Acoustic transmission line
An acoustic transmission line is the acoustic analog of the electrical transmission line, typically thought of as a rigid-walled tube that is long and thin relative to the wavelength of sound present in it. The now mostly obsolete speaking tube served to transmit sounds to a remote location with minimal loss and distortion, as a simple coaxial cable or waveguide does for electrical signals. Musical wind instruments such as pipe organs, woodwinds and brass instruments can be also be modeled in part as transmission lines, though their job also includes generating the sound, controlling its spectrum, and coupling it efficiently to the open air, functions analogous to those of electronic oscillators, filters and antennas.
In particular, "transmission line" is the name of a specific audio speaker enclosure topology, in which sound from the back of the bass speaker chassis passes along a long (generally convoluted) path within the speaker enclosure. The energy is absorbed on this path, or emerges from the open end in phase with the sound radiated from the front of the driver, enhancing the output level at low frequencies.
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[edit] Theory
Proper transmission line loudspeakers employ a tube-like resonant cavity whose length is set between 1/6 and 1/2 the wavelength of the fundamental resonant frequency of the loudspeaker driver being used. The cross-sectional area of the tube is typically comparable to the cross-sectional area of the driver's radiating surface area. This cross section is typically tapered down to approximately 1/4 of the starting area at the terminus or open end of the line. While not all lines use a taper, the standard classical transmission line employs a taper from 1/3 to 1/4 area (ratio of terminus area to starting area directly behind driver). This taper serves to dampen the buildup of standing waves within the line, which can create sharp nulls in response at the terminus output at even multiples of the driver's Fs.
Essentially, the goal of the transmission line is to minimize acoustical or mechanical impedance at frequencies corresponding to the driver's fundamental free air resonance. This simultaneously reduces stored energy in the driver's motion, reduces distortion, and critically damps the driver by maximizing acoustic output (maximal acoustical loading or coupling)at the terminus. This also minimizes the negative effects of acoustic energy that would otherwise (as with a sealed enclosure) be reflected back to the driver in a sealed cavity.
Older acoustical models discuss transmission lines in terms of "impedance mismatch" or pressure waves "reflected" off the terminus opening back into the cavity. In actual fact, there is no "reflection". The driver mounted in a resonant cavity exhibits behavior akin to "cavitation" in which a series of gas pressurizations and rarefactions oscillate back and forth in a captive state. As the driver propagates this alternating train of weak adjacent pressure and vacuum pulses down the transmission line - waves that fit neatly within the cavity (anti node at terminus) remain largely captive (low acoustic output) while waves that do not (node or peak pressure at the terminus) exhibit high levels of energy transfer. Those that meet neither condition exactly produce output that is neither maximum nor minimum. There is no physical phenomenon that can cause "reflection". The electrical circuit analogy upon which the concept of "reflection" is based has no physical embodiment in an acoustical transmission line. As discussed below, the degree of acoustical coupling achieved and hence, loading, is determined by the difference between the distance from the driver to the terminus and the length of the quarter-wave peak of the fundamental wavefront (Fs) and its odd-ordered harmonics. The greater the difference, the lower the acoustical coupling. The smaller the difference, the greater the acoustical coupling and hence the lower the acoustical impedance.
[edit] History of transmission line loudspeakers
This type of loudspeaker enclosure was proposed in October 1965 by Dr A.R. Bailey and A.H. Radford in Wireless World (p483-486) magazine. The article postulated that energy from the rear of a driver unit could be essentially absorbed, without damping the cone's motion or superimposing internal reflections and resonance, so Bailey and Radford reasoned that the rear wave could be channeled down a long pipe. If the acoustic energy was absorbed, it would not be available to excite resonances. A pipe of sufficient length could be tapered, and stuffed so that the energy loss was almost complete, minimizing output from the open end. No broad consensus on the ideal taper (expanding, uniform cross-section, or contracting) has been established.
[edit] Operation
Transmission line speakers fall into essentially two categories: closed or vented.
Closed type transmission lines typically have negligible acoustic output from the enclosure except from the driver. Open ended lines exploit the low-pass filter effect of the line, and the resultant low bass energy emerges to reinforce the output from the driver at low frequencies. Well designed transmission line enclosures have smooth impedance curves, possibly from a lack of frequency-specific resonances, but can have low efficiency if not properly designed.
One key advantage of transmission lines is their ability to conduct the back wave behind the transducer more effectively away from it - reducing the chance for reflected energy permeating back through the diaphragm out of phase with the primary signal. Not all transmission lines designs do this effectively. Most offset transmission line speakers place a reflective wall fairly close behind the transducer within the enclosure - posing a problem for internal reflections emanating back through the transducer diaphragm.
[edit] Commercial and amateur loudspeaker designs
Commercially successful folded transmission lines have been produced, although some have suffered from reflections at the bends.
One example of a transmission line enclosure design was by Vivan Capel called the "Kapellmeister" published in Electronics Today International, circa 1975. This was a double-folded line which placed the first, third, and fifth harmonics of the line's resonant frequency at the bends and the exit, where they would cause least movement. The Kapellmeister suffered from poor deep bass, and was designed around a low power driver. Capel, like Bailey, believed that the pipe's cross-sectional area needed to be equal the driver's cone area.
There are not many companies producing commercial transmission line loudspeakers as the technology is difficult to get right. One company that does successfully manufacture them is UK based PMC or the Professional Monitor Company. Its hi-fi and studio monitor designs use a development of the transmission line that they call the Advanced Transmission Line.
[edit] Sound ducts
A duct for sound propagation also behaves like a transmission line (e.g. air conditioning duct, car muffler, ...). Its length may be of similar to that of the wavelength of the sound passing through it, but the dimensions of its cross-section are normally smaller than one quarter of a wavelength. Sound is introduced at one end of the tube by forcing the pressure across the whole cross-section to vary with time. An almost planar wavefront travels down the line at the speed of sound. When the wave reaches the end of the transmission line, behaviour depends on what is present at the end of the line. There are three possible scenarios:
1) The frequency of the pulse generated at the transducer results in a pressure peak at the terminus exit(odd ordered harmonic open pipe resonance) resulting in effectively low acoustic impedance of the duct and high level of energy transfer.
2) The frequency of the pulse generated at the transducer results in a pressure null at the terminus exit (even ordered harmonic open pipe anti -resonance) resulting in effectively high acoustic impedance of the duct and low level of energy transfer.
3) The frequency of the pulse generated at the transducer results in neither a peak or null in which energy transfer is nominal or in keeping with typical energy dissipation with distance from the source.
[edit] See also
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Wikimedia Commons has media related to: Loudspeaker |
[edit] References
[edit] External links
- Quarterwave loudspeakers – Martin J King, developer of TL modeling software
- Transmission Line Speakers Pages – TL projects, history & more
- Brines Acoustics Articles (Archived 2009-10-24) – Application, tips, essays
- Quarter Wave Tube - DiracDelta.co.uk - description of operation, equation and online calculation
