Acoustic transmission lines

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. Pipe organs, woodwinds, and the like can be modeled as transmission lines.

Applications to loudspeaker systems

A 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 channelled down a long pipe. If the acoustic energy was absorbed, it would not be available to excite resonaces. A pipe of sufficient length could be tapered, and stuffed so that the enegy loss was almost complete, minimizing output from the open end. No broad consensus on the ideal taper (expanding, uniform cross-section, or contacting) has been established.The difference between a transmission line loudspeaker and a vented loudspeaker system is clear: the rear wave is audibly absorbed and the cavity does not form a tuned system.

Transmission Line Loudspeakers have:
# minimal acoustic output from the enclosure except from the driver;
# accurate bass, without 'boom';
# excellent transient response;
# typically, extended bass below a half wave frequency of the reflected line length e.g. 30Hz=8 foot length;
# typically, smoooth impedance curves, possibly from a lack of frequency-specific resonances;
# low efficiency.

Many popular and conventional enclosure designs have a large cavity behind the driver, and a back wall that is partially acoustically reflective. This allows a portion of the energy to be reflected back to (and through) the driver after travelling 300 to 900 mm, inducing an identifiable re-radiated spike of energy 1 to 3 milliseconds later than the original, and causing narrow dips and peaks in the frequency response. Transmission lines lack a large rear cavity, so reflections, while still present, occur at short distances, typically 300 mm, shifting the interference caused by the delayed signal upweards in frequency to the range above 500 Hz.

Commercially successful folded transmission lines have been built, although some have suffered from reflections at the bends, unless properly designed.

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.

In 2003, a new design, SUHTL, using a low resonance enclosure material (not wood), and a single drive unit, has provided improved bass, which, although it requires some equalisation to provide 'full-range' response, improves on some the modest output level ability of previous designs.

A duct for sound propagation also behaves like a transmission line (e.g. air conditioning duct, car muffler, ...). The duct contains some medium, such as air, that supports sound propagation.Its length is normally of a similar order to the wavelengths of the sound it will be used with, 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. A plane wave will travel 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:

* A low impedance load (e.g. leaving the end open in free air) will cause a reflected wave in which the sign of the pressure variation reverses, but the direction of air displacement remains the same.
* A load that matches the characteristic impedance (defined below) will completely absorb the wave and the energy associated with it. No reflection will occur.
* A high impedance load (e.g. by plugging the end of the line) will cause a reflected wave in which the direction of air displacement is reversed but the sign of the pressure remains the same.

Since a transmission line behaves like a four-terminal model, one cannot really define or measure the impedance of a transmission line component. One can however measure its input or output impedance. It depends on the cross-sectional area and length of the line, the sound frequency, as well as the characteristic impedance of the sound propagating medium within the duct. Only in the exceptional case of a closed-end tube (to be compared with electrical short circuit), the input impedance could be regarded as a component impedance.

Where a transmission line of finite length is mismatched at both ends, there is the potential for a portion of the energy to be reflected until it is absorbed by frictional losses. This phenomenon is a kind of resonance and will tend to exaggerate the duration and level of a pulse or tone. This phenomena is exploited most effectively in pipe organs, where a specific column of air, with a specific sized exit port is tuned to resonate at a specific frequency, as a Helmholtz resonator.

The application of transmission line theory is however seldom used in acoustics. An equivalent four terminal model which splits the downstream and upstream waves is used. This eases the introduction of physically measurable acoustic characteristics, reflection coefficients, material constants of insulation material, the influence of air velocity on wavelength (Mach number), etc. This approach also circumvents unpractical theoretical concepts, such as acoustic impedance of a tube, which is not measurable because of its inherent interaction with the sound source and the load of the acoustic component.

"Transmission line" is also the name of a specialized audio speaker enclosure topology, in which sound from the back of the bass speaker chassis passes along a long (generally convoluted) path within speaker enclosure and emerges from the open end of the path "in-phase" with the sound radiated from the front of the driver, enhancing the output level at low frequencies.

See also

* Loudspeaker acoustics
* Voigt pipe
* Loudspeaker measurement

External links

* [http://www.quarter-wave.com/ Quarterwave loudspeakers] -- Martin J King, developer of landmark TL modeling software
* [http://www.suhtl.com/ 'S'ingle Drive-unit 'U'ltra-low-resonance 'H'alf-wave 'T'ransmission 'L'ine Speaker Page & forum]
* [http://www.t-linespeakers.org/ Transmission Line Speakers Pages] -- TL projects, history & more
* [http://www.geocities.com/rbrines1/Articles.html Brines Acoustics Articles] -- Application, tips, essays
* [http://www.diracdelta.co.uk/science/source/q/u/quarter%20wave%20tube/source.html Quarter Wave Tube - DiracDelta.co.uk] - description of operation, equation and online calculation.