Greg: Room gain is very difficult to calculate and will somewhat vary with size of the room and speaker placement within the room. This is why good engineers design a speaker for specific placement within a room. Bare in mind that i'm not just talking about bass loading characteristics either. That way, they can factor in specific low frequency reinforcement factors AND dispersion characeristics consistent with the placement that the speakers will be used in.
While many people don't take such things into consideration when making their purchases and can't figure out why their speakers don't sound good where they have them placed in their room, they may also be the same type of people that buy a 4 wheel drive SUV to drive around in the city and / or take long trips on the highway with. While one can argue "vehicles are a matter of personal preference", one can also say "mis-application of a product outside of its' intended use will deliver less than optimum results". One can use such a product and be happy with it, but that doesn't mean that something else that was more suitable for the task at hand wouldn't have worked even better.
This is why i've stressed factoring in room size and placement in varous threads. Great speakers in the wrong room and / or great speakers that are improperly placed soon become "bad speakers" that they can't get rid of fast enough. Too many folks end up buying speakers that were designed to operate in a different environment than how they want to use them and then end up paying the price.
Ernie: I would suggest that you read Vance Dickason's Loudspeaker Design Cookbook. Your understanding of cabinet size and bass extension / output needs some help. I don't mean this to sound rude, as i was under many of the same false assumptions when i first started reading / learning about speaker design myself*. The fact that there are loudspeaker designers / manufacturers that don't fully understand many of the variables involved speaks of how complex of an issue this really is.
Part of the extension / total output / lower F3 on a vented system comes from the fact that, with such a high amplitude peak at resonance, the output, which is frequency related, has to fall off quite a bit before going below the average output level.
For sake of an example, let's assume we have a speaker that averages 88 dB's across the band. Due to the undamped oscillation at resonance of the driver / vent combo, there is a +5 dB peak in the low frequency region. As we've seen, this high of a figure on a vented design is not unrealistic and is possibly even conservative on some designs. This means that at the point of resonance, the output of the speaker is at 93 dB's. It is only after the lowest tuning frequency of the vent occurs that the speaker begins to roll off. That means that roll-off starts AT the peak.
Starting off with such a high peak means that we now have to lose 5 dB's of output just to get back to the reference output level of 88 dB's. In order to find our actual F3 ( -3dB point ) of this design, we've still got to lose yet another 3 dB's of output. This would give us a total of an -8 dB drop before we actually made it to the frequency where F3 is measured.
As you can see, since roll-off occurs at the same rate that frequency is lowered, building in a bigger peak at resonance automatically gives you more extension. That is, as it looks on paper using a -3dB reference point. Other than that, one can introduce such a peak into a sealed system with an EQ and still enjoy the better transient response of the sealed box. If you want to mention the phase shifts that the EQ brings with it as being detrimental, i'd like to mention the phase shifts that the vent brings with it.
As to your question about "what's wrong with a 24 dB slope", that answer has to do with linearity, transient response and ringing. The sharper the slope, the poorer the transient response, the more ringing and the less phase accuracy. This is why most "high end" audio gear strives for wider bandwidth with gradual roll-off. Better out of band performance equates to better & faster in-band performance. Same goes for speakers.
The question here is does one want more total output with a lower F3 at the expense of added bass bloat aka "lack of control", reduced linearity, poorer transient response, etc.. or is a slightly higher F3 with improved transient response and linearity more desirable? Since F3 only tells a small percentage of the picture, take a look at this. For sake of clarity, these figures are based on the accepted principles that vented systems fall at a rate of 24 dB's an octave and sealed designs fall at a rate of 12 dB's an octave:
-3 dB's on a 40 Hz vented system
-12 dB's at 30 Hz
-24 dB's at 20 Hz.
-3 dB's on a 50 Hz sealed system
-12 dB's at 25 Hz
-24 dB's at 12.5 Hz
While the initial -3 dB point on the vented design looks better on a spec sheet, it actually offers LESS extension when all is said and done. This is true even though the sealed design looks "weak" at an honest 50 Hz rating. On top of that, the vented design has all of the other problems i.e. reduced transient response, increased ringing, more phase errors, out of phase leakage from the port into the upper bass / lower midrange region, etc... You have to deal with all of these sonic drawbacks as tis type of design tries to get you the limited extension that if does offer.
This is not to mention that the vented system is completely "unloaded" or "undamped" below 40 Hz. Any low frequency notes fed into the speaker below that point will only result in massive excursion with the potential for damage / increased distortion. If you've got vented speakers and play vinyl, DO NOT try to play massively warped records at high volume. This will cause MASSIVE "woofer flutter", possibly resulting in permanent damage.
As a side note, it is quite possible to design a bass hump / resonant peak into a sealed design. By increasing the Q, you get such a peak. Like the vent, the transient response is reduced and ringing is increased, but unlike the vent, the slope remains shallower and phase integrity is not damaged quite as badly. As such, it is possible to match the F3 of a vented design with a sealed design, but the benefits of improved transient response are partially negated.
Vented designs DO look "more impressive" on paper, but that is only because the spec's that we use to quantify the performance of speakers aren't quite as sophisticated as those that we use for electronics. On top of that, there is no such thing as electronics / room interphase like there is with speaker / room interphase.
Vents vs sealed boil down to quantity vs quality. Vents will almost always give you more total output, but at great expense. Sean
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*To be honest, i was under the impression that vented systems allowed smaller cabinet size and greater extension for many, many years. I could never understand why someone would want to buy a bigger cabinet that didn't play as low and took more power to operate. That's because i was reading spec's but didn't know how to interpret them, nor had i actually listened to a lot of sealed designs at that point in time.
The reason why the sealed cabinets were "bigger" was because they were properly designed and tuned for extension. The vented cabinets were tuned for more apparent bass and higher output i.e. the illusion of "deeper" bass via "more" bass. This is how most "Pro" speakers are also designed and you can see further evidence of this by reading Bill Fitzmaurice's articles in Audio Xpress.
