Transmission Line Speaker Project
Work In Progress
PART 1. Information Search:
The 1965 Wireless World article A non-resonant Loudspeaker Enclosure Design by A.R.Bailey is worth reading, there were several successful commercial designs based on this work, an example being the IMF TLS80, and a DIY variation is described in great detail in The Audio Amateur.
The Bailey article shows in Fig.4 the results of his comparison of different absorbent materials, suggesting a substantial improvement from the use of long fibre wool. There appears to be widespread dissent on this point, for example there was a slightly heated discussion at AudioKarma, but there is probably no need to worry too much whether wool has any advantage over polyester fibres, I have seen no suggestion that it could be worse, so if it is available there seems no good reason not to use long fibre wool. Availability may in fact explain part of the problem, a paper sometimes quoted to compare different absorbents is Loudspeakers on Damped Pipes by G.L.Augspurger which fails to include the recommended long fibre wool in tests on the surprising grounds that 'bulk wool is not easy to find in the US'.
Here in the UK we don't have that problem, here is an example of a source of wool products, World of Wool, which lists 35 different breeds of sheep together with their fibre size and length including Lincoln at 36-40 microns which would qualify as 'long fibre wool' and may be just what we need. The price of £1.60 per 100g (plus £4.95 delivery in UK) compares very well with Visaton lambs wool which I bought a while ago for another project, currently at £12.50 for 125g, said to be enough for 20 litres. I still have a pack so I will do a comparison (see Part.2). A commonly recommended stuffing density is around 8g per litre.
Another reference for the effects of fibre is by L. J. S. Bradbury, 'The use of fibrous materials in loudspeaker enclosures,' J.Audio Eng. Soc., pp. 390-398, Apr. 1976. I have a copy but it is not freely available online. The diameter of long fibre wool is specified by Bradbury as 28 microns, whether larger diameters have any advantage is not entirely clear.
Wool does have a few problems worth mentioning, it is not entirely flame resistant, but it compares well to some other absorbent materials, according to this Fact Sheet, also it should ideally be treated to make it moth proof. In time it has a tendency to sink to the bottom of an enclosure, so some method of support is needed.
In the Bailey design there is quite a large volume directly behind the bass driver before the start of the line, and this sort of arrangement can work as a low-pass acoustic filter, a technique sometimes used for bass horns where a cavity between the driver and the throat of the horn reduces high frequency output. Used with a transmission line this can reduce problems with higher frequency resonances in the line. I don't know if the same equation used for horns (Dinsdale Fig.7) is applicable, but for example it suggests a 5 litre 'cavity' feeding a 10cm diameter line will have a cutoff frequency around 80Hz, above which there is a 6dB/oct attenuation, which may be a good idea rather than relying entirely on stuffing to damp higher resonances. The cutoff frequency is proportional to the line area and inversely proportional to cavity volume. This is a well known technique, used in the Daline.
The analysis of acoustic filters usually only considers an expansion chamber inserted in a transmission line, for example at Filter Design and Implementation but the equation is almost the same as that for a bass horn if we include the total areas of input plus output lines instead of the single exit area, so I think it is reasonable to assume the equation for the horn is close enough for a Daline type enclosure.
There are other possibilities such as adding something like a conventional reflex port near the end of the line. Using a Daline type enclosure loses the option of mounting the driver some distance along the line to improve resonance rejection, but an alternative mentioned in the Augspurger paper and shown in his Fig.9 is an 'abrupt change in pipe diameter at one third its length', said to reduce problems at the '4th harmonic', so that may be an option to try. There may be no need to stuff the entire line, the maximum velocity of the standing waves we want to damp are primarily in the first third of the line, so we could use a larger area with increased absorbent density in the first third. Augspurger suggests the optimum Daline type design uses a third of the total volume for the cavity and the rest for the line, but without presenting any detailed analysis.
Probably the simplest, maybe over-simplistic, way to think about the Daline type enclosure is to start with a conventional small closed box design with typical Q of 0.7, giving -3dB around 70Hz, then add the line with area chosen for a low-pass cutoff around 70Hz, and with a length determined by the low frequency extension required. The Daline version with a KEF B110 bass driver has cavity volume 10 litres as required for that driver in a closed box, and the line length around 1.7 metres, which is claimed to extend output down to 20Hz. The 'terylene wool' stuffing specified may not have the same benefits (if any) as long fibre wool, so maybe this would allow a shorter line. The area of the line varies from about 79 to 60 square cm.
PART 2. Experiment:
Given the disputes concerning the relative merits of various line stuffing materials a simple comparison seems like a good starting point. So what properties do we actually want? To reduce the length of line needed we would like the maximum possible phase delay at low frequencies, but to give the maximum bass augmentation we want minimum attenuation below about 70Hz, but maximum attenuation above that frequency so that line resonances are reduced. Can these properties be found? Previously published tests suggest not, so the most we can hope is to find which of the materials tested comes closest.
The speaker used is the 8in bass speaker of one of my Mordaunt-Short MS20s, and the two lines are 5cm diameter 63cm long cardboard 'postal tubes'. One of the reasons for using two tubes is so that two materials can be compared, and we can be certain they are both being driven from the same sound pressure level. The test signal used is a 20Hz to 1kHz swept frequency, and the microphone is positioned 2.5cm from the ends of the tubes. The coupling chamber has a volume about 4 litres and two 5cm diameter holes for the tubes. The red traces are from the 'peak hold' function and is what interests us, the green trace is just background noise after the frequency sweep has finished, and can be ignored. The dips at 600Hz are nothing to do with tube resonances, they are still there with no tubes fitted and measured near the holes in the coupling chamber, so results with tubes fitted are probably only meaningful up to about 550Hz.
First is the output from one empty tube, with the other hole in the coupling chamber blocked. The expected resonant peaks are clearly seen.
The next results are with tubes fitted. The materials tested are Visaton lambs wool, and three different types of long fibre wool: Eider (27-31 micron), Welsh (31-35 micron) and Lincoln (36-40 micron).
So what can we conclude from this? There appears to be no great advantage for the long-fibre Lincoln, Welsh or Eider compared to the short-fibred Visaton Lambs wool, apart from a 3dB higher output at 20Hz. This is somewhat disappointing, I had hoped for something more dramatic, but even so there is at least one big advantage for the long fibre wool, it is considerably cheaper than Visaton's lambs wool. In a practical transmission line speaker we would of course use a much longer line with a larger area. The important resonances will then be further down the frequency range. The test was repeated with two tubes in series to double the length. The first half contains Visaton lambs wool and the second half Lincoln. They were also tried in reverse order, but there was only a slight difference. The resonances are again adequately damped.
The tests are not entirely conclusive, the long fibres may become more effective in a wider tube, but from these few limited tests there is no evidence of any magical effects of long fibre wool compared to shorter fibres. It may be that a different stuffing density would eliminate the differences, the Visaton also has greater attenuation at higher frequencies, so reducing the density could possibly match the long fibre results at both high and low frequencies. The Welsh wool is more messy, with loose fibres falling out easily, and my preference for a practical design would be the Eider or Lincoln. The Eider plot seems marginally smoother, so for now is my first choice.
I did a few other tests, including a fixed frequency test with microphone output displayed on an oscilloscope, and at 20Hz the Lincoln had an output level higher than the Visaton by a factor of 1.54, so close to a 4dB advantage. Using the signal generator output to trigger the oscilloscope the relative phase shift could also be found, and at 20Hz there was a relative phase delay about 14 degrees for the Lincoln. Although it is tempting to interpret this entirely as a different speed of sound through the materials, the impedance mismatch at input and output of the line also adds phase shifts.