Adventures modeling a tower as a TL
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 Multi-Way Conventional loudspeakers with crossovers

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 26th May 2018, 12:23 AM #11 cyberstudio   diyAudio Member   Join Date: Mar 2018 Location: Burnaby, BC Sorry... I tried a sealed box first and then added a port to it and see how it went. BTW, incidental to this... Is the length of a ML-TL still 1/4 wave? Anyway please forget the 0.48 figure. For sealed and for vented where the air volume in the port is insignificant compared to the box volume the optimum position is 0.5. This is based on the assumption that higher harmonics are easier to absorb by stuffing so the aim should be to eliminate the first harmonic. Last edited by cyberstudio; 26th May 2018 at 12:39 AM.
 26th May 2018, 04:03 AM #12 GM   diyAudio Member     Join Date: Jun 2003 Location: Chamblee, Ga. 0.5 is optimum for a closed pipe; add a vent and it shifts to an odd harmonic, though it shifts down the pipe a little due to the vent, so 1/5 = ~0.21, 1/3 = ~0.349, 2/5 = ~0.424, which is as far down as one would normally want to go for a straight pipe. Vents work well at 4/5 = 0.848 and near/at the bottom as Paul noted. Re a typical cubic or rectangular cab where its air mass has a ~uniform particle density, driver down ~0.424 is optimum for both sealed, vented and the vent can be anywhere on the cab since it's a simple Helmholtz regulator. Yes, it'a 1/4 WL resonator and the vent is a 1/2 WL resonator. Note that for a MLTL to get enough vent damping to audibly effect vent length [shortens it compared to predicted for a given tuning], the cab needs to fairly long, so look for at least a 5 Hz lower tuning than predicted for a simple reflex. The 60+" cabs I normally spec usually require going to a much larger vent just to be long enough as a hole in ~3/4" thick baffle. GM __________________ Loud is Beautiful if it's Clean! As always though, the usual disclaimers apply to this post's contents.
 26th May 2018, 04:59 AM #13 cyberstudio   diyAudio Member   Join Date: Mar 2018 Location: Burnaby, BC Wow, that was exactly the information I needed. Thank you!!! May I ask one more question? Is there any rule saying the cross section along the entire line must exceed 1 * Sd at any given point? (It was just my intuition that otherwise the line will be operating as a horn-loaded compression driver in reverse, so maybe it is just me making this up.)
 26th May 2018, 05:05 AM #14 planet10   frugal-phile(tm) diyAudio Moderator     Join Date: Oct 2001 Location: Victoria, BC, NA, Sol III Sd has nothing to do with optimum cross-section. It turns out that for drivers that work well in TLs cross-section is considerably larger than Sd. dave __________________ community sites t-linespeakers.org, frugal-horn.com, frugal-phile.com ........ commercial site planet10-HiFi p10-hifi forum here at diyA
cyberstudio
diyAudio Member

Join Date: Mar 2018
Location: Burnaby, BC
Prompted by your valuable responses I tried to model standing waves in... LibreOffice.

The chart plots the sum of the first 10 harmonics but not all are given equal weighing. 100% for n=1, 90% for n=2, 81% for n=2, and so on. You would want to place the speaker at one of the minimums.

Long story short, the take away is, other than the beginning or the end, there is virtually no bad place to be.

The number of ripples in the sum has no significance. I added the first 10 harmonics so there are 10 ripples. It follows that if an infinite number is summed the ripples would average and become a straight line.

If I change the weighing so that it is 50% for n=2, 25% for n=3, and so on, the curve becomes a simple bowl shape, favoring placement at 0.5m.

If we give equal weighing for the first 3 and completely ignore the others, 0.21m is a great place to be, and that might have been where one of GM's magic numbers came from.

I have zero idea how the weighing is supposed to be assigned, and that obviously depends heavily on the stuffing (amount and type). All in all, this exercise explains why we were taught the cabinet dimensions must not be rational ratios of each other, but we were not typically told about any special position for driver placement, other than taking diffraction into account by offsetting.

If we have to find some magic numbers anyway, here is a list when we consider only the first n harmonics, giving them equal weighing, and ignore all higher ones above n. This may not be realistic as no stuffing material has such property, but is useful if you specifically want to minimize lower harmonics but ignore the higher ones.
1 or infinite: 0.5
2: 0.29
3: 0.21, 0.5
4: 0.16, 0.39
5: 0.13, 0.32, 0.5
Attached Images
 first10harmonics.png (62.8 KB, 153 views) halving.png (29.4 KB, 152 views) first3.png (28.1 KB, 80 views)

Last edited by cyberstudio; 27th May 2018 at 02:49 AM.

 27th May 2018, 02:17 PM #16 cyberstudio   diyAudio Member   Join Date: Mar 2018 Location: Burnaby, BC Another way to place the driver is to simply use any rational ratio, like 0.5, 0.33, 0.25, 0.2, 0.4, etc. Summing may reduce the overall result but may accentuate certain harmonics. For example, when position is at 0.5, n=1 is minimized but n=2 is maximized. Sometimes it may be desirable to even out the anomalies even though it may mean the total as measured by summation may be slightly worse (again, ignoring the higher harmonics). If that is the case, 0.25 and 0.4 look good, as can be seen in the 3rd graph. Last edited by cyberstudio; 27th May 2018 at 02:20 PM.
 27th May 2018, 06:36 PM #17 Jerms   diyAudio Member   Join Date: Jun 2015 Location: High Wycombe, Bucks, UK. One example to try in TL. Dayton DA175 120cm pipe, both ends closed. 308cm2 cross section. Port/branch of 32cm2 x 20cm @ 105cm/15cm. (68mm mini guttering downpipe in upvc). Stuff @ 3kg/m3 for the first 105cm. Play with the stuffing densities above 2kg/m3 to alter the "slope" of the bass output.. Try the driver at 30cm and at 57-58cm. With a single DA175 playing down to 30Hz, maximum SPL will be low (dependant on source material). group delay is quite low around 50hz however. Use it with a subsonic filter or with most music and it'll be fine. Or use it with a subwoofer for loud action movies. 2 way DA175 designs I have seen have been MTM. (Zaph audio bargain aluminium MTM). A single DA175 might be matched to a wide ranger like the FR58EX if SPL requirements are modest. i.e not a church hall. J.
planet10
frugal-phile(tm)
diyAudio Moderator

Join Date: Oct 2001
Location: Victoria, BC, NA, Sol III
Quote:
 Originally Posted by Jerms 120cm pipe, both ends closed. 308cm2 cross section. Port/branch of 32cm2 x 20cm @ 105cm/15cm.
Again contradictory information. The port makes for one end open.

dave
__________________
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Jerms
diyAudio Member

Join Date: Jun 2015
Location: High Wycombe, Bucks, UK.
Quote:
 Originally Posted by planet10 Again contradictory information. The port makes for one end open. dave

It's more LATL speak than the physics of pipe modes.

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