30 HZ from a 10 X 7 box

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I am building a few Bookshelf speakers for the Grand-kids. Using a Low Vas speaker so I can get a +- 3db 30-20K from a 10 X 7 X 7 box. I need some advice. when can you use just a hi freq blocking cap, a first order, and when do you need a 2nd order crossover.
 
For low distortion I want to use the lowest order crossover I can use.

Besides very low distortion, I wanted very low bass – 30 Hz, a flat frequency response +/- 3db. To get these I needed a relatively “big” enclosure. The “biggest” enclosure is an infinite baffle.

Infinite baffle = 5 X Vas

For Tang Band W3-1876S 3”
Vas = 0.03 ft^3
5 X 0.03 = .15 ft^3

Anything over 0.15 ft^3 is an infinite baffle and will give me “extremely clean and uncolored sound with very low bass output capabilities”. So my tiny ~.3 ft^3 box is an infinite baffle.
Some sub-woofer formula for infinite baffle use:
Vb = 10 X Vas which is 0.30 ft^3.

To insure I made the internal:
Vb = 10 X 7 X 7.5 = 0.304 ft^3
after subtracting the volumes of the speaker and port tube.

It had to have a high Qts-above 0.40 to work properly in an infinite baffle. This Woofer has a Qts of .43. Higher Qts’s are more appropriate for the Chebyshev alignment to eliminate boomeness, with the side effect of lower bass.
I tuned the box to 33Hz, a true Chebyshev would be tuned in the 20’s and require an equalization boost in the low frequencies an fs of 33 Hz does not.

I do have a couple of other problems. Vas is the ratio of reactive to resistive elements. So a low Vas speaker has more energy losses to the resistive elements so is lower efficiency. Matching a tweeter to a 76 db sensitivity speaker takes some looking, or lots of resistance in the crossover.
 
How about a graph?
All drivers simulated on power that reaches xmax at ~35Hz

Grey: w3-1876S, 0.3 ft³ tuned to 33Hz, 10W
Green: w3-1876S, 1 liter tuned to 55Hz, 6W
Blue: w4-1720, 0.3 ft³ tuned to 55Hz, 3.5W

In other words, consider these: https://sites.google.com/site/undefinition/speedster
 

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TB w3 -1873 in enclosure 2.jpg [/ATTACH]Thanks Dump-truck.
Here are some other graphs

The tweeter I will be using is the Dayton Audio DC28F-8
Frequency range: 1,300-20,000 Hz, 8 ohm at 2K
SPL: 89 dB 1W/1m
The tweeter drops off below 1500.
The woofer drops off above 2K, 8 ohm at 15-18K
If only a cap, 10 uf
Crossover if used 1800 Hz
 
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my thinking, not yet put to the test, is that it is easier to equalize the 40 to 80 Hz that is 3-4 db low, than to try to resurrect sub 60 hz music that is -40db. This was discussed in Thiele & Small 's papers. Yes dumptruck I agree, without equalization it would weaken the music. The kids boost the bass to distortion normally trying to get the very low non-existant bass. If you or anyone has experience in this I'm open to ideas
 
And you'll lose even more output from the EQ. Getting bass at 30Hz that actually sounds like anything requires more like 100dB+. I may be wrong, but I'd put some money on the suggestion I gave you in post #3 (or another vented design with that woofer, there are several out there) sounding like more bass, EQ or not. ;) Speakers that struggle to get above 80dB do not tend to impress anyone. Just use higher output designs and drop the upper mids as needed to make them sound beefy, that's my advice for small speakers meant to run full-range.
 
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Still cant get deep bass, in a small box from high Vas speakers.

From this 5 watts should give output in the 80db's.

I built a set of 40" exp folded rear firing horns, 40 Hz at 86 db on less than 2 watts but rarely use it that loud, normally in low 70's at less than 1% distortion.

When I added 6 db of equalization it only added .05% at 76 db.

Here is 30Hz from the .188 ft^3 Vas woofer W4 1720 in small .4 ft^3 box

Should have the small speakers built and tested in a week, will share the test results. It will be interesting as formula and software, even test eq are not ears.

Do you have a preference as to type of enclosure?
 

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Still cant get deep bass, in a small box from high Vas speakers.
No, you sure can't. I was talking about the 1720 tuned higher being more impressive sounding than the 3" "subwoofer". My opinion/experience is that deep bass is worth nothing at limited SPL because you can't even hear it. Better output 50-80Hz would steal the show, and you're limiting yourself there a great deal by trying to reach 30Hz. Nothing wrong with trying it, just don't proclaim it works great without good basis for comparison.

Do you have a preference as to type of enclosure?
Nope. Whatever works best for the driver and the application.
 
Still cant get deep bass, in a small box from high Vas speakers.

From this 5 watts should give output in the 80db's.
Classic Hoffman's Iron Law- loud, low or small, pick two. You have already chosen small, only one choice left.

80 dB at 30 Hz is barely audible, and most pop music "bass" is in the 60 Hz range.

Given a speaker the size of what you are going to make I'd choose "loud" (which for most kids is more like at least 100 dB) over low, and like Dumptruck suggests make the Fb around 55-60 Hz, so the speaker has a chance of producing some useful musical LF output.
Sacrificing the "guts" for nearly inaudible LF will result in a couple burnt voice coils rather quickly, if your grandkids are like most kids I know.
 

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You folks have made some very good arguments. Thanks

Maybe I am dense but if I have a flat, +/- 3 db, system at 80 db and I have to equalize the bass +20 db to get 100 db to sound correct. Why can I not just equalize it + 23 db, if the power is available?

My current system, folded horns, flat to 40 Hz, do not need equalization, (but my ears).

The kids use much less than the 12 db of bass boost on their systems, (for their ears). It would be rare to find more than 12 db of boost / cut available.

After listening to your arguments I will only invest in building one speaker for testing as a precaution
 
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There are two things which I think are throwing you off with regards to this last post. Firstly, adjusting your signal gain by any amount of dB is not the same as getting that amount of dBSPL. In essence, you're fighting physics. You put a certain amplitude of voltage signal into a speaker and it produces 80dbSPL. To put this into perspective, a doubling of sources (that is, if you add another speaker producing 80dBSPL) will yield a theoretical 83dBSPL. This is a log scale as I'm sure you know.

Power and pressure don't behave the same because of a simple case of Ohm's law. Voltage gain works on the principle of 20dB = 10x. However, power is proportional to voltage squared, which means that 20dB increase in power means 100x more power. So, in order to increase your output by 20dB, you need to increase your input voltage by 10x which yields 100x more input power which is akin to having 100x as many sources. You can imagine therefore that if you have a single speaker, 100x more power on a single 3" speaker is going to end up a bit smoky.

My point is twofold: the dB levels that you're looking at are not the same. The bass boost is an increase in signal or a voltage gain which does not behave like power. That means that by adjusting your equalizer to get +20dB, you're not getting 20dB more SPL. You're getting a 20dB gain on your signal which unfortunately for your speaker means 100x the power. Therefore in the real world, in order to get that extra 20dBSPL that you want, you're not going to be able to rely on the EQ. You're going to simply need more speakers.
 
It's a good thing that I will only need 3 db to make it flat. one watt for 76 db and a little over 2 watts for 80 db. I doubt they, the kids, will rarely go above that, but they do have 15 to 20 watts. Too much SPL or bass and they will exceed the "PP" point. (PP for parents patience)

This is not a home theater speaker system. Just a small low distortion extended frequency bookshelf speaker for near field audio using a C4 alignment as Thiele and Small called it. I do agree that for loud Movie soundtrack in a home theater a lot may be lacking. It will be interesting to see (hear) how they really work.

Yes P = (E^2)/R
&
db of a ratio of two powers = 10*(LOG((A/B),10))
and
Db of a ratio of Amplitude or Acoustics =20*(LOG((A/B),10))
 
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Nobody meant to say you should be +20dB in the low bass to sound correct. It's that you don't really hear much down there until the overall level (including the low bass) is very high. Your speaker, EQ'd to flat bass, would hit xmax at around 80dB. That is not a path to the low distortion you keep mentioning.

If you take your test speaker and play a 30Hz sine wave, unless your ear is right up to it, you're probably not going to hear anything at all until you turn it up enough to get audible 60Hz (and higher harmonics) distortion. This will still sound like "bass", but it's just distortion, and is why a small speaker that has very good output at 60Hz but not much of anything below 40Hz does not need to sound wimpy (within reason).
 
I checked my home system at the volume we normally have it at. Here is what it looks like. level checked with a db meter. Really nice clean bass. A 40 Hz note comes across loud and clear.

Have had it at 87 db but would be painful, (for me and the neighbors), for long. We use mid 70's for movies etc.

Do not understand why more than 85 db would normally be necessary even if the room was "dead" that would be accounted for in the measurements.
 

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Do not understand why more than 85 db would normally be necessary even if the room was "dead" that would be accounted for in the measurements.

Because music is about an emotional connection, and occasionally a piece comes along that requires more than 80dB peak (at which point Xmax is reached) levels to 'get' it.
Remember that 80dB peak is usually around 70dB average.

Chris
 
fwbutler, I think you misunderstood the point of my post. It was intended to steer you to the conclusion that simply increasing input power to a seriously power limited speaker is going to leave you with a huge amount of distortion. EQ'ing isn't a process of tuning by graph. You need to listen first, and when you listen to a 3" speaker trying to produce an authoritative 30Hz, it's going to sound awful. As people have already said, if it can produce 60Hz with good impact, then you will never care about anything below that. The brain works in mysterious ways, so those lower frequencies will not even be missed if everything else is nice and clean.
 
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