Just wave!

My understanding is that the strongest reinforcement from a transmission line is when line is 1/2 wavelength long. At that frequency, the backwave emerges from the terminus in-phase with the front wave, which gives full reinforcement. Unfortunately 1/2 wavelength lines are impractically large (and no, you can’t shrink the cross-sectional area significantly and still get good performance).

The lowest frequency at which the line is effectively reinforcing the front wave is when the line is about 1/4 wavelength long. At that frequency the backwave emerges from the terminus 90 degrees apart from the front wave, in "phase quadrature", which gives partial reinforcement.

Unfortunately at the frequency where the line length is equal to 1 wavelength, the backwave emerges 180 degrees out-of-phase with the woofer and we have a cancellation notch. Fortunately this notch largely disappears in the farfield response, but ime it is often still noticeable.

Various techniques exist to mitigate the 1 wavelength cancellation notch, including: Offsetting the woofer from the closed end of the line; incorporating a Helmholtz absorber into the enclosure; using a LOT of stuffing to absorb as much of that 1-wavelength energy as possible (and maybe using a high-Qts woofer so that the low bass is still strong); and using two woofers at significantly different locations along the line so that they are not both notching at the same frequency.

Incidentally no stuffing material, not even the best New Zealand lamb’s wool, slows down the speed of sound in the line to any significant extent.

I am NOT a transmission line expert; just happened to learn a few of the pitfalls the hard way.

Duke

Ime TL’s are very good in the midrange, as there is essentially zero reflection back into the cone. That may well be their biggest advantage.

As for where the terminus (line opening or vent) is located relative to the woofer I’m sure that makes a difference but haven’t really analyzed it. My instinct would be to spread them apart as far as is reasonably possible in as many planes as you can, in pursuit of modal smoothing. Like if the woofer is up high on the front, and the terminus is down low on the back, if you toe the speakers in, now the woofer and terminus are displaced relative to one another in all three dimensions.

But I cannot reliably say that’s the best strategy for choosing where the terminus winds up - other considerations that I’m not taking into account may dominate. For instance the internal geometry may matter more.

I remember delivering a pair of my rear-ported speakers to the home of a customer who was replacing transmission lines that had the terminus on the front at the bottom. One of the first things he commented on was that the bass was smoother with my fairly low-tuned rear-ported box. Whether that was because of the terminus location versus my port location, or my speaker’s freedom from the half-wavelength bump and/or one-wavelength notch, I do not know. I was surprised that my speaker was competitive with the transmission line in the bass region.

Duke

@mjking57 -

Thank you Martin, apparently I have some misconceptions. I hope you don’t mind if I ask a question or two.

I recall many of my primitive transmission lines of yesteryear having a distinct notch in the response that seemed to correspond with a line length of one wavelength. You can see what I assume is the same sort of notch in these measurements:

https://www.soundstage.com/measurements/pmc_gb1/

https://www.soundstage.com/index.php?option=com_content&view=article&id=775:nrc-measurements...

What’s causing that notch?

Thanks,

Duke

Thank you very much Martin for taking the time. Your last post makes sense to me.

I was having a hard time with the second half of this sentence:

"You cannot produce a half wave resonance and the output will never be in phase with the driver output. "

But this from your last post makes sense to me:

"At 100 Hz – the driver and terminus are now in phase."

So at 100 Hz (where the line length is equal to 1/2 wavelength) there is NO standing wave resonance, BUT the outputs from the driver and terminus are IN PHASE.

Have I finally got that right?

And "At 200 Hz – the driver and terminus are now out of phase."  (But there is no standing wave resonance.)  So IN THEORY at least, assuming a lightly-damped line, couldn't we get a cancellation notch in the summed response in that region?

Duke

Thank you for replying, Martin.

Those measurements were made in the anechoic chamber at the Canadian NRC, so I don’t think the notches are floor-bounce cancellations.

Both of the speakers in my links above are marketed as "transmission lines", and both are floor-standing two-ways with a small mid-woofer near the top and the terminus on the front near the floor.

https://pmc-speakers.com/products/archive/archive/gb1

https://pmc-speakers.com/products/consumer/twenty/twenty24

Does that shed any light on the source of the notch?

Also, could you clarify something you said for me?  "At frequencies where the TL enclosure is producing output from the open end the phase must be +/- 90 degrees with respect to the driver."

So is the output from the open end ALWAYS in phase quadrature with the output from the cone, regardless of the frequency? 

Or is it ONLY in phase quadrature at the quarter-wave resonance frequency? 

My apologies if I'm asking something that should be obvious.

Thanks!

Duke

Thank you once again Martin!  I REALLY appreciate your taking the time to go through and explain this to me and correct my misunderstandings.  Your example above of the 50 Hz line is extremely educational for me.  I had failed to appreciate that a standing wave occurs every time the line length puts its output at phase quadrature relative to the cone.  Imo this is valuable information. 

So now you have my wheels turning about making the enclosure deeper and putting the terminus on the back and using the path-length-difference (relative to the listening position) to help mitigate that one-wavelength cancellation notch.  What imo makes this approach promising is that, on either side of the one-wavelength frequency, we have standing wave resonances which shift the output primarily to the terminus, so there would be insufficient output from the cone itself for a cancellation notch.  I'd have to do some math to optimize it, but for now it looks like a possible window of opportunity.  Of course this isn't the only thing that would need to be juggled.

Duke