A question on box depth from the old days

[GenoT]

Back in the 1970s I built a number of enclosures. At first the Phillips/Norelco booklet was my guide. I bought a number of other books too. I only vaguely remember suggestions back then about recommended box depth being related to to the woofer and a fraction of some frequency... maybe the free air resonance? I have a Anthology kit sitting here ready to go, but I was just curious if the old way of worrying about box depth has been tossed aside. I've searched high and low on the innerwebs and see no discussion about getting the best response from a woofer related to box depth... or if it even matters.

[JonMarsh]

Well, in consideration of your mention of the "old days", I would go back to a short story by Issac Asimov published in 1956, "The Last Question", and the often re-used quote from that story,

"Insufficient data for meaningful answer".


That being said, however, I can offer some examples for consideration, from manufacturers and personal experience, though some of that is even related to midrange drivers and even tweeters.

But, regarding that "insufficient data for meaningful answer" quip, I could pose a few basic questions....

• Which type of driver are you calling a "woofer"?
• A mid woofer intended for a two way system with upper crossover between 1500Hz and 3kHz?
• A larger woofer intended for a three or four way system with a crossover point in the range of 250Hz to 600Hz?
• A woofer termed more as a subwoofer, with an upper crossover point between 80Hz and 150Hz?
• A sealed fully stuff system or a ported or PR system with a cabinet only lined? (though they can be stuffed loosely, too).

And what is your quality target, as regards system linearity and freedom from artifacts, such as rear waves interacting with the front wave in the radiated output?


You mentioned the 70's, so that gives me an excuse to set the wayback machine to the mid 70's, and describe an experiment I did then...

I was a co-owner in a high end Audio shop, among the brands we sold was Bower and Wilkins. The top of the line back then was the DM6 model, which at the time I thought had some rather nice drivers, but was rather compromised by the effort they put in towards making these drivers work (after a fashion) in as small an enclosure as possible. This even included using an auto former on the woofer, which achieved bass level control, but introduced response irregularities due to the impedance interaction between woofer Fb and the auto-former inductance.





Being an authorized B&W service provider also, I was able to order a full set of DM6 drivers, and set about seeing what might be realized if the size and dimensions were relaxed, and different crossover topologies employed. While I had a 1/3 octave White analyzer at the time, with an HP mic preamp with B&K 4133 pressure zone omni, another tool I used a lot was a pulse generator and oscilloscope, because developing minimum phase speakers and understanding the transient response impulse behavior of the drivers was also something I believed to be quite important.

The resulting speakers were much deeper, larger volume for the woofer and midrange, and much better damped as regards system Q for the mid and woofer, and time aligned also, with a true time aligned crossover, which the DM6 actually lacked. The overall results, as ET might say, were "most satisfactory".

Now the folks at B&W are not ignorant, but they bow to commercial realities for most of the production systems. OTOH, they have a model, the B&W Nautilus, which has been in production for 30 years now with some updates and tweaks, since 1993. John Bowers was certainly aware of the issues of dealing with the rear wave successfully to optimize the front wave radiation:





Now, one way this design could be "described" is as using sealed terminated transmission line loading... to absorb upper frequency components as well as control the damping effect for Fb. This requires carefully matched driver design to the application, as well as good physical design for the enclosure.


So, one might say that a key initial question is what are your goals, and how far are you willing to go? Treating the enclosure as merely an additional compliance load modifying Fb from Fs is, IMO, a simple minded approach, BUT, may be perfectly adequate depending on your expectations and the driver quality. Using conventional golden mean dimensioning in combination with variable density damping may be perfectly adequate for your intentions. And for midrange components, open back is popular with some designers, as there is no reflection within the enclosure and the room reflection is at a somewhat lower level, due to distance, but also unpredictable, due to variability in room materials and acoustics.


I'll relate one more class of examples, not woofer related, but at higher frequency ranges, midrange and treble planar film driver loading. The issues differ in the details, but are fundamentally related. In the case of these drivers, controlling the Fb frequency range and damping is a factor, but so is the reflection of the rear wave back through the driver to sum and null with the forward wave, depending on phase. This has often resulted in building 4 or more prototype configurations with different depths and damping material, before arriving at a reasonably optimum combination of characteristics.

These results are for the same GRS planar tweeter, the PT2522, with an added rear enclosure to define and control the rear wave impact on Fb and SPL response. The PT2522 is available with a shallow rear cup, with a part number PT2522c, but the response is rather irregular due to lack of rear cavity damping and the reflections.


B&G had their own version of a "deep cup" tweeter with some kind of rear damping material- I have not had the opportunity to disassemble one, but I have measured a pair.


Looking at the polar response in 10 degree increments, 0-50 degrees, this is how it looks:



Due to the larger cup size, the Fb is lower than optimum, and the overall response flatness suffers from that as well as response irregularities I believe are due to rear side reflections, perhaps an unoptimized choice of damping material.


Next up is a variation with a hand built rear chamber using denim damping material and a rear plate from the PT2522c, that was optimized for overall flatness of response above Fb to the top end, as regards the total internal volume:





If one uses Fuzzmeaure to calculate the RMS average of these plots, this produces a relatively level response, though with the Fb rise in the 1400-1600Hz area, which is easily dealt with in the crossover. But note the response swings in the area above 5kHz; this is in a frequency range where I suspected the impact of rear wave reflection. Note, similar spikes are present in a commercial speaker, the PS Audio FR3, which uses a driver with with very similar construction, though possibly a different film material. This driver is probably built by GRS for PS Audio, as GRS bought out the B&G technology, but apparently improved the tooling and materials, as well as the documentation.


Here is a deeper version of this construction, same materials but nearly twice the depth, though not as deep as the B&G "Deep Cup" version:





Now, this test build was not as flat overall, but the response curve is still very easy to work with for a crossover design at 2400Hz, and the polar response spread in the region from 3 to 8 kHz is significantly lower, and the peaking and dip in the 5-7 kHz area is greatly reduced.

This is due to rear wave behavior- test platform is identical, tested on same enclosure.

So, yes, I recommend paying some attention to rear wave issues, use golden mean dimensioning, and favor depth for back wave absorption, and high performance materials like denim insulation. If the result is worth the effort to you.

[GenoT]

Since it was 50 years ago... my carbon based sub-cranial hard drive doesn't seem to do well in data retrieval. Back then I was building sealed enclosures with the low-end driver being what I called a woofer. I lined the interior with fiberglass batting. Heaven knows what cross-over frequencies I shot for... but I usually did have a mid and a tweeter.

Best I can recall the documents were intimating that to get the best low end out of a driver you'd take the fs (I think) and divide it by x. Heck the fs (or whatever it was) might have translated the actual wavelength into feet or meters and then divided. Then each and every time the equation would give you the ideal depth to avoid waves bouncing back to the speaker detrimentally. Of course you'd have to know the recommended volume. That would leave you with two flexible dimensions... width (at least enough for the driver) and height. Shorter meant wider, taller meant less wide. But, depth remained the same. I was always interested in getting the most low end out of a driver with as much efficiency as possible. I guess it would have applied for a three way, four way, or sub.

In the intervening half century, somebody might have figured out that such a calculation was hogwash. Maybe that's why I couldn't find any mention of a way to determine recommended depth for particular bass driver numbers.

[JonMarsh]

Since it was 50 years ago...

In the intervening half century, somebody might have figured out that such a calculation was hogwash. Maybe that's why I couldn't find any mention of a way to determine recommended depth for particular bass driver numbers.

There is probably some truth to your intuition... following in that same vein of thinking, once you have a calculated what you believe to be a useful volume, do consider applying the golden mean rule, where the relationship of height, width, and depth are golden mean ratios - this will reduce the potential additive effect of standing waves in the enclosure.

[Reet]

Technology has come a long way is the past 50 years, computers and such we can evaluate cabinet dimensions and resonant modes with ease via computer software and acoustic measurements. Rules of thumb can be thrown away in favour of good design practice and acoustic evaluation.

It is easy to calculate and measure internal cabinet reflections relating to wavelength and distance. Simple calculations as these are built into software like VituixCAD to provide easy identification of which frequencies may be excited by internal cabinet reflections.



Actual resonant modes when the cabinet is built can be evaluated through impedance and near field acoustic measurement. Cabinet fill and other complex cabinet shapes, angles and such can complicate things, but in general a longer cabinet depth will push the internal resonant mode lower in frequency while also allowing for more damping material to absorb/dissipate the resonant mode. In general, a deeper cabinet can be technically better in this aspect, but in any cabinet, adequate bracing and damping is where the focus should be. I find it more important to ensure that length, width, height, and port modes do not occur at the same frequency and the cabinet is well braced and with damping fill. A cube should be avoided for anything other than a subwoofer for example.