# Acoustic transmission line

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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 of the electrical transmission line, typically conceived as a rigid-walled duct or tube, that is long and thin relative to the wavelength of sound present in it.

An acoustic waveguide is a physical structure for guiding sound waves.

Acoustics is the branch of physics that deals with the study of all mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries.

Analogy is a cognitive process of transferring information or meaning from a particular subject to another, or a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction, in which at least one of the premises, or the conclusion, is general rather than particular in nature. The term analogy can also refer to the relation between the source and the target themselves, which is often a similarity, as in the biological notion of analogy.

## Contents

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 instruments such as the pipe organ, woodwind and brass 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 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. [2] 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.

A speaking tube or voicepipe is a device based on two cones connected by an air pipe through which speech can be transmitted over an extended distance. While its most common use was in intra-ship communications, the principle was also used in affluent homes and offices of the 19th century, as well as expensive automobiles, military aircraft, and even locomotives. For most purposes, the device was outmoded by the telephone and its widespread adoption.

A wind instrument is a musical instrument that contains some type of resonator, in which a column of air is set into vibration by the player blowing into a mouthpiece set at or near the end of the resonator. The pitch of the vibration is determined by the length of the tube and by manual modifications of the effective length of the vibrating column of air. In the case of some wind instruments, sound is produced by blowing through a reed; others require buzzing into a metal mouthpiece.

The pipe organ is a musical instrument that produces sound by driving pressurized air through the organ pipes selected via a keyboard. Because each pipe produces a single pitch, the pipes are provided in sets called ranks, each of which has a common timbre and volume throughout the keyboard compass. Most organs have multiple ranks of pipes of differing timbre, pitch, and volume that the player can employ singly or in combination through the use of controls called stops.

## 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:

${\displaystyle \ell ={\frac {344}{\,4\times f\,~}}}$

where:

${\displaystyle f\,~~~~}$ is the sound frequency in Hertz (Hz)
344 ms is the speed of sound in air at 20°  C
${\displaystyle \ell \,~~~~}$ is the length of the transmission line in meters.

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 [3] 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 loudspeakers in the 1960s and 1970s. In 1965, A R Bailey’s article in Wireless World, “A Non-resonant Loudspeaker Enclosure Design”, [4] detailed a working Transmission Line, which was commercialized by John Wright and partners under the brand name IMF and later TDL, and were sold by audiophile Irving M. "Bud" Fried in the United States.

A loudspeaker is an electroacoustic transducer; a device which converts an electrical audio signal into a corresponding sound. The most widely used type of speaker in the 2010s is the dynamic speaker, invented in 1925 by Edward W. Kellogg and Chester W. Rice. The dynamic speaker operates on the same basic principle as a dynamic microphone, but in reverse, to produce sound from an electrical signal. When an alternating current electrical audio signal is applied to its voice coil, a coil of wire suspended in a circular gap between the poles of a permanent magnet, the coil is forced to move rapidly back and forth due to Faraday's law of induction, which causes a diaphragm attached to the coil to move back and forth, pushing on the air to create sound waves. Besides this most common method, there are several alternative technologies that can be used to convert an electrical signal into sound. The sound source must be amplified or strengthened with an audio power amplifier before the signal is sent to the speaker.

Irving M. "Bud" Fried, was one of the well known American audiophiles of the "Golden Age" of stereophonic reproduction such as Saul Marantz and David Hafler.

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 (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. [5] Irving M. Fried, 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 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.

## Related Research Articles

A subwoofer is a woofer, or a complete loudspeaker, which is dedicated to the reproduction of low-pitched audio frequencies known as bass and sub-bass. The typical frequency range for a subwoofer is about 20–200 Hz for consumer products, below 100 Hz for professional live sound, and below 80 Hz in THX-approved systems. Subwoofers are intended to augment the low frequency range of loudspeakers that cover the higher frequency bands. While the term "subwoofer" technically only refers to the speaker driver, in common parlance, the term often refers to a subwoofer driver mounted in a speaker enclosure (cabinet), often with a built-in amplifier.

A woofer or bass speaker is a technical term for loudspeaker driver designed to produce low frequency sounds, typically from 40 Hz up to 500 Hz. The name is from the onomatopoeic English word for a dog's bark, "woof". The most common design for a woofer is the electrodynamic driver, which typically uses a stiff paper cone, driven by a voice coil surrounded by a magnetic field.

An electrostatic loudspeaker (ESL) is a loudspeaker design in which sound is generated by the force exerted on a membrane suspended in an electrostatic field.

A horn loudspeaker is a loudspeaker or loudspeaker element which uses an acoustic horn to increase the overall efficiency of the driving element(s). A common form (right) consists of a compression driver which produces sound waves with a small metal diaphragm vibrated by an electromagnet, attached to a horn, a flaring duct to conduct the sound waves to the open air. Another type is a woofer driver mounted in a loudspeaker enclosure which is divided by internal partitions to form a zigzag flaring duct which functions as a horn; this type is called a folded horn speaker. The horn serves to improve the coupling efficiency between the speaker driver and the air. The horn can be thought of as an "acoustic transformer" that provides impedance matching between the relatively dense diaphragm material and the less-dense air. The result is greater acoustic output power from a given driver.

Klipsch Audio Technologies is an American loudspeaker company based in Indianapolis, Indiana. Founded in Hope, Arkansas in 1946 as 'Klipsch and Associates' by Paul W. Klipsch, the company produces loudspeaker drivers and enclosures, as well as complete loudspeakers for high end, high fidelity sound systems, public address applications, and personal computers.

Thiele/Small parameters are a set of electromechanical parameters that define the specified low frequency performance of a loudspeaker driver. These parameters are published in specification sheets by driver manufacturers so that designers have a guide in selecting off-the-shelf drivers for loudspeaker designs. Using these parameters, a loudspeaker designer may simulate the position, velocity and acceleration of the diaphragm, the input impedance and the sound output of a system comprising a loudspeaker and enclosure. Many of the parameters are strictly defined only at the resonant frequency, but the approach is generally applicable in the frequency range where the diaphragm motion is largely pistonic, i.e. when the entire cone moves in and out as a unit without cone breakup.

A bass reflex system is a type of loudspeaker enclosure that uses a port (hole) or vent cut into the cabinet and a section of tubing or pipe affixed to the port. This port enables the sound from the rear side of the diaphragm to increase the efficiency of the system at low frequencies as compared to a typical sealed- or closed-box loudspeaker or an infinite baffle mounting.

An acoustic horn or waveguide is a tapered sound guide designed to provide an acoustic impedance match between a sound source and free air. This has the effect of maximizing the efficiency with which sound waves from the particular source are transferred to the air. Conversely, a horn can be used at the receiving end to optimize the transfer of sound from the air to a receiver.

A full-range loudspeaker drive unit is defined as a driver which reproduces as much of the audible frequency range as possible, within the limitations imposed by the physical constraints of a specific design. The frequency range of these drives is maximized through the use of a whizzer cone and other means. Most single driver systems, such as those in radios, or small computer speaker designs, cannot reproduce the entire audio range.

Acoustic resonance is a phenomenon where acoustic systems amplify sound waves whose frequency matches one of its own natural frequencies of vibration.

A loudspeaker enclosure or loudspeaker cabinet is an enclosure in which speaker drivers and associated electronic hardware, such as crossover circuits and, in some cases, power amplifiers, are mounted. Enclosures may range in design from simple, homemade DIY rectangular particleboard boxes to very complex, expensive computer-designed hi-fi cabinets that incorporate composite materials, internal baffles, horns, bass reflex ports and acoustic insulation. Loudspeaker enclosures range in size from small "bookshelf" speaker cabinets with 4" woofers and small tweeters designed for listening to music with a hi-fi system in a private home to huge, heavy subwoofer enclosures with multiple 18" or even 21" speakers in huge enclosures which are designed for use in stadium concert sound reinforcement systems for rock music concerts.

Loudspeaker measurement is the practice of determining the behavior of loudspeakers by measuring various aspects of performance. This measurement is especially important because loudspeakers, being transducers, have a higher level of distortion than other audio system components used in playback or sound reinforcement.

A speaker enclosure using a passive radiator (PR) usually contains an "active loudspeaker", and a passive radiator. The active loudspeaker is a normal driver, and the passive radiator is of similar construction, but without a voice coil and magnet assembly. It is not attached to a voice coil or wired to an electrical circuit or power amplifier.

Acoustic suspension is a type of loudspeaker speaker enclosure design which uses one or more loudspeaker drivers mounted in a sealed box or cabinet. Acoustic suspension systems reduce bass distortion that can be caused by stiff motor suspensions in conventional loudspeakers. It was invented in 1954 by Edgar Villchur, and brought to commercial production by Villchur and Henry Kloss with the founding of Acoustic Research in Cambridge, Massachusetts Speaker cabinets with acoustic suspension can provide tight and accurate bass response, especially in comparison with an equivalently-sized speaker enclosure which has a bass reflex port or vent; the bass vent boosts low-end output, but at the tradeoff of introducing phase delay and accuracy problems. Sealed boxes are generally less efficient than a ported cabinet, so a sealed box speaker cabinet will need more power amplifier wattage to deliver the same amount of bass output.

The Voigt pipe is a type of loudspeaker enclosure that embodies a combination of transmission line, ported enclosure and horn characteristics. It is highly regarded by some speaker designers, as evidenced by established manufacturers such as Castle. Due to its relatively high efficiency the design is frequently employed in full-range loudspeaker designs. The concept is that the sound emitted from the rear of the loudspeaker driver is progressively reflected and absorbed along the length of the tapering tube, almost completely preventing internally reflected sound being retransmitted through the cone of the loudspeaker. The lower part of the pipe acts as a horn while the top can be visualized as an extended compression chamber. The entire pipe can also be seen as a tapered transmission line in inverted form, that is, widening rather than narrowing from top to bottom. The driver is usually positioned close to the middle of the baffle or slightly lower. Its relatively low adoption in commercial speakers can mostly be attributed to the large resulting dimensions of the speaker produced and the expense of manufacturing a rigid tapering tube. The Voigt pipe was designed in 1934 by Paul G. A. H. Voigt and is also referred to as a tapered quarter-wave pipe (TQWP) or tapered quarter-wave tube (TQWT).

The moving iron speaker was the earliest type of electric loudspeaker. They are still used today in some miniature speakers where small size and low cost are more important than sound quality. A moving iron speaker consists of a ferrous-metal diaphragm or reed, a permanent magnet and a coil of insulated wire. The coil is wound around the permanent magnet to form a solenoid. When an audio signal is applied to the coil, the strength of the magnetic field varies, and the springy diaphragm or reed moves in response to the varying force on it. The moving iron loudspeaker Bell telephone receiver was of this form. Large units had a paper cone attached to a ferrous metal reed.

The Linn Isobarik, nicknamed "Bariks" or "Briks", is a loudspeaker designed and manufactured by Linn Products. The Isobarik is known for both its reproduction of low bass frequencies and being very demanding on amplifiers.

A transmission line loudspeaker is a loudspeaker enclosure design (topology) that uses an acoustic transmission line within the cabinet, compared to the simpler enclosures used by sealed (closed) or ported designs. Instead of reverberating in a fairly simple damped enclosure, sound from the back of the bass speaker is directed into a long damped pathway within the speaker enclosure, which allows far greater control and use of speaker energy, and the resulting sound.

## References

1. Beranek, Leo (1954) Acoustics. American Institute of Physics. ISBN   978-0883184943
2. L J S Bradbury, “The Use of Fibrous Materials in Loudspeaker Enclosures”, Journal of the Audio Engineering Society, April 1976, pages 404-412
3. A R Bailey, “A Non-resonant Loudspeaker Enclosure Design”, Wireless World, October 1965, pages 483-486