There are 2 ways of tapering a transmission line: expanding and diminishing. Commercial ones, and older diy ones are decreasing cross section to the open end. But almost all of the present day diy MLTL are of the expanding variety. In the Martin King site he shows that a diminishing pipe can be much shorter than an expanding one, and shows that there are fewer (though possibly deeper) harmonic resonances and suck outs.
So my question is why is the expanding line the more popular?
So my question is why is the expanding line the more popular?
They aren't. I think you are mistaking the terminology. Which isn't necessarily exact in all particulars.
-MLTL is a term coined for a straight (untapered) quarter-wave pipe, mass loaded by a restricted terminus.
-An expanding pipe is often referred to as a TQWT or TQWP (Tapered Quarter Wave Tube / Tapered Quarter Wave Pipe). These may mass loaded via a restricted terminus, in which case you'll usually encounter the ML prefix. They are strictly speaking conical horn variations, albeit not impedance-matched down to the QW cut-off frequency. Ironically enough, the TQWT terminology used to apply to the exact opposite geometry, i.e.
-Reverse (narrowing) QW pipes. These are inherently mass-loaded to varying extents (depends on the degree of taper).
All other things being equal, expanding pipes have a broader gain BW than untapered or narrowing, which within limits, can be useful depending on the requirements of the driver. As you would expect given that they are horns. Anyway, as far as relatively recent QW enclosures go, expanding pipes are not necessarily more popular at present, although they probably had an edge in those terms up until the first years of this century. As for reverse taper lines, there isn't often much reason to use them now, since you can usually get similar results with a simpler MLTL. Not always, and as ever, it depends on the design requirements / goals, so YMMV.
-MLTL is a term coined for a straight (untapered) quarter-wave pipe, mass loaded by a restricted terminus.
-An expanding pipe is often referred to as a TQWT or TQWP (Tapered Quarter Wave Tube / Tapered Quarter Wave Pipe). These may mass loaded via a restricted terminus, in which case you'll usually encounter the ML prefix. They are strictly speaking conical horn variations, albeit not impedance-matched down to the QW cut-off frequency. Ironically enough, the TQWT terminology used to apply to the exact opposite geometry, i.e.
-Reverse (narrowing) QW pipes. These are inherently mass-loaded to varying extents (depends on the degree of taper).
All other things being equal, expanding pipes have a broader gain BW than untapered or narrowing, which within limits, can be useful depending on the requirements of the driver. As you would expect given that they are horns. Anyway, as far as relatively recent QW enclosures go, expanding pipes are not necessarily more popular at present, although they probably had an edge in those terms up until the first years of this century. As for reverse taper lines, there isn't often much reason to use them now, since you can usually get similar results with a simpler MLTL. Not always, and as ever, it depends on the design requirements / goals, so YMMV.
TQWT used to refer to a narrowing pipe. I suspect GM and I are the only people who use that definition any more though. Alas.
As I stated above, a tapered / reverse taper (narrowing toward the terminus in the parlance employed above -the term 'taper' itself is problematic in that it depends whether you're using the throat or terminus as the baseline criteria) pipe is inherently mass loaded. So yes: it is close in that sense to an MLTL, particularly if a high taper ratio is employed. There are always exceptions, but generally speaking, there isn't all that much reason to use one over an MLTL if you're after LF gain.
As I stated above, a tapered / reverse taper (narrowing toward the terminus in the parlance employed above -the term 'taper' itself is problematic in that it depends whether you're using the throat or terminus as the baseline criteria) pipe is inherently mass loaded. So yes: it is close in that sense to an MLTL, particularly if a high taper ratio is employed. There are always exceptions, but generally speaking, there isn't all that much reason to use one over an MLTL if you're after LF gain.
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So, just so that I can nail this:
if the Fs of a drive unit is, say 50 Hz, and the un mass loaded length of the line was "x" to match it, would mass loading the line lower the response of the combined speaker/box to say 45 Hz.
Or would the response stay at 50, and the line would need to be shortened to match 50 Hz.
if the Fs of a drive unit is, say 50 Hz, and the un mass loaded length of the line was "x" to match it, would mass loading the line lower the response of the combined speaker/box to say 45 Hz.
Or would the response stay at 50, and the line would need to be shortened to match 50 Hz.
Could you give an example where a TQWT (your definition) would have a desirable advantage over a comparable MLTL? I realise this may be a broad question. I came up with a TQWT for FF165WK that sims quite well in HR sometimes last year, so I'm wondering. I know there's at least Bob Brine's design out there as for MLTL.
S0= 7"x7"
SL = 7"x1.5"
L = 48"
Vb = 22L
Fb = 48Hz
f3 = 48Hz
driver offset ~1/3
IG
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Depends on circumstance & what you're trying to do. They can be useful for heavily damped mid-lines for e.g. (as in approaching a TL in the strict sense of impedance flattening), or for hitting a damped alignment with a given volume when a vent might be of impractical dimensions. Or if you simply don't want to use a duct.
This may seem naive (probably because it is), but why don't all MLTL designs include a means of specifically directing waves down through the pipe or column so there is less direct reflection from the back? (e.g. an internal panel that runs from the top to the back at 45 degrees like you see in some horns)? Since most designs lack this kind of sound directing panel then I can only conclude that my understanding of how MLTL's work must be deeply flawed.
The wavelengths involved are really too long to be so "directed" and the pipe modes will dominate AFAIK. The resulting column of air can be driven from any point along its length and this is often used to good effect with driver placement at 1/3 or 1/5 down from the closed end. The main QW mode is used for bass reinforcement, while the harmonic modes (3/4, 5/4, 7/4...) are suppressed with driver offset and stuffing. So we can see that any frequency that would really be directed by a slant reflector is already dealt with by other means.
It really helps to read MJK's various papers. Multiple readings may be required, I know it was/is for me. I ought to flip through these once more, it's been a while.
IG
It really helps to read MJK's various papers. Multiple readings may be required, I know it was/is for me. I ought to flip through these once more, it's been a while.
IG
Basically as above, and since MLTLs are damped, this usually is sufficient to kill reflections back through the cone in a competent design. You can use an acoustic or golden ratio if you feel so inclined as well, although in many cases a square cross section is fine. An MLTL is also untapered, and adding an angled panel would add taper. 
Apologies, perhaps i misunderstood your explanation Scott. I'd still call a horn a reverse taper, perhaps that's just me ��.
In my own 18:1 taper QWP I noticed some degree of mass loading, subjectively at least, and often wondered what difference, if any, would be the result of converting it to a straight MLTL.
I understand the taper spreads/bunches the higher pipe modes. Isn't that a benefit/difference from a straight MLTL?
Yeah, and AFAIK I'm the one who first used the term 'reverse' around here to delineate between straight and the traditional tapered TLs, but not too long ago it was pointed out to me that since we're fundamentally describing a mathematical problem, the correct term is 'inverse', so what I use now.
GM
Hmm, the response will for sure be lower and if by 'x' you mean its path-length is a 1/4 WL of Fs/whatever, it will de facto be tuned too low even without the added vent due to its terminus end correction that makes the pipe a bit longer acoustically than its physical length and why venting any type of TL alignment using a BR's simple Helmholtz calculation always turns out much lower than predicted.
If it doesn't, then the cab's height:[width x depth] aspect ratio isn't acoustically high enough to support TL pipe/horn action.
GM
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