Thanks for the add, folks.
My ?uestion: What are the advantages of a transmission line speaker with ever widening channels, as opposed to the channels being of parallel walls?
The reason is that it broadens the frequencies over which the driver is supported and therefore the port output has a broader range of frequencies and lower Q. A TL speaker is a very specialized version of the Gadeckt organ pipe. The differences are.
1). It is tapered, most often 3:1 unlike an organ pipe you you want a specific frequency plus harmonics, which in Gadeckt pipes are the odd and not even harmonics. The taper is reverse unlike a bassoon say. So the widest point is the stopped closed end. The narrowest part is the opening or mouth. There are various variable tapers, and end correction schemes, but the hard facts show these not to be improvements but detrimental. I strongly advise a linear taper. The pipe is also folded to prevent HF radiation from the open end.
2). The point at which the pipe is excited (driver placement) is designed to minimize and not maximize generation of the odd harmonics which in a speaker is odd harmonic distortion.
3). The port output is critically damped, but not enough to prevent driver assist. This together with the taper lowers the system Q. This results in a broader based output of lower amplitude. That is the very definition of low Q. An organ pipe requires high Q.
Now in a stopped pipe, which is what the Gadeckt stop is, you have zero displacement of air at the stopped (closed) end, obviously. In any acoustic pipe be it stopped or open air pressure and air displacement are 180 degrees out of phase. So at the stopped end pressure changes are maximal, whereas at the open end, there are zero pressure changes, but maximal air displacement. So driver placement is at the anti node of the third harmonic, as the intensity of the harmonics decreases with their frequency. That is why the driver is not placed right at the closed end of the pipe, but at the location where there is still very high pressure and control of driver/cone displacement.
Now the recent contributions in math, experiment and modelling (Auspergerer et al) have shown in a speaker, matching not only length with Fs to be important to get Fp, but also matching volume of the pipe Vp to the driver VAS. This understanding has virtually eliminated the possibility of getting a dud design if you do your design correctly.
Now the damping is crucial. The new models show the damping should be evenly spaced throughout the pipe but stop about 6" or so from the open end.
An undamped pipe will have 2 peaks of impedance on the driver impedance curve, just like a standard ported Qb4 box. Roll off is fourth order 24 db per octave just like a Qb4 box.
Damping is added to the pipe to just suppress one peak of impedance. Roll off then becomes second order 12 db per octave just like a sealed Qb2 box. However unlike a sealed box F3 is extended and close to Fs of the driver and not much higher than Fs whereas it is much higher in a sealed alignment. The relatively recent improved models, also calculate the correct weight of a wide variety of damping materials.
So the whole point of all this is to build a speaker with extended deep bass with shallow 12 db per octave roll off that is low Q and non resonant. If you use a driver with Qts in the 0.35 to 0.4 range, which is the sweet spot, you end up with an optimal Qtc around 0.5.
The end result is a speaker with very accurate deep non resonant bass that encircles the room, as only pipes can. The result is a bass that is phenomenally real, producing absolutely uncolored and perfect bass registers of pianos, organs tympani and the bass winds and also the deeper ranges of the human voice.
A properly designed TL gives by far the most accurate bass of any method of loudspeaker loading I know. Properly done the bass detail and accurate articulation is truly astonishing. These speakers are in a total class of their own in terms of accurate uncolored bass.
In recent times most TLs commercially produced have been mass loaded with the pipe exiting via a tuned ported chamber. This reduces speaker size but gives up most of the advantages of traditional TL design I feel.
These designs have two peaks of impedance to the driver impedance curve and roll off at 24 db per octave just like a Qb4 box. So I regard these designs as essentially modified Qb4 designs. They do lower Q some and extend F3 a little. They are not the true deal however and their impedance curve and roll off point to that.
