TransmissionLine 1/3 1/5 Question

[theSuede]

So.... Tapering a transmissionline lowers the fundamental resonance frequency a bit - by affecting the way the pressurewave converts from pressure (closed end of line) to velocity (open end of line) - if I'm understanding the principles of this right.
I have a transmissionline that is 170cm long, that has a linear taper from 2:1.
The question I would like to ask is this:

WHERE on the line is the 1/3 point located? (in reality, concerning acoustic properties...)
Do I have to compensate for the taper in any way, or do I just do the maths (170cm / 3 = 57cm)?
Or should I integrate with respect to line area and suppose that the 1/3'd point is actually closer to the wide end of the taper? (linear maths then give me that the "area-compensated" 1/3-point is at about (170x0.268) = 46cm down from the closed end?)
This seems to me to be the better way - don't ask me why, just a hunch...
My guesstimate would be somewhere in between. Again, just a hunch.

Or am I overlooking something here?

Redoing the baffles will be a lot of work for me, so I would really like to get as close to acoustic target as possible.... Does anyone know how to do this, or does someone have experience with offset drivers in tapered TL's?
All help and comments appreciated!

/Joakim

[GM]

Originally posted by theSuede
WHERE on the line is the 1/3 point located? (in reality, concerning acoustic properties...)

Or should I integrate with respect to line area and suppose that the 1/3'd point is actually closer to the wide end of the taper? (linear maths then give me that the "area-compensated" 1/3-point is at about (170x0.268) = 46cm down from the closed end?)

Greets!

Your hunch is correct up to a point, though it's not as simple as using linear math since we're dealing with pressure waves. Anyway, MJK has done the math for a variety of taper ratios including 2:1 in his Classic Alignment tables: http://www.quarter-wave.com/Theory/Alignment_Tables.pdf

GM

[theSuede]

It would seem that the 1/3 point is almost exactly 1/3 LENGTHWISE down the line...
Okies, thanks for the link and the info!

Greetings from Sweden... / Joakim

[GM]

You're welcome! Not hardly, if you read the text it tells you that it's at the 3/4 WL, not 1/3, point acoustically. I don't recommend it, but if you really want it at the 1/3 WL point (much more stuffing required), then you'll have to do the wave equation math AFAIK to find it.