Acoustic transmission lines

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Theoretically perfect enclosure type. Abbrev. 'TL', for housing a loudspeaker. First described in October 1965 by Dr A.R.Bailey and A.H.Radford in an article in Wireless world(p483-486). It was known that the rear wave of the loudspeaker needed to be completely absorbed without damping the loudspeaker's motion or modulating it from internal reflections and resonance, so A Bailey / A Radford reasoned that the rear wave had to be channelled down a pipe or line, long enough to resist resonance below the desired frequency (e.g., 8 feet for 30 Hz). Dr A Bailey / A Radford reasoned that if the rear wave resonanted the enclosure it would cause interference, which a line would not. If the line were sufficiently long but evenly stuffed with wadding, then the exiting wave would be relatively inaudible. The difference between a Transmission Line loudspeaker and a Reflex or Labyrinth is clear: the rear wave is audibly absorbed and not used for reinforcement. Also the resonance of the enclosure is virtually gone.

[edit] Applications to loudspeaker systems

Transmission Line Loudspeakers have:

virtually no sound emanating from the enclosure except the loudspeaker;
precisely defined imaging, particularly in the bass region and vocals;
precicely timed bass without echo or reverberant 'booming';
excellent transient response and uncompressed dynamics;
typically, extended bass below a half wave frequency of the reflected line length e.g. 30Hz=8foot length;
typically, even loudspeaker-impedance, from the unchanging consistent load(no reflection resonances);
high efficiency.

Normal enclosure designs allow the rear wave to be reflected back to the loudspeaker within a foot or so, which causes distortion, or the 'high bass' (approx 100-350Hz) to exit the enclosure in audible quantities. Although this extra loudness is gained, the compromise is that it is out of synchronisation with the loudspeaker and creates a blurred reproduction of the bass. Clear Low bass (10Hz-100Hz) is only possible in an enclosure of this type, since the wavelengths require an enclosure approx 3-24 feet long.

Folded transmission lines have been attempted many times, but always suffer in varying part from early reflections at the bends, unless ceramic-faced acoustic mirrors are employed - making the enclosure expensive to build.

Arguably the best domestic TL design was done by Vivan Capel called the 'Kapellmeister' published in Electronics Today International, circa 1975. The Kappelmeister 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 Kappelmeister suffered from a severely attenuated low bass, low power and wood-resonances. Capel, like Bailey, thought the line's cross-sectional area had to equal the loudspeaker's cone area.

Recently (2003) a new design, SUHTL, using an 'U'ltra-low resonance enclosure material (not wood) and a more capable 'S'ingle loudspeaker, has allowed the bass to be far less attenuated and within reach of conventional tone-control correction or full-range equalisation with enough power for loud domestic performance and enough range (20Hz-20kHz) to be considered 'full-audible-range', without blurred or boomy bass.

Definitively, to reproduce a human voice precisely, without positional or reverberant problems of bass emanating late or elsewhere from the single loudspeaker, the TL is the only enclosure type capable.

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 wave to bounce back and forth many times until it is absorbed. This phenomenon is a kind of resonance and will tend to attenuate any signal fed into the line.

When this resonance effect is combined with some sort of active feedback mechanism and power input, it is possible to set up an oscillation which can be used to generate periodic acoustic signals such as musical notes (e.g. in an organ pipe).

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 type of audio speaker design in which sound from the back of the bass speaker chassis is channeled along an acoustic transmission line within the speaker. At the other, open end of the transmission line, low frequencies are in phase with the front of the speaker chassis, which improves irradiation of bass frequencies. The disadvantage of this design, that the transmission line causes certain frequencies to be suppressed, can be alleviated by judiciously tuned Helmholtz resonators.