Transmission line speaker design – Acoustical labyrinth
What is a transmission line speaker ?
Also called acoustic labyrinth or maze, the transmission line speaker design is a type of enclosure that follows a simple concept, yet hard to achieve. The design is pretty straight forward, but the hard part is that there is 
no reliable software to model the enclosure results in an accurate fashion. Of course, you can model the dimensions and internals of the box, but the problem is the damping material. The transmission line speaker design relies on heavy use of damping material. The different types of material used, the amount, the thickness, the location where it is placed, all contribute to a different end result.
That’s why it is very hard to predict the result with a transmission line. The ways you can place damping material inside the enclosure are practically endless. How you do so, will dictate whether the enclosure will sound good or bad. Trial and error is key to making a good transmission line. This makes it difficult for a mass producer (which is the reason why you rarely see transmission lines in your local audio store), but some DIY-ers love to tinker, and the fact that the transmission line speaker design is difficult and time consuming, will only attract them even more.
How does a transmission line speaker design work ?
Transmission lines (TL for short) work a bit differently, compared to sealed and ported boxes. When you make a sealed or bass reflex enclosure (passive radiator slips into this category as well), you alter the resonant peak of the speaker. Transmission line just takes the back waves generated from the speaker, inverts their phase, and throws them back in front of the speaker, to combine with the front waves. This is the main principle around how the transmission line works. You have to understand that this is just the concept behind how the transmission line is designed. You will soon discover, that TL has some serious problems with resonant modes, which need adequate damping.
Here is how to design the transmission line :
- Take your speaker and find out what is the resonant frequency in free air (Fs).
- Find the corresponding wavelength for that Fs.
- Find the length of the transmission line by dividing that wavelength by 4 (the quarter wavelength).
- Make a path from the back of the speaker to the front of the speaker, which is exactly the length you just calculated.
- The path can take different shapes. A labyrinth is popular because it saves spaces (so enclosure doesn’t get enormous).
- Damp the path with different materials of various thicknesses.
- The damping material will absorb the upper frequencies, which introduce some resonance problems.
- If the upper frequencies are successfully absorbed, all that is left is the low frequencies from the back of the speaker, which will combine with those in the front.
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These are the general milestones you need to go through, when you are designing and building your transmission line enclosure. Of course, there are other things to worry about, but let’s just keep it simple for now, so you can get the main idea on how the transmission line speaker design works.
What shape should the line be ?
Various shapes are available for you to choose. Using different techniques will yield different results, but sometimes the physical aspect is just plain ugly. Most of the time, you cannot turn a blind eye to this issue. One of the first transmission line speaker design, featured a pipe to guide the back waves. The length of the pipe was 25% of the wavelength of the resonant frequency (Fs) of the speaker. The diameter of the pipe was in correlation with the diameter of the speaker. To be more exact, the cross section of the pipe was equal to the Sd (cone area + half of surround) of the speaker.
I know this is hard to imagine, because you probably never seen such intricate design. No boxes, no baffles, just a pipe which is attached to the back of the speaker, at one end, and the other end pointing in the same direction as the front of the speaker. You could make the look more industrial, and fit them in an steampunk style room, otherwise, you will have a bad time explaining those “speakers” to your wife.
Line shapes
While you could be a little eccentric, and make a transmission line using just a pipe, reason will guide you to more traditional solutions. Here are the usual shapes for the line :
- Straight line.
- Tapered line. Line larger near the speaker and narrower near the exhaust (like an inverted horn).
- Flared line. Line is narrower near the speaker and larger near the exhaust (similar to horn).
- Folded versions of the previous mentioned types of transmission lines.
There are studies made on the transmission lines we just mentioned, without damping material, and here are the conclusions :
- All types suffer from resonant response anomalies above 100 Hz.
- Tapered line lowers the f3 of woofer, which makes it an attractive line design.
- Folding the line will reduce the upper frequency response anomalies.
- Folding the line will also increase the f3, but insignificantly
- Flared line raises the f3 of the woofer, which practically excludes it from the selection.
Folded lines
When you are folding the line, like in the above examples, you are essentially making the box more compact. Let’s say, your line needs to be 2 meters long. A straight 2 m transmission line would be ridiculous. To decrease the length you will have to fold the line. On the other hand, it will increase the height or the width (depending on how you design it), to make it a bit more proportional. Tapered line is a popular choice among those who wish to make a transmission line enclosure, because of the several benefits we mentioned earlier.
To make the enclosure an acceptable size and shape, the tapered line is folded in such a way, that is similar to folded horn, but in a reverse manner. Folded horn, shapes a path for the back waves to travel from a narrow opening to a larger one (at the exit). Folded tapered line, is the other way around, starting from a large opening (near the speaker), and leads to a progressively narrower path, till the exit.
Another advantage of folded lines is the direct effect on the overall sound quality. There needs to be some kind of phase correlation between the speaker and the exhaust. In a perfect world, they would radiate sound from the same spot. Since that is not physically possible, compromise is the solution. The two need to be firing in the same direction and need to be as close as possible to each other. Now imagine a straight line, which has the port and the speaker on opposite sides, leading to a significant non-correlation.
Damping materials and techniques
The damping of the line is an important step in achieving a successful transmission line speaker design. The purpose is to eliminate the anomalies caused by the upper frequencies. As the line gets more complex, and factoring the numerous types of damping materials available, we can conclude that the damping possibilities are endless. Regardless of that, we can make a few observations that happen consistently, when adding more damping material.
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Increasing the density of the damping material has several effects :
- Smoother frequency response (as the high frequencies are absorbed).
- Exhaust output decreases.
- Impedance becomes progressively damped.
- F3 increases.
This is somewhat similar to the effects of damping a sealed box. Using damping material in a sealed box, alters the speed of sound, which is similar to making the box bigger. This decreases Qtc, which makes roll-off smoother and increases the f3. If we make a quick analogy, we can conclude that by damping the line, we are changing the speed of sound, thus we can make the line shorter for similar results. While this is true to some degree, in practice it is better to keep the line length at the original dimensions.
Types of damping materials
There are various materials which can be used to damp the line. Depending on the material, you will have to use different quantities, because they have different densities. The whole point of the damping material is to reduce the ripple as much as possible. Considering ±1 dB of ripple acceptable, here are the quantities needed to reach this effect, for different materials and different path lengths. This data was confirmed to have some consistency over various trials with tapered lines.
All of these materials will work well in suppressing the upper frequencies. If you use the correct quantities they will have a similar effect. What is not so similar is the effect they have on the overall frequency response. This is the part that is hard to predict, because there are a lot in inconsistencies in overall frequency response when using damping material. Because of this, the conclusion about which material is better is purely subjective. Experienced transmission line builders will rank long-fiber wool as one of the best damping materials for TL, followed by Acousta-stuf. Polyester fill and fiberglass will yield inferior results. Again, these are all subjective conclusions.
Another variation of damping is to place different materials along the line. Starting with lower density near the speaker, and progressively increasing the density of the damping material as we reach the exit. Not uncommon is to leave the last 20% of the line without damping. Final tuning will result in just making adjustments to the last few feet of the transmission line.
Conclusion
The transmission line speaker design is definitely something that is more on the exotic side. Pretty difficult to design, to build and with no guarantees for the end result. I have to mention that there are more line shapes out there that have been studied (like coupled chamber and offset lines), which I didn’t cover in the article. The subject is very vast, with lots of unknown variables. This is definitely not the enclosure you should try if you are an absolute beginner. However, if you have some speaker building skills, love trial and error, and wish to work for your prize, then I encourage you to try it.
References
- Loudspeaker Design Cookbook 7th Edition by Vance Dickason (Audio Amateur Pubns, 2005). (Amazon affiliate link)
- Image source : link.
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51 comments
Thanks, good article. I am designing a hybrid design which uses Passive Radiators, multiple drivers, a port, and a labyrinth for a subwoofer. I plan to finish and test it in a couple of weeks. I will let you know how it goes. Came across th design through a lot of thought and research. I built a Transmission Line 30 years ago, with a large enclosure, folded line, it worked very well.
Good luck with your project and let me know how it goes!
Hi Reginald,
I would like to know a bit about your TL design. I am happy to sign a non-disclosure.
I am a retired real estate developer in the Salt Lake area of Utah. I maintained a custom home theater business in conjunction with residential housing I represented.
This interest is lifelong. I have built and developed stereo-home theater systems/TL loudspeakers.
I’d be happy to share anything perhaps helpful to you!
Respectfully,
Greg Vandenberghe
11497 S. Kestrel Rise rd.
South Jordan, Utah. 84009
gvdb52@gmail.com
First of all stuffing does not reduce speed of sound.
TL can be designed by the models from Martin J King. There is no mysterious about a TL just several parameters to use in the design process.
Hi
Actually, it does. The technical term is isothermal propagation. Pressure and temperature are correlated (for example if pressure goes up, temperature goes up). In our case, we talk about sound pressure. Now, when we add dampening material into the mix, it creates this isothermal environment to some degree. This material, although not a good temperature conductor, it conducts temperature better than air. In this case the pressure drops, which means the velocity of sound drops.
Designing a TL might sound easy on paper, but when actually building one, you will encounter some difficulty, because they are very unpredictable.
Actually, when air passes through any constriction (a tapered tube, in this case) the velocity increases and the pressure decreases. It’s the Venturi effect.
Ok just to correct the stuffing argument . the temperature change changes air density thus resistance to travel .. but in a speaker its not enough to make a real difference .
The stuffing itself doesnt change the speed of sound it changes the distance the sound has to travel.. it now has to weave its way around the fibers thus increasing the distance at has to travel and making making the box actually longer as far as the waves are concerned .. like swimming over waves and swell vs swimming on flat water .
Using the models done by Martin J King shows that stuffing has close to none effect of the tuning frequency. In best case it will drop 1 or 2 Hz.
Can you use PVC pipe for a folding line..
You sure can.
Martin King and George Augsberger both have come the conclusion that the speed of sound does not differentiate with stuffing densities, it’s very minimal. I’ve used both of their programs and the results are very preditable. The group delay, bass depth and lower room mode reactions due to shallower roll off are superior in everyway to a Helmholtz system.
can someone make a step by step math guide . I would like to build a 3 way t-line with 8″ woofer, 5-1/2″ mid and a tweeter. please with musical notes on top 🙂
i finally built one,it actually fit behind the seat of my truck,2 8in cerwin vega subs,tapered line.it hits hard ,low and clean.range is great it doesn’t seem to be as sensitive to temperature an a bandpass can be .i am very pleased with it ,i will build another one with some better speakers,maybe one 10 or 12 or 3 8s but with 2 my trucks door has lost its locking rod,outside door handle rod and all incandescent bulbs have shaken and quit
I’d like the dimensions of your box to help me build a box for a vfl 8″ I have if u have the time any help would be greatly appreciated.
Hi there, your table of “Quantities of different damping materials needed to reduce ripple to ± 1dB” is clearly ‘adapted’ (without reference, thank you very much) from Augspurger (J. AES, 48(5), 2000, p 424). Where George Augspurger provided clear recommendations for stuffing densities (in mass/volume), you mumbo’d it into mass per area …? Perhaps this was intended to illustrate the “hard to predict” nature of TL stuffing requirements, but this is in no way helpful, I am afraid.
Actually, I got the numbers from Vance Dickason’s book, and you can see the reference at the end of the article. Probably he got the numbers from the JAES paper you mention.
I see, perhaps the confusion was introduced in mr. Dickason’s book. Anyway, somewhere along the line information was lost. My basic remark remains the same: from a clear indication (mass of stuffing per volume) to an unclear mass per unit of area (with another problem: what area ?).
Marius Great piece of work shame people try to pick it to pieces I have built dozens of speakers over the years and made a sub woofer before the existed, and I have owned almost every type of design and make I think just build it !! We have lost the do it your self innovation in so many computer modeling is close but close only counts in horse shoes and hand grenades
If you are using purely as a subwoofer with a roll off above 80hz, do you even need stuffing at all? At what higher frequency ranges do we worry about It discoloring the output of the line?
That’s pretty much the max spot. And you would need something with a very steep roll-off curve like 48 dB/Oct, active filter. It might work without stuffing that way.
Hello! What is the most difficult thing to achieve that takes tje most tinkering? The labyrinth or the damping? Thanks!
The damping of course. It might not come out like you want it at first and you have to try out different materials in different positions of the line.
I’m confused as to why the line length would be 1/4 the resonant frequency rather than 1/2. Wouldn’t the half-wavelength be in phase with the front-directed sound waves?
That is the sweet-spot, at 1/4 or 3/4 wavelength (but 3/4 is too long and impractical). You have to understand that there are other frequencies exiting the line (not just the resonant frequency of the driver)
I think you must realize that you don’t want to boost the resonant frequencies, right? They’re already too high in amplitude (read: loud.) What you want is to carry – for lack of a better term – the antiresonant frequencies to the front.
I don’t know what you mean by antiresonant but bear in mind that the line is quarter wavelength. If you really want to boost the resonant frequency the line should be half of wavelength (of the resonant frequency).
Exactly my point Marius. There are likely several peak resonant frequencies in addition to Fs. In order to achieve the flattest response, we wish to boost -bring in phase to the front- the frequencies which correspond to the valleys in between the peaks. This is why we choose 1/4 wave and not 1/2 wavelenth of Fs.
I build tL enclosures often now, i find them to be superior for behind and underneath seats in trucks. You can get a great deal of high quality bass with just a pair of 8″ drivers or some 6″ subwoofers. I never damp the pipe. I feel as though I dont need to because I am using active crossovers to cut freq’s above 80hz anyhow. here is my simple equation.
speed of sound divided by FS of subwoofer= length of full wave in feet.
full length of wave, divided by 4 multiplies by 12 gives you the length of the pipe in inches.
i will you an fs of 30 as a base.
1125/30=37.5 37.5/4=9.3 9.3×12=112.5″
i equal the pipe area as close to the actual cone area of the drivers as possible and keep the that cross sectional area as close as possible the entire lenght.
This is my winning TL design when building a folding style TL design.
If you deviate from Sd it will merely create a proportionally different output level for total volumne(2x displacement yields 3dB). So changing the crossectional area from Sd isnt a deal breaker, especially
When tapering yields a wider bandwidth(with less output for given volume) and expanding yields a higher output while narrowing the bandwith(for same displacement).
thanks for posting this information it’s a big help to me.
Marius Tanasescu what is your contact email address I have to get one TL speaker rebuild with there crossover.It will be nice if you can share some input about it.
You can find my email at the end of each article, in the contact us section. Don’t want to write it here as it will attract spam bots.
Can tilting the woofer(s) mount (baffle) to 70 degrees to fit the depth of the magnet in a ‘skinny’ cabinet also result in the minimizing of standing wave formation within the parallel confines of conventional designs(rectangle)?
Also, in a ‘taped’ version of the 1/4 wave cabinets is there a basic guideline for speaker placement to compliment the combined output at the terminus(mouth)? Like an offset (1/3-1/5)stub in the line can reduce 3/4,5/4,7/4…. resonants, is the geometry of the ‘taped’ configuration have a generic reference(length from mouth exit and length from throat entrance)? Thanks, Great website!!
Yes, having a panel at an angle will reduce standing waves. Regarding the shape of the taper, you can think about a horn in reverse. A horn start from small to large. A tapered transmission line is the other way around, from large to small. The development of this taper, can have different shapes, just like a horn : conical, exponential, hyperbolic etc. You can study horn design and do the transmission line in reverse.
Hello Marius. Very interesting article. I have a few questions. If i use a smaller diameter pipe than the Sd should i increase it’s lengh? I am planning on actually using a pipe same like the link in your article and i would rather have a longer thinner diameter pipe than a short wide one. If the pipe would terminate in a cone would that improve sound characteristics? Can you share some other book titles apart from the referenced one or online calculators? Thnx
If you want large diameter, you have to make the port longer (in order to maintain the same tuning frequency of the box). This is better sound-wise but as you increase the diameter, the port needs to be longer and longer until it won’t fit inside the box anymore. So, there are some limitations. And yes, flaring the ends of the port will result in less air turbulence. If you want to learn more you can check out my course page : https://audiojudgement.com/courses.html
The first Acoustics 101 course should be enough for what you want to achieve.
I am thinking outside the box :). I do not want to build the speaker into a box. I want to employ a small chamber for the speaker with pipe coming out of it like a maze and to also support the speaker like a piedestal if you can imagine what i am saying. But a longer pipe would not be quarter wave anymore. What about 3/4 wavelenght? Would that be alright?
Yes, that is the theory of the transmission line. To make is 1/4 or 3/4 of the wavelength of the resonant frequency of the driver. No one makes it 3/4, because there is no reason to make it longer than it needs to be. But since your project needs a long line, you might as well do it.
Very interesting discussions. I designed a transmission line years ago. Lots of trial and error but the end result was worth it im my view. As far as the speed of sound is concerned I took a simplistic view that the stuffing fibers actually move with the air molecules back and forth increasing the effective density of the air and hence lowering the speed of transmission of the wave altering the tuning. My trials seemed to bear this out. I think it is important to realize that the air doesn’t travel through the labyrinth, only the pressure waves.
You are absolutely right. Air molecules vibrate, and pass on the vibration to the air molecules near them. When air molecules move, that is basically wind.
In retrospect I have to agree with Bjorn Johannesen’s comment earlier where he says the speed of sound is only minimally affected by the acoustic fill. Since the Martin J King alignment tables do seem to calculate the required length of the line accurately regardless of the amount or density of the fill then the speed of sound must remain effectively the same.
Dear Sir
Thank you, i can learn more about TL box speaker
Keep to the simple formula of 1/4 .
Folded turns need to be precise in keeping your diameter. Follow these simple steps and with the fee I’ve built no dampening needed. Sub in the center of the face has given be better sound but both positrons seen to work. Been a machinist for 20 years(metal). My first enclosure I made was a tline for an older JL 12w1 2-4 in a tundra . Sounded better than most 2 15” applications hitting in the low 20hz very accurately all the way up to 80. Love these enclosures. Take your time do your math and your results will be quite pleasurable!! One last thing finding the SD on drivers is usually my only issue anyone got any hints on locating or measure on my own will be appreciated!
To measure Sd, you simply take a ruler and align it across 2 opposing screw holes. This will ensure you are measuring the diameter and not some odd line across the circle (speaker driver). To measure the effective diameter of the speaker you have to choices : 1) Measure from the middle of the surround on one side to the middle of the surround on the other side; 2) Measure from the exterior edge of the surround on one side to the interior edge of the surround on the other side. After that, you divide the diameter by half, to get the radius (R). Finally Sd = R x R x 3.14
I notice designs that show tweeters that aren’t boxes off. I realize most tweeters are somewhat closed in the back. I’d guess any of those high frequencies that are in the TL will cause problems and should be removed by closing completely?
Thank you Marius for posting this. Very interesting and helpful. There is one detail though, that I am not getting. You explained:
“the cross section of the pipe was equal to the Sd”
but then you go on to say that tapered TLs are generally preferred to parallel pipes. So what should the cross section of the tapered pipe be? Presumably the exit port must have some diameter, and the cross sectional area next to the driver can be larger than Sd? Does that mean that the average cross section of the pipe (calculated over it’s entire Fs quarter wavelength) should be equal to Sd? How small can the port be, if its cross section is to be a fraction of the area at the driver end? Perhaps a “counterflare” should be built into the pipe at the exit to reduce port noise?
Well it’s a bit more complicated. These are some general tips. Normally you would need modeling software as T-lines are pretty difficult to pull off. But to answer some of your questions: Easiest way is to have the line area the same size as Sd. This way you will be the most efficient with the size of the box. Making the pipe larger is no problem, but you are making the box unnecessarily large and in my experience the response is slightly worse (just slightly). A tapered t-line goes from large to small (smaller than Sd at the exit). Having a smaller than Sd straight pipe is not something you want to do. And a small to large t-line is basically a horn. You are asking me about rations between the area of the beginning of the line and the end. I have no idea. The response needs to be modeled in Hornresp or some other software to check if you are doing something right.
If you want to make a T-line without modeling software I suggest to make a line, same area as Sd, quarter wave length long of Fs, and place the driver 1/3 of the way along the line. Don’t place the driver at the beginning of the line. Fill the first 1/3 of the line with high density damping material and you pretty much have a high chance of making a successful T-line.
Thank you very much for that info. I will have to look into Hornresp.
What I am proposing to do is *very* unconventional. It’s more that I am going to be building the box in any case, so I will have a lot volume which I might as well use as an enclosure for a pair of subwoofers! I can lay out the t-line pretty much any way I want. But I greatly appreciate that insight about placing the driver 1/3 of the way along the line, and using high density fill in the first third of the pipe.
Actually my idea is to build a raised platform for the rear of the home theater — so that there can be two rows of seats with a decent view of the screen. I am thinking to build a very heavy and sturdy platform and use it to enclose the subs! My biggest concern is how to prevent dirt and stuff falling into the drivers! One possibility is to mount them in bottomless cabinets, attached and sealed directly over holes in the platform–holes which are the entry points to the t-lines. Sounds crazy I know, but it’s all part of trial and error!
Dear
Sir
I am thinking to make cabinets with 2 woofers.
Can you please give me some advice ?
Value of Sd and length are should stay at for 1 speaker or double?
I will be very thankful.
Regards
Jeff
Fs is the same, so length is the same. Sd is double though.
I understand that for ported enclosures, as port cross sectional area gets bigger, the port must be longer to conserve the tuning frequency. Hypothetically, at some point, the port will need to be as long as 1/4 wavelength. Suppose you build this folded port “outside” the box (main chamber). How would this box with a very long folded port attached compare against a proper T-Line? Will they behave similarly or differently?