Toccata Grande, Part 1

By Lars Mytting
20 Jan 1998

Modelling the transmission line

As mentioned, this is my first t-line, so you should look elsewhere for expert advice. But I will try to describe some basic principles.

A t-line cabinet consists of a long tunnel, which (ideally) works so that everything except the low frequencies are absorbed in the line. The common design criteria for a t-line are as follows:

1. The length of the line should be 1/4 of the wavelength of the resonance frequency of the driver.

The wavelength of sound is be found by this formula: 343/f

f is the frequency, and 343 is the speed of sound in metres pr. second. If we want to tune a such "quarter wavelength"-cabinet to 40 Hz, the line length should be:

343/40 = 8.575
8.575/4 = 2.14 m
For 50 Hz, the length is ca. 1.7 m, for 25 Hz ca. 3.4 m.

2. The line should be tapered so that it is more narrow at the end. The area at the end should be the same as the Sd of the driver. The area at the beginning of the line should be from 1.25 to 2.5 times the Sd. Many use a chamber behind the driver.

3. Dickason [5] describes the effect of the taperings like this: "Low ratios (around 1.25) give a lean and tight sound quality. Past 1.4-1.5, the emphasis is placed more on the low bass area, and a better sounding midbass".

4. The line is usually folded, so that reasonable dimensions can be achieved.

5. The line is damped with wool or similar material. Density is usually highest at the beginning of the line, with progressively less material towards the end. The damping is highly a question on trial, error and measurement.

6. The impedance of a t-line will be quite flat, with very damped resonance peaks.

7. The frequency response of many t-lines have a lift in the 50-100 Hz region, and a dip in the 150-200 Hz region.

Examples of T-line tuning
Fig. 2. Unfolded T-line model

Example 1:

One 8" driver (Sd 235 cm2), tapering ratio 1.3, tuned to 50 Hz:
a: 305 cm2
b: 1,7 m
c: 235 cm2

Example 2:

One 15" driver (Sd 800 cm2), tapering ratio 2.2, tuned to 25 Hz:
a: 1760 cm2
b: 3,4 m
c: 800 cm2

From example 2 we see that large drivers are quite size-hungry on cabinets, and that the tuning frequency will have great domestic impact.

The Toccata cabinet is tuned to a ratio of 1.5 for a single 10", and the length to 40 Hz. With two drivers, the line is to narrow to correspond with theory, but I did this anyway to add scientific value. To make the line easy to build, the line has just two folds. I found that the Toccata performed best with quite a lot damping material. I guess that this is because the line is so narrow. The t-line tradition prescribes pure wool for damping. I used a combination of wool and a house insulation material called Rockwool of 3 cm thickness.

My opinion is that damping material should sit firmly in place in the cabinet. If not, it may be moved by the internal air pressure, soaking bass energy. Therefore, I stapled the Rockwool to the walls, and filled the space left open with wool. I intensely suggest that you keep one side of the speaker detachable, so that you can add or remove damping material easily. When you are satisfied with the tuning, fasten the side permanently.

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