Posted by Wayne Parham [ 70.234.139.243 ] on November 24, 2006 at 17:55:57:
In Reply to: What do you make of this "white paper"? posted by bill epstein on November 22, 2006 at 22:45:23:
Transmission lines are similar to vented speakers in that they employ a resonator to load the woofer at a low frequency. They use 1/4λ standing wave pipe modes instead of Helmholtz resonators, but the end result is similar.
In a transmission line, the system is tuned to a single frequency, just like the Helmholtz frequency of a bass-reflex box. Since standing waves are the tuning mechanism in a transmission line, there are unwanted harmonics to deal with above the primary 1/4λ mode. Because of this, line length, driver and mouth position are very important. The idea is to resonate the line at 1/4λ but to reduce the unwanted pipe mode harmonics above that. That's why 1/4λ pipes rarely have the driver at the end of the line; Usually, they're placed somewhat down the length. Careful placement can reduce the next (unwanted) harmonic up by standing wave cancellation and stuffing in the line can reduce the harmonics above that.
The best work on transmission lines, in my opinion, is by Martin King.
Another relationship worth mentioning is basshorns, which are also tuned pipes. Basshorns are tapered, but their mouths are usually small in relation to wavelength, so they act something like transmission lines. If the mouth is large enough, the horn acts like a wide band resonator. If too small, it acts more like a tuned pipe with peaks at odd multiples of 1/4λ and dips in between. The larger the mouth area is, the more it acts like a true horn with flat response through its pass band.
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