Transmission line: a long damped line

A transmission line, TL for short, guides the sound from the back of the cone through a long line filled with damping material. At the end of the line there is an opening. In the lowest bass, sound comes out of it and supports the bass, while the material in the line absorbs the higher frequencies.

Section through a column with a transmission line. The line starts closed at the top, runs down along the front panel with the driver, folds at the bottom and goes up to the outlet in the rear panel. An angled baffle narrows it gradually, and the first part is damped.

How it works

The line has a resonance at the frequency where its length is a quarter of the wavelength. Around it the outlet plays in phase with the cone, much like the port in a bass reflex. But the line also resonates higher up, at three times, five times and so on. Damping material and the right driver position suppress these higher resonances.

Martin J. King summed up the rules: the line should taper, a line tapered 5:1 is shorter than a straight one with the same tuning, the driver should sit about a third to a fifth of the length from the closed end, and the damping should fill the first two thirds to three quarters of the length.

What the calculation shows

All charts in this series on enclosure types are calculated by Loudsmith for the same 6.5" woofer, the SB Acoustics SB17NRX2C35-8 (Fs 36.5 Hz, Qts 0.43, Vas 27 l), so they can be compared. The 0 dB level is the driver's level in the midrange. A classic tapered line following King's rules: length 204 cm, cross-section from 212 to 42 cm², tuning 30 Hz and the driver at a fifth of the length. Volume 25.9 l.

TotalConeLine outletSealed box 13.6 l for comparison

Tapered transmission line 25.9 l. The −3 dB point is at 43 Hz. The higher line resonances show up as ripple in the outlet above 100 Hz.

The line plays 20 Hz deeper than the sealed box with the same driver, and the roll-off below the tuning is slower than with a bass reflex. The price is a bigger and more complex box with a baffle inside.

The impedance has several peaks, 16 Ω at 18 Hz and 27 Ω at 59 Hz, and smaller ones at 120 and 289 Hz. These are the line resonances.

Pros and cons

Pros: deep bass with a slow roll-off, less cone excursion in the bass, an outlet with no noise because it is large.
Cons: a big box with a folded line, a demanding build. The result depends heavily on the amount of damping, which is fine-tuned by measurement. Simple models are only valid up to 600 to 700 Hz.

Which driver and which room

It suits woofers and full-range drivers with a low to medium Qts, and floorstanding speakers, where height comes for free.

Well-known designs

Satori TL by Martin J. King: a 186 cm line tapered 5:1, a Satori WO24P-4 woofer at a third of the length, damping of 0.5 lb/ft³ over three quarters.
SEAS THOR: two 7" woofers in a folded 206 cm line tapered 3:1. The measured F3 is 44 Hz, and 41 Hz with less damping. For the same line Loudsmith calculates 39 to 43 Hz depending on the damping.
The test line by Martin J. King: a straight 123 cm pipe in which he measured all the resonances. Loudsmith calculates them to within 1 to 2 Hz.

In Loudsmith

The transmission line is one of the box types. Loudsmith designs it as a tapered line by Martin J. King's rules: a 5:1 or 3:1 taper, the driver at a fifth of the length and damping in the range that matched measured lines (0.2 to 0.3). You can then adjust the length, the cross-section at the closed end, the taper, the driver position and the damping with sliders.

Enclosure types series: sealed · bass reflex · passive radiator · aperiodic · transmission line · TQWT · ML-TL · open baffle · back-loaded horn. You will find the formulas in the article Speaker box calculations step by step.