Prof. John Vanderkooy presented an AES paper offering analytical proof and compelling evidence that the acoustic center for low frequencies resides in front of the loudspeaker at a distance of approximately two-thirds of the baffle radius.
This phenomenon could account for the so-called “fudge” factor (figure 1) encountered when setting the delay for inverted-stack gradient (CSA) arrays where the required delay always exceeds the depth of the enclosure.
Using non-linear regression, I’ve condensed Vanderkooy’s BEM results into equations that predict the position of the acoustic center for a single sealed or vented enclosure, based on its physical dimensions and driver diameter, within ±10% accuracy.
Most of the time, the predicted values are in very good agreement with my own observations. A subwoofer placed in a polar circle, at equal time-of-flight in all directions and therefor equal distance, optically won’t end up in the middle of the circle (figure 2).
For frequencies that are low enough where ka << 1 (ka is the driver circumference divided by wavelength), spherical waves emanate from the acoustic center rendering sealed and vented enclosures virtually omni-directional (figure 3).
Click here to download the calculator.
Baffle radius is simply the radius of a circle with an equal area as the typically rectangular area of the loudspeaker's baffle (figure 4).