I present three classic resonant pipes. Each of these examples is modeled With Martin King's Mathcad worksheets using the Fostex FE164. The length of each pipe is adjusted to give an F1 at 50hz. They are:
The classic TL tapers from 2*Sd at the driver to Sd at the mouth. the driver is a close to the top as possible, here 6". The line length is 55". (It is interesting to note that the classic formula for pipe length: L=c/4f gives a length of 67" See Speed of Sound)
The combined response is: (The red line is the pipe response, the blue an infinite baffle)
The Driver response (red) and the port response (blue):
The combined response with the pipe heavily stuffed end-to-end.
The classic TL, like all resonant pipes has a dip between F3 and F5, where the driver and port are out of phase. The designer is faced with the choice of smoothing out the dip and killing the bass or keepng good bass response and suffering lumpy med-base/low treble. Actual in-room performance will be better than the graph indicates, because room lift will help out below 80hz. The in-room response of the heavily stuff pipe will probably exceed the infinite baffle curve all the way down. The classic TL really isn't that bad. I does tend to be thin in the bass, as is obvious.
There is a better approach to the classic TL. By increasing the pipe area at the driver end, The bass output is substantially increased, while the out of phase dip is reduced. It looks like this:
The combined response.
The driver and port response.
Note that the pipe resonance went from 55hz in the classic TL to 40hz in the strongly tapered TL. This results in nearly 6db increase in output at 40hz. Stuffing is applied only to the top half of the pipe:
This configuration goes much deeper, and the out-of-phase dip is much smoother. The penalty, there is always a consequence, is that the roll-off is steeper, implying degraded transient response. However, the transient response should be better than a comparable bass reflex cabinet, because the initial roll-off is shallower.
The "Voigt" pipe is named after Paul Voigt, who, interestingly enough, never advocated this design. The throat area is equal to zero and the mouth area some large number. I chose the mouth area equat to 3*Sd, so that the SPL below 100 hz would equal that at 1000 hz. The port area is equal to Sd. The length of the pipe to make F1 = 50 hz is 99". The driver is at 1/2 the pipe length to satisfy the equation:
The combined response is: (The red line is the pipe response, the blue an infinite baffle)
The Driver response (red) and the port response (blue):
The combined response with the upper end of the pipe stuffed:
There are two main problems with the "Voigt" pipe: First, because of the positive tape, this is the longest of all configurations for the same F1. Second, the hole between F3 and F5 is so deep that is cannot be stuffed out. It gives a hollow sound to the pipe. There is no reason to use this configuration. Others are better.
This configuration was proposed by David Weems. It is a folded TQWT. However, a single fold does not materially affect the performance of a pipe. Therefore, it was modeled as a straight pipe. In order to make the driver position work out at the top of the narrow section with the port at the bottom of the narrow section, Weems uses a 3/4" wide throat block. Using a mouth area of 3*Sd, that works out to a throat area of .3*Sd (cabinet width assumed to be 8"). The driver position becomes .43*L, by the formula above. The length to produce F1=50 hz is 88".
Other than being shorter than the "Voigt" pipe, there is no advantage here. For all practical purposes, the Weems' pipe is nothing but a folded "Voigt" pipe.
Top of Page>One of the tenets of classic TL theory is that the speed of sound is decreased when passing through a fibrous tangle, i.e., stuffing. There are a number of studies that show the effect and demonstrate that it is frequency dependant. Then there are studies that show that wool is better than Fiberglas�, etc. But wait! Look at this table:
| Length | Taper | F0 | F3 | F5 | F7 | -- |
| 60 | 3 | 77 | 180 | 280 | 370 | (So=.01*Sd, Sm=3*Sd) |
| 60 | 2 | 63 | 170 | 270 | 370 | (So=Sd, Sm=3*Sd) |
| 60 | 0 | 53 | 166 | 270 | 375 | (So=Sd, Sm=Sd) |
| 60 | 0 | 52 | 160 | 265 | 370 | (So=3*Sd, Sm=3*Sd) |
| 60 | -2 | 42 | 160 | 260 | 360 | (So=3*Sd, Sm=Sd) |
| 60 | Free Air | 56 | 168 | 280 | 393 | -- |
Beginning with Bradbury, The assumption was that the individual fibers in a fibrous tangle moved with the sound waves, therefore adding moving mass to the air column. More recent experiments indicate that this is not the case. The individual fibers do mot move, and are therefore a pure resistance to the sound waves. The speed of sound is not changed in a fibrous tangle.
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