I know that the frequency response of a closed or ported speaker is a function of both the driver and cab; what about open-backed speakers?
The speaker still has whatever frequency response that's built into it. Frequency response isn't the big problem with open backed cabs...lows at a decent enough volume to work on a gig is.
Both of those things still hold, and the size and shape of the baffle always matter and change native driver response. But speaker placement/boundary reinforcement effects add another layer of important variables to the equation with open-backed cabs above and beyond how they influence sealed or ported cabs. There can also be some box tuning effect depending on just how open the back is or isn't.
So what are the acoustical properties of a Fender-style cab? What's the frequency response of a classic Fender 2x12?
What problem are you trying to solve? An open-back cab is almost never going to perform well for bass guitar. Is that what you're asking?
Open baffle or open back cabs will not work for bass guitar on stage. Don't try to re-invent the wheel. There are sealed boxes, ported boxes, passive radiator boxes, front mounted horns, back mounted horns, folded horns, transmission lines, back mounted waveguides, line arrays, isobaric alignments, .5 alignments, but no open baffle or open back bass cabs for a reason.
Yep. Back in 1960 when Jess Oliver invented the B-15's ported cab, Everett Hull immediately discontinued all the open backed bass combos he had because ported was so much better. With a guitar, a good open backed cab can be a silk purse. With bass it's a sow's ear.
These are all "pressure generators" when it comes to low end reproduction , that's the big difference. Open baffles don't work like that, to get "bass" out of an open baffle you need at least two things, lot's of cone area and correct roomplacement (no, placing them in a corner won't increase low-end performance like "normal" cabinets do, it will actually decrease it's low-end output if you place them there). Btw. a well designed and well positioned open baflle subwoofer will drop your jaw, these have some qualities that regular designs will never have. Through these, low-end sounds very different, they don't offer the pressure you would feel in your belly like a normal sub would do these subs offer what I would call feather light accurate bass, you'll hear details in recordings that you've never heard before.
I make open baffle speakers for hi-fi use. It's a very different type of sound. Given all that, they are not practical or effective for on-stage use for electric bass.
Frequency response depends on loads of factors mostly the drivers and the room position. But its the power handling that makes them not useful for bass.
With an open backed speaker cabinet the low frequencies come around the cabinet (Lows are non-directional) and cancel the waves from the front of the cabinet, so there is little or no bass as far as we are concerned. Also - the speaker will not be well controlled and will be easily damaged by excessive movement. Open backed cabinets are often used for guitar amps since the lows generated are not enough to worry about (in general), and it is cheap -the cab is there only to hold up the amp and speaker with little acoustic consideration. Front and rear ported cabinets are tuned so that the port wave and main wave from the driver reinforce each other instead of cancelling. Sealed cabinets keep the rear wave contained inside the cabinet so it cannot cancel the front wave (at the expense of efficiency).