comparison to
a monopole, where the reflected response would
have the same shape as the forward wave. The
impact of this on how a dipole interacts with a
given room is not clear at this time. However, it is
clear that equalization of a dipole woofer system,
based on assuming the 6dB/octive roll off
continues to zero Hz is incorrect and, depending
on the listening distance, can results in a