Acoustic Transmission Lines
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An acoustic transmission line is the use of a long duct, which acts as an acoustic waveguide and is used to produce or transmit sound in an undistorted manner. Technically it is the acoustic
analog Analog or analogue may refer to: Computing and electronics * Analog signal, in which information is encoded in a continuous variable ** Analog device, an apparatus that operates on analog signals *** Analog electronics, circuits which use analo ...
of the electrical
transmission line In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
, typically conceived as a rigid-walled duct or tube, that is long and thin relative to the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
of
sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
present in it. Examples of transmission line (TL) related technologies include the (mostly obsolete) speaking tube, which transmitted sound to a different location with minimal loss and distortion,
wind instrument A wind instrument is a musical instrument that contains some type of resonator (usually a tube) in which a column of air is set into vibration by the player blowing into (or over) a mouthpiece set at or near the end of the resonator. The pitc ...
s such as the
pipe organ The pipe organ is a musical instrument that produces sound by driving pressurized air (called ''wind'') through the organ pipes selected from a keyboard. Because each pipe produces a single pitch, the pipes are provided in sets called ''ranks ...
,
woodwind Woodwind instruments are a family of musical instruments within the greater category of wind instruments. Common examples include flute, clarinet, oboe, bassoon, and saxophone. There are two main types of woodwind instruments: flutes and reed ...
and
brass Brass is an alloy of copper (Cu) and zinc (Zn), in proportions which can be varied to achieve different mechanical, electrical, and chemical properties. It is a substitutional alloy: atoms of the two constituents may replace each other with ...
which can be modeled in part as transmission lines (although their design also involves generating sound, controlling its timbre, and coupling it efficiently to the open air), and transmission line based loudspeakers which use the same principle to produce accurate extended low
bass Bass or Basses may refer to: Fish * Bass (fish), various saltwater and freshwater species Music * Bass (sound), describing low-frequency sound or one of several instruments in the bass range: ** Bass (instrument), including: ** Acoustic bass gui ...
frequencies and avoid distortion. The comparison between an acoustic duct and an electrical transmission line is useful in "lumped-element" modeling of acoustical systems, in which acoustic elements like volumes, tubes, pistons, and screens can be modeled as single elements in a circuit. With the substitution of pressure for voltage, and volume particle velocity for current, the equations are essentially the same. Electrical transmission lines can be used to describe acoustic tubes and ducts, provided the frequency of the waves in the tube is below the critical frequency, such that they are purely planar.


Design principles

Phase inversion is achieved by selecting a length of line that is equal to the quarter wavelength of the target lowest frequency. The effect is illustrated in Fig. 1, which shows a hard boundary at one end (the speaker) and the open-ended line vent at the other. The phase relationship between the bass driver and vent is in phase in the pass band until the frequency approaches the quarter wavelength, when the relationship reaches 90 degrees as shown. However by this time the vent is producing most of the output (Fig. 2). Because the line is operating over several octaves with the drive unit, cone excursion is reduced, providing higher SPL’s and lower distortion levels, compared with reflex and infinite baffle designs. The calculation of the length of the line required for a certain bass extension appears to be straightforward, based on a simple formula: :\ell = \frac where: : f\,~~~~ is the sound frequency in Hertz (Hz) : 344  is the speed of sound in air at 20°  C : \ell\,~~~~ is the length of the transmission line in
meters The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefi ...
. The complex loading of the bass drive unit demands specific Thiele-Small driver parameters to realise the full benefits of a TL design. Most drive units in the marketplace are developed for the more common reflex and infinite baffle designs and are usually not suitable for TL loading. High efficiency bass drivers with extended low frequency ability, are usually designed to be extremely light and flexible, having very compliant suspensions. Whilst performing well in a reflex design, these characteristics do not match the demands of a TL design. The drive unit is effectively coupled to a long column of air which has mass. This lowers the resonant frequency of the drive unit, negating the need for a highly compliant device. Furthermore, the column of air provides greater force on the driver itself than a driver opening onto a large volume of air (in simple terms it provides more resistance to the driver's attempt to move it), so to control the movement of air requires an extremely rigid cone, to avoid deformation and consequent distortion. The introduction of the absorption materials reduces the velocity of sound through the line, as discovered by Bailey in his original work. Bradbury published his extensive tests to determine this effect in a paper in the Journal of the Audio Engineering Society (JAES) in 1976 and his results agreed that heavily damped lines could reduce the velocity of sound by as much as 50%, although 35% is typical in medium damped lines. Bradbury’s tests were carried out using fibrous materials, typically longhaired wool and glass fibre. These kinds of materials, however, produce highly variable effects that are not consistently repeatable for production purposes. They are also liable to produce inconsistencies due to movement, climatic factors and effects over time. High-specification acoustic foams, developed by loudspeaker manufacturers such as PMC, with similar characteristics to longhaired wool, provide repeatable results for consistent production. The density of the polymer, the diameter of the pores and the sculptured profiling are all specified to provide the correct absorption for each speaker model. Quantity and position of the foam is critical to engineer a low-pass acoustic filter that provides adequate attenuation of the upper bass frequencies, whilst allowing an unimpeded path for the low bass frequencies.


Discovery and development

The concept was termed "acoustical labyrinth" by Stromberg-Carlson Co. when used in their console radios beginning in 1936 (see http://www.radiomuseum.org/r/stromberg_acoustical_labyrinth_837.html). 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.


Uses


Loudspeaker design

Acoustic transmission lines gained attention in their use within
loudspeaker A loudspeaker (commonly referred to as a speaker or speaker driver) is an electroacoustic transducer that converts an electrical audio signal into a corresponding sound. A ''speaker system'', also often simply referred to as a "speaker" or " ...
s in the 1960s and 1970s. In 1965, A R Bailey’s article in Wireless World, “A Non-resonant Loudspeaker Enclosure Design”,A R Bailey, “A Non-resonant Loudspeaker Enclosure Design”, Wireless World, October 1965, pages 483-486 detailed a working Transmission Line, which was commercialized by John Wright and partners under the brand name
IMF The International Monetary Fund (IMF) is a major financial agency of the United Nations, and an international financial institution, headquartered in Washington, D.C., consisting of 190 countries. Its stated mission is "working to foster globa ...
and later
TDL TDL may refer to: Businesses and organizations * Technical Design Labs, a former microcomputer- and software company * Texas Digital Library, a consortium of institutions * TDL Group, former company name of Tim Hortons Places * Tokyo Disneyland, ...
, and were sold by audiophile Irving M. "Bud" Fried in the United States. A transmission line is used in loudspeaker design, to reduce time, phase and resonance related distortions, and in many designs to gain exceptional bass extension to the lower end of human hearing, and in some cases the near-
infrasonic Infrasound, sometimes referred to as low status sound, describes sound waves with a frequency below the lower limit of human audibility (generally 20 Hz). Hearing becomes gradually less sensitive as frequency decreases, so for humans to perce ...
(below 20 Hz). TDL's 1980s reference speaker range (now discontinued) contained models with frequency ranges of 20 Hz upwards, down to 7 Hz upwards, without needing a separate subwoofer.http://www.imf-electronics.com/Home/imf/speaker-range/reference-speakers
Irving M. Fried Irving M. "Bud" Fried (November 3, 1920 – March 21, 2005), was an American audiophile of the "Golden Age" of stereophonic reproduction, along with Marantz, Saul Marantz and David Hafler. As a young boy, Fried fell in love with the art and scienc ...
, an advocate of TL design, stated that: : ''"I believe that speakers should preserve the integrity of the signal waveform and the Audio Perfectionist Journal has presented a great deal of information about the importance of time domain performance in loudspeakers. I’m not the only one who appreciates time- and phase-accurate speakers but I have been virtually the only advocate to speak out in print in recent years. There’s a reason for that."'' In practice, the duct is folded inside a conventional shaped cabinet, so that the open end of the duct appears as a vent on the speaker cabinet. There are many ways in which the duct can be folded and the line is often tapered in cross section to avoid parallel internal surfaces that encourage standing waves. Depending upon the drive unit and quantity – and various physical properties – of absorbent material, the amount of taper will be adjusted during the design process to tune the duct to remove irregularities in its response. The internal partitioning provides substantial bracing for the entire structure, reducing cabinet flexing and colouration. The inside faces of the duct or line, are treated with an absorbent material to provide the correct termination with frequency to load the drive unit as a TL. A theoretically perfect TL would absorb all frequencies entering the line from the rear of the drive unit but remains theoretical, as it would have to be infinitely long. The physical constraints of the real world, demand that the length of the line must often be less than 4 meters before the cabinet becomes too large for any practical applications, so not all the rear energy can be absorbed by the line. In a realized TL, only the upper bass is TL loaded in the true sense of the term (i.e. fully absorbed); the low bass is allowed to freely radiate from the vent in the cabinet. The line therefore effectively works as a low-pass filter, another crossover point in fact, achieved acoustically by the line and its absorbent filling. Below this “crossover point” the low bass is loaded by the column of air formed by the length of the line. The length is specified to reverse the phase of the rear output of the drive unit as it exits the vent. This energy combines with the output of the bass unit, extending its response and effectively creating a second driver.


Sound ducts as transmission lines

A duct for sound propagation also behaves like a transmission line (e.g. air conditioning duct, car muffler, ...). Its length may be similar to the wavelength of the sound passing through it, but the dimensions of its cross-section are normally smaller than one quarter the 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 In physics, the wavefront of a time-varying ''wave field'' is the set (locus) of all points having the same ''phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal freque ...
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: # 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. # 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. # 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.


See also

* Frequency response * Loudspeaker acoustics *
Loudspeaker measurement Loudspeaker measurement is the practice of determining the behaviour of loudspeakers by measuring various aspects of performance. This measurement is especially important because loudspeakers, being transducers, have a higher level of distorti ...
* Speaking tube *
Transmission line loudspeaker A transmission line loudspeaker is a loudspeaker enclosure design which uses the topology of an acoustic transmission line within the cabinet, compared to the simpler enclosures used by sealed (closed) or ported (bass reflex) designs. Instead of re ...


References


External links

{{Wikibooks, Computation of an acoustic Transmissionline
Quarterwave loudspeakers
– Martin J King, developer of TL modeling software
Transmission Line Speakers Pages
– TL projects, history & more

2009-10-24) – Application, tips, essays

– description of operation, equation and online calculation Loudspeaker technology Audio engineering