TQWT and the Voigt pipe: a line that widens

TQWT stands for tapered quarter-wave tube, a quarter-wave line whose cross-section changes along its length. It is narrow at the driver and widens towards the outlet. Its predecessor is the Voigt pipe, which Paul Voigt patented in 1934. It is a popular cabinet for a single full-range driver in a slim column.

Section through a column with a TQWT. An angled baffle turns the column into a line that is narrow at the closed top and widens towards the outlet at the front bottom. The driver sits at about 40 % of the length, with damping only at the closed end.

How it works

As with a transmission line, the line resonates at the frequency where its length is a quarter of the wavelength, and around it the outlet supports the bass. The widening pushes the higher resonances further apart and makes them weaker, so a TQWT needs less damping than a classic transmission line. The driver goes at about 40 to 45 % of the length, where it cancels the resonance at three times the frequency.

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 TQWT with a length of 280 cm, a cross-section from 94 to 189 cm² and a volume of 39.7 l.

TotalConeLine outletSealed box 13.6 l for comparison

TQWT 39.7 l. The −3 dB point is at 48 Hz. The outlet supports the bass from about 30 to 60 Hz.

The impedance has two low peaks, 16 Ω at 23 Hz and 18 Ω at 50 Hz. The damped line keeps them low.

For a 6.5" woofer with a Qts of 0.43 the TQWT is large and does not go as deep in the bass as a bass reflex. It shines most with a low-Qts full-range driver that sounds thin in a bass reflex.

Pros and cons

Pros: full bass from a full-range driver, a slim column, a simple build with one angled baffle, little damping.
Cons: the result depends on the exact geometry and driver position. It will not get deep bass from a small driver, only fuller bass. A folded line behaves a little differently from the straight model.

Which driver and which room

Best with full-range drivers with a Qts of 0.3 to 0.45, and in living rooms where the speaker can stand further from the wall.

Well-known designs

Needle from Acoustic Design Magazin: a Dayton RS100-4 in a 95 cm tall column. I built it and measured it. The Loudsmith calculation matches the measurement in the bass within 1.6 dB on average.
Mindstorm from HiFi-Selbstbau, described as the original TQWT of the German DIY world.
Martin J. King shows in his line alignment tables that a line widening 1:5 has the lowest impedance peaks of all shapes.

In Loudsmith

TQWT is a box type that Loudsmith designs together with a drawing of the line and the angled baffle. The Needle template loads the exact geometry from the original plans. You set the damping with a slider; for the Needle a value of 0.2 to 0.5 matches the measurement.

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.