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 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

Assume we have a driver with an fs of 50 Hz and it is installed at the closed end of a straight TL tuned to 50 Hz, the simplest form of TL design. The TL will produce standing waves at the 1/4, 3/4, 5/4, … frequencies of 50 Hz, 150 Hz, 250 Hz, … as expected. Neglect the acoustic impedance at the open end or terminus and assume the TL is completely empty so there is no damping of any kind. At a standing wave resonance, the back pressure on the driver cone will attenuate the motion, almost stopping the driver like in a BR design, and almost all of the SPL output will be from the terminus, like the port in a BR enclosure. The SPL and phase of the outputs will behave as follows.

Well below 50 Hz – as the driver moves into the TL it displaces a volume of air and an equivalent volume of air is pushed out of the terminus. The driver and the terminus are 180 deg out of phase and the SPL almost cancels producing a 24 dB/octave roll-off below 50 Hz.

At 50 Hz – the 1/4 fundamental standing wave is excited, the driver motion is significantly attenuated, and most of the SPL output comes from the terminus. The driver and the terminus are 90 degrees out of phase.

At 100 Hz – the driver and terminus are now in phase. There is no standing wave and the SPL from the driver and terminus are equal. This is because sound radiated from the back of the cone is the same as from the front of the cone but 180 degrees out of phase, the sound traveling down the TL is constrained so it does not decrease with distance, and the distance it travels is equal to a half of a wavelength (another 180 degrees). Theoretically, the system SPL will be 6 dB greater than the driver’s SPL in an infinite baffle.

At 150 Hz – the 3/4 standing wave is excited, the driver motion is again significantly attenuated, and most of the SPL output comes from the terminus. The driver and the terminus are 270 degrees (-90 degrees) out of phase.

At 200 Hz – the driver and terminus are now out of phase. There is no standing wave and the SPL from the driver and terminus are equal. This is because sound radiated from the back of the cone is the same as from the front of the cone but 180 degrees out of phase, the sound traveling down the TL is constrained so it does not decrease with distance, and the distance it travels is equal to a full wavelength (another 360 degrees). The driver and the terminus are 180 deg out of phase and the SPL almost cancels producing a deep null, maybe this is what the measurements are showing.

The phase and SPL pattern repeat as frequency increases and moves through the higher quarter wave frequencies. Below is a list of key frequencies and the phase differences between the driver and terminus.

10 Hz – 180 deg SPL --> 0 dB

50 Hz – 90 deg fundamental 1/4 wave and SPL mostly from terminus

100 Hz – 0 deg SPL + 6 dB

150 Hz – 270 deg (-90 deg) 3/4 wave and SPL mostly from terminus

200 Hz – 180 deg SPL --> 0 dB

250 Hz – 90 deg 5/4 wave and SPL mostly from terminus

300 Hz – 0 deg SPL + 6 dB

350 Hz – 270 deg (-90 deg) 7/4 wave and SPL mostly from terminus

400 Hz – 180 deg SPL --> 0 dB

The pattern repeats in steps of 50 Hz. I hope that is clear.

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 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

https://pmc-speakers.com/technology/atl

The commentary says it's tapered, but the cut-away doesn't look tapered to me.  Mixed in with the advertising copy, there are little technical nuggets dotted throughout the 3 mins.