Benefits of a cardioid subwoofer?

"...What am I missing?"

The time delay on the rear woofer corresponds to the time it takes for the output of the front woofer to wrap around the cabinet and reach the rear woofer. So the reversed-polarity rear woofer "fires" just as the output from the front woofer reaches it, and this way cancellation occurs behind the sub, rather than off to the sides, as with a dipole. The rear woofer's output might also be attenuated a bit relative to the front woofer, I dunno... never actually done it.

Duke

Duke,

So the null is behind, rather than beside the cabinet (normal dipole) - I'm not sure how that plays out. If the sub is in free space, there will be less/no subsequent reflection off the wall behind the woofer which should reduce random destructive interference from that reflection - yes? But can't you drive that cancellation frequency up in pitch and down in amplitude by placing the woofer flush to the rear wall, anyway?

Is the idea basically to allow placement away from the rear wall, or is there another benefit here?

This is kind of a brain teaser for me - I can't visualize the impact that the designer is attempting to generate.
Sorry if I'm a bit slow on the uptake here, but any explanation is - as always - appreciated.

Marty

Cardioids and dipole sub-woofers couple differently to room modes than monopoles in the same location. This works very well with dipoles and the height mode.

Cardioids implemented with an acoustic delay and dipoles don't benefit or suffer from room gain (a 12dB/octave boost below the room's fundamental resonance assuming an infinitely rigid room) which is one source of boomy bass in small rooms.

The disadvantage to cardioids implemented with an acoustic delay (this is the case for the BASIS 11K sub-woofer, which has one driver plus an output slot on one side) and dipoles is that maximum output decreases 6dB/octave compared to a monopole which is already decreasing 12dB/octave. In a domestically friendly enclosure you get 18dB less output at 20Hz which is the difference between sufficient and inaudible.

You can also tame room modes with multiple conventional sub-woofers without this drawback. You can even eliminate eliminate room gain and fix the height mode problem with a pair of sub-woofers at each room corner wired with opposite polarity.

Complicating the discussion a bit is the fact the Basis sub doesn't appear to use a rearward-facing driver, rather it seems to have some vents on the sides which I assume is part of its pattern control. Also, the picture in the link of the Legacy speaker shows two drivers front-to-back in free air, which will produce very different results from that of i.e. a pair of sealed boxes back-to-back.

The theory behind a cardioid radiator is pretty straightforward, pretty much a cardioid microphone in reverse. In all cases, the pattern control is frequency-dependent . . . in the case of both microphones and loudspeakers, playing with different configurations of diaphragms and vents can affect both the directivity and frequency response.

The limitations of these approaches are peculiar to a domestic application, as the wavelengths of concern are larger than the rooms in which the speaker resides. There's also the issue that a woofer is frequently placed near a wall, in a manner where one vent or diaphragm is several times the distance from one room boundary than another. So while a woofer may produce a far-field cardioid response in a large room, in a domestic-sized room this is completely out the window no matter what the design of the loudspeaker.

Curiously, there currently seems to be very little theoretical consensus as to how to acheive "proper" bass response in a domestic-sized listening room. One of the most thorough and convincing analyses that I've seen is that of Dr. Earl Geddes, which I belive has been highly influential on Duke's approach to the problem. Crudely paraphrased, he maintains that below a critical frequency (the "Schroeder" frequency) sound in a room behaves completely as excitations of modes, and the key to smooth, even bass response is to use many radiators of diverse characteristics placed about the room.

Drew,

Thanks, the dipole effect on gross output level didn't occur to me in considering this question.

Kirkus,

Your point re: unpredictable distance to various boundaries certainly did occur to me and, intuitively, it seems to suggest that the benefits of controlling directivity at very low frequencies in a typical domestic listening environment would be difficult to determine with any consistency.

Overall, there's more to think about here than I'd have figured, although - after reading all that's been posted here - I'm not sure what net benefit you're likely to get with this approach.

My thanks to Drew, Duke and Kirkus - I feel (a little, at least) more educated already.

Marty