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Definition Transmission Line One of the famoust TML's: IMF TLS50 A transmission line enclosure is a waveguide in which the structure shifts the phase of the driver's rear output by at least 900, thereby reinforcing the frequencies near the driver's Fs. Transmission lines tend to be larger than ported enclosures, due to the size and length of the guide required (typically 1/4th the longest wavelength of interest). The design is often described as non-resonant, and some designs are sufficiently stuffed with absorbent material that there is indeed not much output from the line's port. But it is the inherent resonance (typically at 1/4 wavelength) that can enhance the bass response in this type of enclosure, albeit with less absorbent stuffing. A variation on the transmission line enclosure utilizes a tapered tube, with the terminus (opening/port) having a smaller area than the throat. The tapering tube can be coiled for lower frequency driver enclosures to reduce the dimensions of the speaker resulting in a seashell like appearance. Most notably Bowers & Wilkins have used this approach in their flagship Nautilus speaker as well as the use of smaller straight tapering tubes in many of their other lines. Recently, numerical simulations by several researchers (eg, George Augspurger and Martin J. King) have brought a degree of order to the theory and practical design of these systems. The Transmission Line has its design roots in the Stromberg-Carlson acoustic labyrinth (1930). It first consisted of a log pipe, (open at one end and the driver mounted at the other) with a cross-sectional area about the same as that driver. The line length was made about 25% of the driver resonance's wavelength. Working with the same basic concept in the early 1960s, A.R.Bailey expermented with different damping materials and techniques in folded labyrinth lines. This work has sinds become the basic bible for most TL designs.   With TLs, the enclosure functions as a low-pass filter with a 90degrees phase shift, absorbing all the rear wave energy of the woofer except for frequencies below about 75Hz. TLs can be characterized by:   Low cabinet resonance Relativley loud deep bass (below 50Hz). Highly damped impedance peak. Decreased cone motion in the 40Hz region. Low degree of mid-bass coloration. Rather low overall efficiency. Line Length and damping material The basic line length criteria for TLs is: 25% of the wavelength at, or just above, the driver resonance. The following are the traditional, and definitely "proven by performance", criteria for TL construction: Make the line length 1.80-2.4 meter (6-8 feet) this corresponds to 1/4-wavelength of an undamped line 35-45Hz. Make the cross-sectional area of the line starting dirctly behind the driver to be at least 25% greater then the driver's radiating ares Sd. The strating cross-sectional area of the line should then taper to the port opening, which should be equal to Sd. This generally means that the last taper section, or the last 60 - 90cm (2-3 feet) of the line.Beginning cross-sectional areas of the line can vary from about 1.25 to 2.5 times the Sd. This defines a taper ratio, beginning area/Sd, which will have a direct effect on the subjective quality of the bass and midbass of the TL. Low ratios generally give the "lean" and "tight" sound quality associated with TL's. As the ratio increase past 1.4 - 1.5, the emphasis is placed more on the low bass area, and a better sounding midbass. This criterion depends upon critical damping of the line, and results will tend to vary with a combination of both line taper and stuffing. Table 1.0 gives the different ranges of the beginning cross-sectional area for the line with different diameter woofers. Damping material, in order of preference: a. Long Fiber wool b. 50% Dacron, 50% long fiber wool c. Darcon d. Fiberglass The line should be stuffed with an average of about 0.5 lbs to 0.7 lbs of acoustical stuffing material per cubic foot of line volume. Decreasing the quantity of the material near the port area will change the midd-bass quality. More very good information about Transmission Line Loudspeakers: Classic TL Design by Jon Risch A gathering of t-line speaker lore & information Table 1.0 TL Line Requirements for differten Line Tapers Diameter Inches Sd m2 Port Area cm2 Port Area in2 Beginning line area (Tapper Range: 2.5 - 1.25) 15 0.0855 858.1 133 333-166 12 0.0450 451.6 70 175-88 10 0.0330 335.5 52 130-65 8 0.0215 212.9 33 83-41 6.5 0.0158 161.29 25 63-31 5 0.0089 90.3 14 35-18 Table 2.0  Line Length vs. Frequency Frequency Undamped c = 344 m/s Damped(Wool-8kg/m3 c' = 123 m/s Hz 1/4 L 1/4 L 20 Hz 4.3 meter 1.55 meter 25 Hz 3.44 meter 1.25 meter 30 Hz 2.86 meter 1.04 meter 35 Hz 2.47 meter 0.88 meter 40 Hz 2.16 meter 0.76 meter 45 Hz 1.92 meter 0.67 meter Calculate change of Speed of Sound in fibrous material L= wavelength in meters c= speed of sound in air c'= speed of sound in long fiber wool P= packing density of the fibrous material = 8kg/m3 Pa= density of air = 1.18kg/m3 Calculated Speed of Sound Speed of sound in air [c]: m/s Packing density of the fibrous material [P]: kg/m3   Calculated Speed of sound in long fiber wool [c']: m/s Basic TML Calculations   Driver Cabinet   fs: Sd: Fitting depth Width of cabinet inside   Hz cm2 cm cm2     Classic tuning   Cabinet height [h] : cm   Depth behind driver [a] : cm   Depth at TML port [c] : cm   Depth at base [b] : cm   Length of TML duct [LTML] : cm   Classic: the unfold length is 1/4 of the resonance frequency's wave length Low tuning   Low tuning [h] : cm     Low tuned: the unfold length is 1/3 of the resonance frequency's wave length Half of transmissionline is to be filled with damping material (dark gray in the picture) Therefore, the velocity of speed in the TML duct drops by 20% to approx. 272 m/s The fill materials themselves also have a frequency dependent nature, which means the line speed will not be exactly the same at all frequencies. Because of this, no one has yet come up with either a design table, or an exact computer model which will always predict the outcome of a practicular TL design. The criteria for selecting a woofer for a TML loudspeaker box are still not clearly defined. There is not (yet) a design methodology which is similar to the Thiele / Small - system with parameters for closed boxes, bass reflex speakers and systems oassieve membranes. Below is a list of woofers that have been successfully used in TM systems: Dynaudio Kef Focal 21W54 B-139 10K515 30W54 B-110 8K516   B-200S 8K011db Transmission Line Length Calculation at specific Sound Speed Transmission Line fres: Hz C m/s: Sd: cm2 Taper Range (1.25 - 2.50):   Line length: meter, ..not folded Beginning Line Area: cm2 TML Port Area: cm2   Woofer Selection The criteria for successful TL woofers still remains unclear, and no established design methodologies exist. The following list, however, represents a group of drivers which have been successfully used to implement transmission line designs: KEF Dynaudio Focal B-139 21W54 10K515 B-110 30W54 8K516 B-200s 8K011db Source: Vance Dickason's Loudspeaker Design Cookbook (5th Edition) "Transmission Line Low-Frequency Systems"