Greetings to all!
My insufficient understanding impels me to ask a few basic questions.
1. As i understand, a 1:10 expanding Quarter wave pipe and a BiB ("0":10) pipe are essentially a very similar geometry as well as the fundamental principle. If the former is a 1/4 wave resonator, why is a BiB talked of as a 1/2 wave resonator? - Rather than saying it is tuned at 1/2 wavelength of the driver Fs, would it not be more consistent with the principle if we understand it as a quarter wave pipe tuned simply an octave lower.... Or tuned simply at Fs*0.5? (Of course, this would be without accounting for the shorter effective acoustic length of the expanding pipe.)
2. Martin King's alignment tables show a roughly 1/1.4 acoustic length for a 1:10 expanding pipe. If i am building such a Qw pipe to be tuned at 50 Hz, i would require a physical length of [(1,128*12)/50/4] * 1.4 = 68" * 1.4 = 95". If building a BiB pipe using the Xls calculator, it would state a 136" pipe. The question is, will the BiB pipe's actual tuning be significantly higher than its physical length would indicate?
3. Martin King's alignment tables suggest a driver offset of roughly 0.41 from the pipe beginning for a 1:10 expanding pipe in order to have minimum ripple. Since a BiB pipe expands at a rate not quite different from it, might using the same driver offset instead of 0.217 help reduce the ripple?
4. Based on the quarter wave principle (as in my probably mistaken understanding) since the BiB pipe (with its huge internal volume) is tuned significantly lower than the driver Fs, would a 1 mm Xmax driver not be at great risk of over excursion at its Fs even at 1 watt? How does such a low sub-Fs tuning support the cone excursion at Fs? Is there something i have failed to see/consider?
5. Am considering a BiB for a 12" wideband unit. Fs = 50 Hz, Vas = 105 litres, Qts = 0.58, Xmax = 2 mm and Sensitivity = 95 dB/watt. Apart from the suggested pipe length of 136", the internal width will be 16.5" and the gross internal depth 22". - Using 12+18 mm MDF for the baffle and 18 mm MDF for the rest of the panels, would it call for a bit of internal bracing? Also, would it hinder the wave flow?
6. I listen in a room which is 16 feet x 22 feet x (H)12 feet, usually at a position not more than 5 metres away. If the speakers can deliver peaks of 100 dB per channel about 1kHz at 1 metre, it is good enough for me. - In the proposed plan above, given the 2 mm Xmax, would it be a silly idea to tune the pipe at 40 Hz instead of 50 Hz?
Would be greatly obliged if the experts can help dispel my confusion and offer their valuable insight! Looking forward to receiving something conclusive from Scott, Dave, GM!
Thanks in advance! 🙏
With warm & sincere regards,
sujat
My insufficient understanding impels me to ask a few basic questions.
1. As i understand, a 1:10 expanding Quarter wave pipe and a BiB ("0":10) pipe are essentially a very similar geometry as well as the fundamental principle. If the former is a 1/4 wave resonator, why is a BiB talked of as a 1/2 wave resonator? - Rather than saying it is tuned at 1/2 wavelength of the driver Fs, would it not be more consistent with the principle if we understand it as a quarter wave pipe tuned simply an octave lower.... Or tuned simply at Fs*0.5? (Of course, this would be without accounting for the shorter effective acoustic length of the expanding pipe.)
2. Martin King's alignment tables show a roughly 1/1.4 acoustic length for a 1:10 expanding pipe. If i am building such a Qw pipe to be tuned at 50 Hz, i would require a physical length of [(1,128*12)/50/4] * 1.4 = 68" * 1.4 = 95". If building a BiB pipe using the Xls calculator, it would state a 136" pipe. The question is, will the BiB pipe's actual tuning be significantly higher than its physical length would indicate?
3. Martin King's alignment tables suggest a driver offset of roughly 0.41 from the pipe beginning for a 1:10 expanding pipe in order to have minimum ripple. Since a BiB pipe expands at a rate not quite different from it, might using the same driver offset instead of 0.217 help reduce the ripple?
4. Based on the quarter wave principle (as in my probably mistaken understanding) since the BiB pipe (with its huge internal volume) is tuned significantly lower than the driver Fs, would a 1 mm Xmax driver not be at great risk of over excursion at its Fs even at 1 watt? How does such a low sub-Fs tuning support the cone excursion at Fs? Is there something i have failed to see/consider?
5. Am considering a BiB for a 12" wideband unit. Fs = 50 Hz, Vas = 105 litres, Qts = 0.58, Xmax = 2 mm and Sensitivity = 95 dB/watt. Apart from the suggested pipe length of 136", the internal width will be 16.5" and the gross internal depth 22". - Using 12+18 mm MDF for the baffle and 18 mm MDF for the rest of the panels, would it call for a bit of internal bracing? Also, would it hinder the wave flow?
6. I listen in a room which is 16 feet x 22 feet x (H)12 feet, usually at a position not more than 5 metres away. If the speakers can deliver peaks of 100 dB per channel about 1kHz at 1 metre, it is good enough for me. - In the proposed plan above, given the 2 mm Xmax, would it be a silly idea to tune the pipe at 40 Hz instead of 50 Hz?
Would be greatly obliged if the experts can help dispel my confusion and offer their valuable insight! Looking forward to receiving something conclusive from Scott, Dave, GM!
Thanks in advance! 🙏
With warm & sincere regards,
sujat
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It's a parabolic horn, so going from dim memory; axial 1/4 wavelength + pipe end correction (0.61r) = acoustic pathlength (Fp) and if mounted against a sufficiently massive/rigid wall, then it's lowered 0.707x or in a corner 8/3pi x.
Original math: https://www.diyaudio.com/community/...ose-fostex-craft-handbooks.66173/post-1191596
I see others have gotten involved and I don't have Excel? anymore to run the spreadsheets or remember there being two different ones, so others will have to update us.
Original math: https://www.diyaudio.com/community/...ose-fostex-craft-handbooks.66173/post-1191596
I see others have gotten involved and I don't have Excel? anymore to run the spreadsheets or remember there being two different ones, so others will have to update us.
As GM said. Briefly going through the questions in order for a few extras:
- All sealed-throat expanding pipes are technically horns in that they have a 1/4 wave fundamental but assuming conical expansion, as the ratio increases & the throat size vanishes to a zero cross section, so you end up with an axial length double that of an untapered pipe. For maximum efficiency, horns are 1/2 wavelength long at the target Fb (i.e. 1/4 wavelength 1 octave below), which is where the 1/2 wave pipe reference comes in. This is ignoring end-correction & boundary loading etc. as GM points out above, which lowers the frequency to which the pipe is impedance-matched & boosts efficiency / reduces harmonic modes.
- Per the above & link provided
- It can, but location for a wideband pipe then becomes an issue, since in many cases that would put it on the floor. For shorter, higher tuned versions, some have been inverted with a floor-firing terminus, which allows the driver to be located at a reasonable head-height
- Depends where you're tuning it, since you're not obliged to use Fs -it's just the 'standard' / most common. Short version is 'potentially', but Xmax is only a quick & dirty guide to the linear operating region of the motor (definition unspecified) -it's not a mechanical limit (Xmech) or, usually, a barrier where on the one side you have Mordor (or Lancashire), and the other you have the sunlit uplands of happy cows, beaming children and Emilia Clarke serving drinks suitable to the weather & occasion (Yorkshire).
- A lot of bracing, especially with MDF. 😉 And no, it won't providing you orient it longitudinally & slightly increase Vb to compensate.
- I'd be inclined to tune it to Fs & leave it there, since the 1/4 wave tuning frequency is already about 25Hz notwithstanding end correction etc.
GM and Scott, thanks a lot for your kind and generous responses.
Will need some time to allow the inputs to assimilate. Will ponder over it and revert with a couple of offshoot questions which have taken form, once am relatively free.
Thank you for your enthusiastic, selfless service to this science of speaker design and to students like me.
Regards,
sujat
Will need some time to allow the inputs to assimilate. Will ponder over it and revert with a couple of offshoot questions which have taken form, once am relatively free.
Thank you for your enthusiastic, selfless service to this science of speaker design and to students like me.
Regards,
sujat
End correction is an adjustment needed due to the shift in loading & acoustic impedance at the terminus of the pipe; the effective acoustical [path] length is that of the pipe for its given geometry plus relevant correction which is taken as 0.61 (sometimes given as 0.6) * radius of the pipe terminus:
http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/clocol.html
https://en.wikipedia.org/wiki/End_correction
http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/clocol.html
https://en.wikipedia.org/wiki/End_correction
Thank you for the detailed pointwise explanations, Scott! A couple of offshoot questions to ensure i have understood your words well....
If a zero throat cross-section expanding pipe requires double the axial length than a straight pipe does for a quarterwave length at same tuning frequency, and also that such a pipe if kept shorter than double the quarterwave length would not help to reduce the severity of the harmonic modes, would it then be correct to understand that a conventional Voigt pipe structure (without mass loading, with zero throat cross-section & with a quarterwave axial length) would be a compromised ("half-hearted" - pun intended) structure as compared to the full axial length BiB structure, both in terms of efficiency and reduction of harmonic modes?
Didn't quite understand what it means by "that would put it on the floor". Could you please?
Quite well understood!
Well, the question was assuming that the pipe is tuned to the Fs of the 1 mm Xmax driver. So would the driver be at risk of over excursion in terms of its linear operating range? Would it deliver 100 dB peaks per channel at 1 metre at 1kHz without apparent distortion? Assuming a 94dB/watt sensitive driver.
Or,
Should the 1mm quoted Xmax not be a concern at all and worthy of being entirely ignored?
Was almost expecting it!
So what would you rather suggest if the internal bracing is to be entirely obviated or at least kept at a bare minimum? Different material?
Thank you once again, Scott! In advance.
Warm and sincere regards,
sujat
Pretty much, but then, we all have to pick our compromises, which can include practical issues like space etc. Some degree of mass loading (however it's achieved) is usually preferable for a shorter type however, both for tuning & helping to suppress harmonics though.
Well, assuming it's a conventional BIB pipe horn tuned to 1/2 wavelength of a given target (usually Fs, but doesn't have to be), think of the pipe dimensions for a moment. Now think of where a 0.416 or similar offset would put the driver. If it's the usual full height type with an upward firing terminus, the driver would be practically at floor level. Shorter variations of the BIB have been made that are inverted, & that allows an offset of roughly that to be at a more usable height.
At 1KHz, probably -you'd need to do some excursion modelling yourself to know for certain, but power demands fall rapidly > 500Hz and the box load itself isn't going to significantly affect driver excursion at that frequency.
Unlikely to be a major concern, but as noted, Xmax doesn't mean all that much -it was only ever intended as a quick & dirty guide to the motor's linear range, and there are multiple different methods of generating a figure for it, all of which give different results if applied to the same driver.
A high quality void-free multiply (Baltic birch, bamboo or similar) will help, though at these sizes some bracing is likely to be useful anyway.
Much belated update; I've historically mistakenly called any simple (Voigt) pipe horn as conical, but DMcB pointed out that a conical expansion where there is a parallel set of walls such as the BIB has makes it parabolic, which according to his Hornresp (HR) doesn't change the expansion audibly enough to matter in the few I checked, but IMNSHO we should still pay 'lip service' to being technically correct and wish I could 'magically' correct all mine across the WWW since going 'live' Christmas '94.
Something I don't recall checking though is if HR includes the parallel wall eigenmodes........
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Thank you, Scott! It greatly helps to clarify and corroborate my understanding which dawned through your earlier explanation.
Okay. It relieves a major concern now!
Your words remind me of many BiB speakers based on "1 mm Xmax" Fostex drivers where listeners are quite happy with the SPLs they are capable of without apparent distortion. Of course, if the pipe is tuned to Fs!
As you rightly say, Xmax is at the most only a simplified indicative number dependent on an undisclosed method of arriving at it which is not universally standard, and therefore, not a conclusively reliable number.