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Dave, the feedback signal hasn't anything to with it bouncing towards the listener at any angle. The reflected signal returns to the woofer and partially nulls the woofer's output. The thing that you hear disappearing when you move to the side and approach the wall is the interaction between the direct signal and the bounce off of the wall that are getting to your ears and cancelling or not cancelling at that point. However, the Allison boundary effect happens everywhere, because it interacts with the woofer and not the listener. The artifact is not listener-position dependent.
In his 1992 interview with David Ranada in The Audio Critic, we have: [Allison] ".... reflections from room surfaces or hard boundaries really do reduce the output of a woofer in the frequency region where those woofers are a quarter-wavelength from the surface.
[Ranada] "This is not merely a listener-position phenomenon, the output of the woofer actually decreases."
[Allison] "Yes, it actually does decrease where one or more room surfaces are a quarter of a wavelength (approximately) from the center of the woofer. The effect is mild where only one boundary is concerned. But when more than one boundary - and in the worst case three boundaries - are equally distant from the woofer, the woofer is effectively operating in a partial vacuum, which reduces its output by 10 dB or more."
[Ranada] "That's because the reflected sound waves alter the emission from the speaker?"
[Allison] "Yes, they are reducing the pressure on the surface of the woofer and reducing the radiation resistance because of that. On the other hand, when the woofer is a very small fraction of a wavelength from one or more boundaries - then the output is actually increased, doubled, quadrupled, or multiplied eightfold, depending upon you have one, two, or three room surfaces."
[Ranada] "So this is the origin of the famed 'Allison dip,' which is a midbass decrease in output."
The Allison boundary effect involves out-of-phase interactions at the woofer and NOT interactions at the listener, and Ranada understands this as one can see by his own responses.
PS: you do not see a cancellation dip with those two woofers on the same baffle that you mention, because they are close enough together for any cancellation artifacts they might generate to be above their operating range. They add together coherently, just as wall-reinforcement does with boundaries that are a very small fraction of a wavelength from the woofer, as Allison noted above. Moving woofers close to boundaries is one solution to the Allison boundary cancellation, provided any potential notches at higher frequencies (due to the close proximity to the boundary) are above the woofer's operating range.
Howard Ferstler
Still not buying it. His math and description in the paper both pertain to the simple sum of the source and its reflection, or virtual source, behind the plane. Nothing includes a woofer model as would be required if the air load on the woofer were causing it to modify its velocity profile. Secondly, none of the 1,2 or 3 boundary cases have the null at .25 wavelength. This is because they are averages of multiple curves that all have their nulls at various frequencies, due to the path difference varying as observed from different angles.
Allison is correct to agree that the emission from the speaker is altered, that is what the power sumation shows. Calling it a decrease in midbass output is equally true. It still doesn't mean that the pressure response being created is independent of angle as you imply when you state that the null is formed "at the speaker". The null remains a function of observation angle and is purely a reflection phenomenon.
Points to ponder: If the Allison dip is quite strong with a woofer in front of a single boundary, when measured straight out from the system, why does it diminish in the power average? (Because it varies strongly with angle.)
Why do ground plane measurements not have aberations related to the distance the woofer is from the ground? (And I have done this in cases where the woofer spacing would have been 1/2 wave apart within the passband. Read Gander on ground plane measurements, no mention of it.)
Why do none of the dips in the power response happen at .25 wavelength off the surface? (.35 for the single boundary case. Even the 3 boundary case is closer to .3 than to .25. Answer: because we are averaging something that varies with angle.)
Where is the woofer modeled in Allisons math? (It is a model of the geometry of two independent sources. The sin Theta term creates the variation with observation angle.)
Why don't side by side sources have a null at a frequency equivalent to a 1/2 wavelength spacing? (because the mechanical impedances, primarily mass, greatly diminish any effect one woofer could have on the other.)
Not quibbling with anything Allison said, just how it is being paraphrased.
David
