Loudspeaker Projects & Experiments for Lesson Plans & Science Fair Projects

An inexpensive low fidelity 3.5 inch driver, typically found in small radios

An expensive 4-way, high fidelity loudspeaker system.

A loudspeaker, speaker, or speaker system is an electromechanical transducer that converts an electrical signal into sound. The term loudspeaker can refer to individual devices (or drivers), or to complete systems consisting of an enclosure incorporating one or more drivers and additional electronics. Loudspeakers are the most variable elements in any audio system, and are responsible for marked audible differences between otherwise identical sound systems. Loudspeaker performance (i.e., their accuracy in reproducing a signal without adding distortion) is significantly poorer than that of other audio equipment. For example, harmonic distortion in a typical loudspeaker can be 100 to 1000 times greater than that in amplifiers. ^[1] The frequency response of a loudspeaker is often referenced as being within ±3 dB of perfect linearity (though many speaker designs fall far outside this range), whereas an amplifier may vary less than 0.1 dB.

To reproduce a wide range of frequencies, most loudspeaker systems require more than one driver, particularly for high sound pressure level or high fidelity applications. Individual drivers are used to cover different frequency ranges. The drivers are named subwoofers, for very low frequencies; woofers, for low frequencies; squawkers, for middle frequencies; tweeters, for high frequencies; and supertweeters, for very high frequencies. An electronic filter called a crossover separates the incoming signal into different frequency bands appropriate for each driver. A loudspeaker system with 'N' separate frequency bands is described as "N-way speakers": a 2-way system will have woofer and tweeter speakers; a 3-way system a combination of woofer, tweeter, and mid-range speakers, and so on.

History

Alexander Graham Bell patented the first electrical loudspeaker as part of his telephone in 1876, which was followed in 1878 by an improved version from Ernst Siemens. Nikola Tesla reportedly created a similar device in 1881, but was not issued a patent.^[2] During this time, Thomas Edison was issued a British patent for a system using compressed air as an amplifying mechanism for his early cylinder phonographs, but he ultimately settled for the familiar metal horn driven by a membrane attached to the stylus. In 1898, Horace Short patented a design for a loudspeaker driven by compressed air, then sold the rights to Charles Parsons, who was issued several additional British patents before 1910. Several companies, including Victor and Pathe, produced record players using compressed-air loudspeakers. However, these designs were significantly limited by their poor overall sound quality and their inability to reproduce sound at low-volume. Variants of the system were used for public address applications, and much more recently other variations have been used to test space equipment for resistance to the very loud sound levels launch rockets produce (ca, 165 dB SPL).

These first loudspeakers used electromagnets because large, powerful permanent magnets were generally not available at a reasonable price. The coil of an electromagnet, called a field coil, was energized by current through a second pair of connections to the driver. This winding usually served a dual role, acting also as a choke coil filtering the power supply of the amplifier to which the loudspeaker was connected. AC ripple in the current was attenuated by the action of passing through the choke coil; however, AC line frequencies tended to modulate the audio signal being sent to the voice coil and added to the audible hum of a powered-up sound reproduction device.

The quality of loudspeaker systems until the 1950s was, by modern standards, poor. Continuous developments in enclosure design and materials have led to significant audible improvements. The most notable improvements in modern speakers are improvements in cone materials, the introduction of higher temperature adhesives, improved permanent magnet materials, improved measurement techniques, computer aided design and finite element analysis.

Driver design

Cut-away view of a dynamic loudspeaker

The most common type of driver uses a lightweight diaphragm connected to a rigid basket, or frame, via flexible suspension which constrains a coil of fine wire to move axially through a cylindrical magnetic gap. When an electrical signal is applied to the voice coil, a magnetic field is created by the electric current in the coil which thus becomes an electromagnet. The coil and the driver's magnetic system interact, generating a mechanical force which causes the coil, and so the attached cone, to move back and forth and so reproduce sound under the control of the applied electrical signal coming from the amplifier. The following is a brief discussion of the individual components of this most common type of loudspeaker.

The diaphragm is usually manufactured in a cone or dome shaped profile. A variety of different materials may be used, but the most common are paper, plastic and metal. The ideal material would be stiff, light and well damped. In practice, all three of these criteria cannot be met simultaneously, and thus driver design involves tradeoffs. Paper is light and well damped, but not stiff. Metal can be made stiff and light, but it is not well damped. Plastic can be light, but typically the stiffer it is made, the less well-damped it is. As a result, many cones are made of some sort of composite. This can either be a sandwich construction or simply a coating to stiffen or damp a cone.

The basket or frame must be designed for rigidity to avoid deformation, which could cause the voice coil to rub against the magnet structure. Baskets are typically cast or stamped metal, although molded plastic baskets are becoming common, especially for inexpensive drivers. The frame plays a secondary role in conducting heat away from the coil.

The suspension system keeps the coil centered in the gap and provides a restoring force to make the speaker cone return to a neutral position after moving. A typical suspension system consists of two parts: the "spider", which connects the diaphragm or voice coil to the frame and provides the majority of the restoring force; and the "surround", which helps center the coil and allows free movement. The spider is usually made of a corrugated fabric disk. The surround can be a roll of rubber or foam or a corrugated fabric, attached to the outer circumference of the cone and to the frame.

The voice coil wire is usually copper, though aluminum, or rarely silver, may be used. Voice coil wire can be round, rectangular, or hexagonal, giving varying amounts of wire volume coverage in the available magnetic gap. The coil is oriented coaxially inside the gap, a small circular volume (a hole, slot, or groove) in the magnetic structure within which it can move back and forth. The gap establishes a concentrated magnetic field between the two poles of a permanent magnet; the outside of the gap being one pole and the center post (a.k.a. pole-piece) being the other. The center post and back-plate are sometimes a single piece called the yoke.

Modern driver magnets are almost always permanent and made of ceramic, ferrite, Alnico, or, more recently, rare earth. The size and type of magnet and the magnetic circuit differ depending on design goals. A current trend in design, due to increases in transportation costs and a desire for smaller, lighter devices (as in many home theater multi-speaker installations), is the use of rare earth magnet instead of ferrite types.

Driver design, and the combination of one or more drivers into an enclosure to make a speaker system, is both an art and science. Adjusting a design to improve performance is done using magnetic, acoustic, mechanical, electrical, and material science theory, high precision measurements, and the observations of experienced listeners. Designers can use an anechoic chamber to ensure the speaker can be measured independently of room effects, or any of several electronic techniques. Some developers eschew anechoic chambers in favor of specific standardized room set-ups intended to simulate real-life listening conditions. Some of the issues speaker designers must confront are lobing, phase effects, off axis response, crossover complications, and psychoacoustics.

Most loudspeaker drivers are currently manufactured in China. The fabrication of finished loudspeaker systems is segmented, depending largely on price point and on shipping costs and weight limitations. High-end speaker systems, often heavier than economic shipping allows outside local regions, are usually made in the same area as their target markets and can command prices of $10,000 or more per pair. The lowest-priced speaker systems are mostly manufactured in China or other low-cost manufacturing locations. Although the manufacture of drivers has become essentially commoditized, the fabrication and subsequent sale of finished speaker systems still carry high profit margins. Partly for this reason, manufacturers are increasingly combining power amplifier electronics (a typically lower profit item) with finished speaker systems to create "powered speakers" with an overall higher market value.

Driver types

Exploded view of a dome tweeter

Full range drivers

A full-range driver is designed to have as wide a frequency response as possible. These drivers are small, typically 2 to 6 inches (5 to 16 cm) in diameter to permit reasonably high frequency response, but this means they often have limited low distortion sound output at low frequencies and limited power handling capacity (due to a small voice coil).

They often employ an additional cone called a whizzer-- a small, light cone attached to the driver's apex-- which usually acts as the dust cap, to extend the high frequency response and broaden the high frequency directivity, which would otherwise be greatly reduced due to cone material breakup at higher frequencies (the cone area away from the coil fails to follow the area near the coil at higher frequencies). The main cone is built so as to flex more in this region at high frequencies than the rest of the cone. The result is that the main cone delivers the low frequencies and the whizzer cone contributes most of the higher frequencies. Since the whizzer cone is smaller than the main diaphragm, dispersion at high frequencies is improved over a driver with a single larger diaphragm. Full range drivers are one approach to avoiding the possible audible effects of multiple driver systems caused by non-coincident driver location and crossover issues.

Subwoofer

A subwoofer is a woofer driver used only for the lowest part of the audio spectrum. A typical subwoofer only reproduces sounds below perhaps 120 Hz; some can go lower than 20 Hz. Because the intended range of frequencies is limited, subwoofer design is usually simpler, often consisting of a single, subwoofer enclosed in a suitable (often bass reflex) cabinet. To accurately reproduce very low bass notes without unwanted resonance, subwoofers have to be large enough and properly braced. Subwoofers are often supplied with power amplifiers and electronic filters, with additional controls relevant to low frequency reproduction, such as phase switches built directly into the cabinet. These subwoofers are known as "active subwoofers". Some subwoofer systems, often called "servo" or "motional feedback" subwoofers, also include sophisticated systems utilizing accelerometers or back EMF sensors to sense cone movement. The actual motion of the cone is compared to the input signal many times per second and the feedback circuitry applies continuous correction to the drive signal to enable the woofer to reproduce the input signal with less distortion.

Loudspeaker system design

Crossover

Used in multi-driver speaker systems, the crossover is a device that separates the input signal into different frequency ranges for each driver. Each driver, therefore, will receive the frequency range it is designed for, so that the distortion in each driver, and interference between the drivers, is reduced. The ideal crossover would have no overlap in the signal sent to different drivers, but this is not achievable in practice with standard analog filters.

Crossovers can be passive or active. A passive crossover is an electronic circuit using a combination of one or more non-polar capacitors, resistors, and inductors. These parts are connected after the amplifier and divide the signal into individual frequency ranges before it is delivered to the speaker drivers. A passive crossover requires no external power. An active crossover is an electronic filter circuit that divides the signal into individual frequency ranges before the amplifier, requiring one amplifier for each bandpass.

Passive crossover are generally installed inside speaker boxes and are by far the most common type of crossover for home and low power use. In car audio systems, passive crossovers are often in a separate box due to the size of some of the passive components used. Passive crossovers convert part of the amplifier power they handle into heat, so when high power output is needed, active crossovers are often used. Active crossovers allow more precise alignment of phase and time between frequency bands; equivalently tight adjustment using only passive components is a difficult engineering problem in part because of part tolerances.

Many new loudspeaker designs have begun incorporating active crossover circuitry and onboard amplification. Such designs typically require AC power and need low level signal inputs instead of high level amplifier output connections. Ideally, this approach offers the advantages of close alignment of phase between frequency bands, active protection circuits to protect drivers, and virtually no loss of amplifier power in long cable runs or passive crossover components. Self-powered loudspeakers are being used in many applications such as small-scale computer sound (for one listener) and large-scale concert sound systems (for large halls full of listeners). Self-powered concert loudspeakers provide the additional benefit of improved predictability in sound quality; the touring concert sound engineer need not worry about customized crossover settings in each venue changing the characteristics of a loudspeaker.

Enclosures

$A 3-way speaker system. The cabinet is narrow to reduce a diffraction effect called the 'baffle step'.$

A 3-way speaker system. The cabinet is narrow to reduce a diffraction effect called the 'baffle step'.

Most loudspeaker systems consist of drivers mounted in an enclosure, or cabinet. The role of the enclosure is to provide a place to mount the drivers and prevent sound waves from the back of a driver from meeting those from the front-- which causes interference, cancellation and significantly alters the level and quality of low frequencies.

The simplest mounting is a flat panel (baffle) with the drivers mounted to it. However, in this design, frequencies with a wavelength longer than the baffle dimensions are canceled out because the antiphase radiation from the rear of the cone interferes with the radiation from the front. With an infinitely large panel interference could be entirely prevented. A sufficiently large sealed box can approach this behavior. ^[4]^[5].

Since panels of infinite dimensions are impractical, most enclosures function by containing the rear radiation from the cone. A sealed enclosure prevents transmission of the sound emitted from the rear of the loudspeaker by confining the sound in a rigid and airtight box. Techniques used to reduce transmission of sound through the walls of the cabinet include thicker cabinet walls, lossy wall material, internal bracing, curved cabinet walls or more rarely visco-elastic materials or thin lead sheeting applied to interior enclosure walls.

However, this rigid enclosure provokes internal reflection of sound which can then be transmitted through the loudspeaker cone, again resulting in degradation of sound quality. This is reduced by internal absorption through the use of absorptive materials (often called "damping") such as fiberglass, wool, or synthetic fiber batting within the enclosure. The internal shape of the enclosure can be designed to reduce this by reflecting sounds away from the loudspeaker where they may then be absorbed.

Other enclosure types alter the rear radiation so it can add constructively to the output from the front of the cone. Designs that do this (including bass reflex, passive radiator, transmission line, etc...) are often used to extend the effective low frequency response of the driver.

To make the transition between drivers as seamless as possible, system designers have attempted to time-align or phase adjust the drivers by moving one or more drivers forward or back, so that the acoustic center of the drivers is in the same vertical plane. This may involve tilting the face speaker back, or providing separate enclosure mounting for each driver, or, less commonly, using electronic techniques to achieve the same effect. These attempts account for some unusual cabinet designs.

A speaker cabinet will cause diffraction, causing peaks and dips in the frequency response. This is usually a problem at higher frequencies where wavelengths are similar to, or smaller than, cabinet dimensions. The effect can be minimized by rounding the front edges of the cabinet, using a smaller or narrower enclosure, strategic arrangement of the drivers, or using absorptive material around a driver.

Wiring connections

Five-way binding posts on a loudspeaker connected using banana plugs.

A loudspeaker with two pairs of binding posts for bi-wiring or bi-amplification.

Most loudspeakers use two wiring points to connect to the source of the signal (for example, to the audio amplifier or receiver). This is usually done using binding posts, or spring clips on the back of the enclosure. If the wires for left and right speakers (in a stereo setup) are not connected in phase with each other (the + and - connections on the speaker and amplifier should be connected to each other) the loudspeakers will be out of phase and destructive sound wave interference will occur when a common signal is sent to each speaker. In this case, any motion one cone (usually the woofer) makes will be opposite to the other. This type of wiring error doesn't damage speakers but does create inverse sound waves that partially cancel those from nearby speakers. Due to the spacing of the speakers, the bass frequencies are where this phenomenon is most apparent. A simple way to check for wiring phase problems in a home or car stereo is to temporarily adjust the bass tone control up and the treble control down, then move the balance control so that sound is alternately heard from the left and right speakers alone, and both together. If the music has the bass tones mixed to mono (a common practice even today) the bass should be loudest with the control centered. If the bass is louder with only one channel playing, either there is a wiring error, or the music signal is not mono in the low bass.

Specifications

Specifications label on a loudspeaker

Electrical characteristics of a dynamic loudspeaker

The load a driver presents to an amplifier consists of a complex electrical impedance -- a combination of resistance, and both capacitive and inductive reactance, which combines properties of the driver, its mechanical motion, effects of crossover components (if any are in the signal path between amplifier and driver), and effects of air loading on the driver as modified by the enclosure and its environment. Most amplifiers (amps) output specifications are given at a specific power into an ideal resistive load. However, a loudspeaker with a nominal impedance of 8 Ω does not really have a constant resistance across its frequency range. Instead, the voice coil is inductive, the enclosure changes the characteristics of the driver, and a passive crossover between the drivers and the amplifier contributes its own variations. The result is a load resistance which varies with frequency, and usually a varying phase relationship between voltage and current as well, also changing with frequency.

Electromechanical measurements

Fully characterizing the sound output of a loudspeaker in words is nearly impossible. Measurements help to put a numerical value on several aspects of performance so intelligent comparisons and improvements can be made. Examples of typical measurements are: amplitude and phase characteristics vs. frequency; impulse response under one or more conditions; directivity vs. frequency; harmonic and intermodulation distortion vs SPL output using any of several test signals; stored energy (ie, 'ringing'); impedance vs. frequency and small signal vs. large signal performance. Most of these measurements require relatively expensive equipment to perform, but the raw sound pressure level output is rather easier to measure and so it is often reported. The sound pressure level (SPL) a loudspeaker produces is measured in decibels (dB_spl).

Efficiency vs. sensitivity

Loudspeaker efficiency is defined as the sound power output divided by the electrical power input. Most loudspeakers are actually very inefficient transducers; about 1% of the electrical energy sent by an amplifier to a typical home loudspeaker is converted to the acoustic energy we can hear. The remainder is converted to heat, typically in the voice coil and magnet assembly. The main reason for this is the difficulty of achieving proper impedance matching between the acoustic impedance of the drive unit and that of the air into which it is radiating.

Driver ratings based on the SPL for a given input are known as sensitivity ratings and are notionally similar to efficiency. Sensitivity is usually defined as so many decibels at 1 W electrical input, measured at 1 meter. The voltage used is often 2.83 V_RMS, which happens to be 1 watt into an 8 Ω (nominal) speaker impedance (nominally true for many speaker systems). Measurements taken with this reference are quoted as dB with 2.83 V @ 1 m.

The sound pressure output is measured at (or scaled to be equivalent to a measurement taken at) one meter from the loudspeaker and on-axis or directly in front of it under the conditions that the loudspeaker is radiating into an infinitely large space and mounted on an infinite baffle. Clearly then, sensitivity does not correlate precisely with efficiency, as it also depends on the directivity of the driver being tested and the acoustic environment in front of the actual loudspeaker. For instance, a cheerleader's horn produces more sound output in the direction it is pointed than the cheerleader could by herself, but the horn does not improve or increase the cheerleader's total sound power output; it merely "focuses" the sound waves by blocking them from dispersing in all directions.

A driver with a higher maximum power rating cannot necessarily be driven to louder levels than a lower rated one, since sensitivity and power handling are largely independent properties. In the examples that follow, assume, for simplicity, that the drivers being compared have the same electrical impedance, are operated at the same frequency which is within both driver's respective pass bands, and that power compression and distortion are low. For the first example, a speaker 3 dB more sensitive than another will produce double the sound pressure level (or be 3 dB louder) for the same power input. Thus a 100 W driver ("A") rated at 92 dB for 1 W @ 1 m sensitivity will output twice as much acoustic power as a 200 W driver ("B") rated at 89 dB for 1 W @ 1 m when both are driven with 100 W of input power. For this particular example, when driven at 100 W, speaker A will produce the same SPL, or loudness, speaker B would produce with 200 W input. Thus a 3 dB increase in sensitivity of the speaker means that it will need half the amplifier power to achieve a given SPL; this translates into a smaller, less complex power amplifier and often to reduced overall cost.

It is not possible to combine high efficiency, especially at low frequencies, with compact enclosure size, and adequate low frequency response. One can, more or less, only choose two of the three parameters when designing a speaker system. So, for example, if extended low frequency performance and a small box size are important, one must accept low efficiency. This rule of thumb is sometimes called Hoffman's Iron Law (after J. A. Hoffman, the H in KLH).

Listening environment

The interaction of a loudspeaker system with its environment is complex and is largely out of the loudspeaker designer's control. Most listening rooms present a more or less reflective environment, depending on size, shape, volume, and furnishings. This means the sound reaching a listener's ears consists not only of sound directly from the speaker system, but also the same sound delayed by traveling to and from (and being modified by) one or more surfaces. These reflected sound waves, when added to the direct sound, cause cancellation and addition at assorted frequencies, changing the timbre and character of the sound. Our brains are very sensitive to these small variations, and this is part of the reason why a loudspeaker system sounds different at different listening positions or in different rooms.

A significant factor in the sound of a loudspeaker system is the amount of absorption and diffusion present in the environment. Clapping one's hands in an empty room, without draperies or carpet, will produce a zippy, fluttery echo which is due both to a lack of absorption and to reverberation (that is, repeated echoes). The addition of hard surfaced furniture, wall hangings, and shelving will change the echoes, due primarily to the diffusion caused by somewhat reflective objects with shapes and textures having sizes on the order of the sound wavelengths being diffused. This somewhat breaks up the simple reflections otherwise caused by flat walls, floors and ceilings, and spreads the reflected energy of an incident wave over a larger angle on reflection.

Adding carpet, curtains, tapestries, people, or soft surfaced furniture will further change the interaction of a loudspeaker with the room by absorbing sound at various frequencies and reducing reflections at those frequencies. The thinner a material is, the less likely it will have an effect at low frequencies. An overabundance of absorption at high frequencies can be caused by large areas of absorptive materials and can cause a speaker system to sound deficient at higher frequencies, and likewise minimal absorption can cause an otherwise adequate loudspeaker to sound too bright or sibilant at those frequencies.

Placement

For good sound in a home environment, a listening room should have a balance of diffusion and absorption. Most systems will sound best when the speakers are set up more or less symmetrically with respect to the listener and also to room boundaries. Early reflections (the first reflection of a particular sound) do the most to color the sound (due to the so-called Haas effect from psychoacoustics), so placing speakers too near the rear or side walls is generally something to be avoided, although judicious use of absorbing or diffusing materials can somewhat moderate an otherwise poor placement location. Mounting a speaker in a wall (or in a bookshelf with books flush with the baffle) somewhat removes reflective boundary concerns, but limits placement flexibility, and introduces some diffraction issues from nearby surfaces. In professional applications, placement is largely controlled by the location of the listening audience, required appearance (for example, prominence or invisibility), and available space. Fine adjustment is often not possible in professional applications.

Another factor in room acoustics is a phenomenon called standing waves. A one-dimensional example is sound bouncing between two reflective surfaces. Sound resonates, or repeatedly reflects at particular frequencies, if the distance between the boundaries corresponds to an integral number of half wavelengths of the sound concerned. Since sound travels at ~345 m/s, a pair of reflective boundaries separated by 5 meters will cause resonances at 34.5 Hz, 69 Hz, 103.5 Hz ..., recalling that wavelength is the speed of sound divided by the frequency. It is best, if possible, to arrange that no room wall length or height is simply related to any other. A cubical listening room would be most resonant since all dimensions are identical, each reinforcing the same resonance modes. One approach is to ensure that each room dimension is related to another by the Golden Ratio, which will ensure that the unavoidable reflections between walls are not reinforced by any others.

In a typical rectangular listening room, this resonant phenomenon happens differently in three dimensions, and there are even more complex interactions that involve four or even all six boundary surfaces. It is primarily an issue for low frequencies which are not much affected by such things as furniture or its placement. In addition, the location of the loudspeakers, and the listener, with respect to room boundaries affect how strongly the resonances are excited. Many people are familiar with certain locations in some rooms, clubs, or buildings which have much more, or less, bass - most usually near room walls or corners. This is because standing wave patterns are most pronounced in these locations and at lower frequencies, below the Schroeder frequency - typically around 200-300 Hz, depending on room size.

Directivity

Acousticians, in studying the radiation of sound sources have developed some concepts important to understanding how loudspeakers are perceived. The simplest possible radiating source is a point source, sometimes called a simple source. An ideal point source is an infinitesimally small point radiating sound. It may be easier to imagine a tiny pulsating sphere, uniformly increasing and decreasing in diameter, sending out sound waves in all directions equally, independent of frequency.

Any object radiating sound, including a loudspeaker system, can be thought of as being composed of combinations of simple point sources. The radiation pattern of a combination of point sources will not be the same as for a single source, but rather the radiation pattern will depend on the distance between the sources, the position relative to them from which we are observing them, and the frequency of sound. Using geometry and calculus, certain simple combinations of sources are easily solved.

One simple combination is two simple sources separated by a distance and vibrating out of phase, one miniature sphere expanding while the other is contracting. The pair is known as a doublet, or dipole, and the radiation of this combination is similar to that of a very small dynamic loudspeaker operating without a baffle. The directivity of a dipole is a figure 8 shape with maximum output along a vector which connects the two sources and minimums to the sides when the observing point is equidistant from the two sources, where the sum of the positive and negative waves cancel each other. While most drivers are dipoles, depending on the enclosure to which they are attached, they may radiate as monopoles, dipoles or bipoles. If mounted on a finite baffle and these out of phase waves are allowed to interact, dipole peaks and nulls in the frequency response result. When the rear radiation is absorbed or trapped in a box, the diaphragm becomes a monopole radiator. Bipolar speakers, made by mounting in-phase monopoles (both moving out of or into the box in unison) on opposite sides of a box, are a method of approximating an omnidirectional point source or pulsating sphere.

In real life, most speaker systems and individual drivers are actually complex 3D shapes such as cones and domes, and they are placed on a baffle to separate front radiation from rear. A mathematical expression for the directivity of a complex shape, based on modeling combinations of point sources, is usually not possible, but in the farfield the directivity of a loudspeaker with a circular diaphragm will be very close to that of a flat circular piston, so it can be used as an illustrative simplification for discussion. The formula for farfield directivity of a flat circular piston in an infinite baffle is $p(\theta) = \frac{p_0 J_1(k_a \sin \theta)}{k_a \sin \theta}$ where $k_a=\frac{2\pi a}{\lambda}$ ,

p 0

is the pressure on axis,

a

is the piston radius,

λ

is the wavelength (i.e. $\lambda = \frac{c}{f} = \frac{\text{speed of sound}}{\text{frequency}}$ )

θ

is the angle off axis and

J 1

is the Bessel function of the first kind.

A planar source will radiate sound uniformly for low frequencies, and as frequency increases, the sound will be focused into an increasingly narrower angle. The smaller the driver, the higher the frequency where this narrowing of directivity occurs. Even if the diaphragm is not perfectly circular, this effect occurs such that larger sources are more directive. Several loudspeaker designs have been built which have approximately this behavior. Most are electrostatic or planar magnetic designs.

Various manufacturers use different driver mounting arrangements to create a specific type of sound field in the space for which they are designed. The resulting radiation patterns may be intended to more closely simulate the way sound is produced by real instruments, or simply create a controlled energy distribution from the input signal (some of these are called monitors, as they are useful in checking the signal just recorded in a studio). An example of the first is a room corner assembly with many small drivers on the surface of a 1/8 sphere. A system design of this type was patented by, and actually produced commercially, by Professor Amar Bose -- the 1801. Later Bose commercial speakers have deliberately emphasized production of both direct and reflected sound by the loudspeaker itself, regardless of its environment. The designs are controversial in high fidelity circles, but have proven commercially successful. some other manufacturers' designs follow related principles.

Directivity is an important issue because it affects the frequency balance of sound a listener hears, and also the interaction of the speaker system with the room. A speaker which is very directive (ie, on an axis perpendicular to the speaker face) may result in a reverberant field lacking in high frequencies, giving the impression the speaker is deficient in treble even though it measures very well on axis (eg, flat across the entire frequency range). Speakers with very wide, or rapidly increasing directivity at high frequencies, can give the impression that there is too much treble (if the listener is on axis) or too little (if the listener is off axis). This is part of the reason why on-axis frequency response measurement is not a complete characterization of the sound of a given loudspeaker.

Other driver designs

Other types of drivers which depart from the most commonly used direct radiating electro-dynamic driver mounted in an enclosure include:

Horn loudspeakers

Horn speakers are the oldest form of loudspeaker, having been used from very early on for cylinder recording players. They use a shaped waveguide in front of or behind the driver to increase the directivity of the loudspeaker and to transform a small diameter, high pressure condition at the driver to a large diameter, low pressure condition at the mouth of the horn. This increases the sensitivity of the loudspeaker and focuses the sound over a narrower area. The size of the throat, mouth, the length of the horn, as well as the area expansion rate along it must be carefully chosen to properly provide this transforming function over a range of frequencies (at most about 3 octaves or so). The length and cross sectional mouth area required to create a bass or sub-bass horn will require a horn many feet long; 'folded' horns can reduce the total size, but will force compromises and increased complications. Some well known horn designs not only fold the low frequency horn, but use the walls in a room corner as a kind of extension of the horn sides. Formerly, largely after WWII and before the stereo era, horns whose mouths took up much of a room wall were not uncommon amongst hi-fi fans, perhaps the most common examples being those made by JBL. Hartley, and Klipsch. Such installations became much less acceptable when two were required, and entirely unthinkable in modern, multi-channel home systems.

A horn loaded speaker can have a sensitivity as high as 110 dB @ 2.83 volts (1 watt @ 8 ohms) @ 1 meter. This is a tenfold increase in output compared to a speaker rated at 90 dB sensitivity, and is invaluable in applications where high sound levels are required or amplifier power is limited.

Piezoelectric speakers

Piezoelectric speakers are frequently used as beepers in watches and other electronic devices, and are sometimes used as tweeters in less-expensive speaker systems, such as computer speakers and portable radios. Piezoelectric speakers have several advantages over conventional loudspeakers: they are resistant to overloads which would normally destroy the voice coil of a conventional loudspeaker, and they are an inherently capacitive electrical load so they usually do not require a complicated external cross-over network. There are also disadvantages: some amplifiers can oscillate when driving capacitive loads, which results in distortion or damage to the amplifier; and additionally their frequency response, in most cases, is inferior to that of other technologies. This is why they are generally used in single frequency (beeper) or non-critical applications.

Piezoelectric speakers can have extended high frequency output, and this is useful in some specialized circumstances; for instance, sonar applications in which piezoelectric variants are used as both output devices (generating underwater sound) and as input devices (acting as the sensing components of underwater microphones). They have advantages in these applications, not the least of which is simple and solid state construction which resists the effects of seawater better than, say, a ribbon based device would.

Electrostatic loudspeakers

Electrostatic loudspeakers use a high voltage electric field (rather than a magnetic field) to drive a thin membrane between two perforated conductive plates called stators. Because they are driven over the entire membrane surface rather than from a small voice coil, they are thought to provide a more linear response than dynamic drivers. They have the disadvantage that their excursion is limited because of practical concerns. The further apart the stators are positioned, the higher the voltage must be to achieve acceptable efficiency, which increases the tendency for attracting dust and arcing. For many years electrostatic loudspeakers had a reputation as an unreliable and occasionally dangerous product. Arcing remains a potential problem with current technologies, especially when allowed to get dirty or when driven with high signal levels.

Electrostatics are inherently dipole radiators and due to the thin flexible membrane cannot be used in enclosures to reduce low frequency cancellation as with common cone drivers. Due to this and the low excursion capability, full range electrostatic loudspeakers are large by nature. In order to reduce their size in commercial products, they are often used as just a high frequency driver with a conventional dynamic driver used to produce the bass frequencies.

Ribbon and planar magnetic loudspeakers

A ribbon speaker consists of a thin metal-film ribbon suspended in a magnetic field. The electrical signal is applied to the ribbon which moves with it, thus creating the sound. The advantage of a ribbon driver is that the ribbon has very little mass; thus, it can accelerate very quickly, yielding very good high-frequency response. Ribbon loudspeakers are often very fragile -- some can be torn by a strong puff of air. Most ribbon tweeters emit sound in a dipole pattern; a very few have backings which limit the dipole radiation pattern. Above and below the ends of the more or less rectangular ribbon, there is less audible output due to phase cancellation, but the precise amount of directivity depends on ribbon length. Ribbon designs generally require exceptionally powerful magnets which make them costly to manufacture. Ribbons have a very low resistance that most amplifiers cannot drive directly. As a result, a step down transformer is typically used to increase the current through the ribbon. The amplifier "sees" a load that is the ribbon's resistance times the transformer turns ratio squared. The transformer must be carefully designed so that its frequency response and parasitic losses do not degrade the sound, further increasing cost and complication relative to conventional designs.

Planar magnetic speakers (having printed or embedded conductors on a flat diaphragm) are sometimes described as "ribbons", but are not truly ribbon speakers. The term planar is generally reserved for speakers which have roughly rectangular shaped flat radiating surfaces. Planar magnetic speakers consist of a flexible membrane with a voice coil printed or mounted on them. The current flowing through the coil interacts with the magnetic field of carefully placed magnets on either side of the diaphragm, causing the membrane to vibrate more or less uniformly and without much bending or wrinkling. The driving force covers a large percentage of the membrane surface and reduces resonance problems inherent in coil-driven flat diaphragms. Many designs touted as "ribbons" are in fact planar magnetic. Many of these designs have small cavities between the magnet structures and the diaphragm. This is not ideal and it sometimes creates a "cavity resonance" response peak that requires corrective filtration. Failure to correct this cavity resonance is a cause of the steely or shrill sound sometimes attributed to these designs.

Bending wave loudspeakers

Bending wave transducers use a diaphragm that is intentionally flexible. The Manger bending wave transducer is a point source variant of the bending wave scheme, in which vibration waves start from the center of a round flat diaphragm and travel to the outside. The rigidity of the material increases from the center to the outside. Short wavelength sound therefore radiates primarily from the inner area, while longer waves reach the edge of the speaker. To prevent reflections, long waves are absorbed by a surrounding damper. The Manger transducer covers the frequency range from 80 Hz to 35,000 Hz, and is close to an ideal point sound source.

The Walsh loudspeaker systems from Ohm Acoustics are quite similar in their bending scheme, though they face downwards into the enclosure and expose the diaphragm in the shape of a long narrow cone. The traveling waves move downward along the axis of the cone and radiate in a cylindrical pattern.

Flat panel loudspeakers

There have been many attempts to reduce the size of speaker systems, or alternatively to make them less obvious. One such attempt was the development of voice coils mounted to flat panels to act as sound sources. These can then be made in a neutral color and hung on walls where they will be less noticeable than many speakers, or can be deliberately painted with patterns in which case they can function decoratively. There are two related problems with flat panel techniques: first, a flat panel is necessarily more flexible than a cone shape in the same material, and therefore will move as a single unit even less, and second, resonances in the panel are difficult to control, leading to considerable distortions. Some progress has been made using such lightweight, rigid, materials as Styrofoam, and there have been several flat panel systems commercially produced in recent years.

Distributed mode loudspeakers

A newer implementation of the flat panel speaker system involves an intentionally flexible panel and an "exciter", mounted off-center in a location such that it excites the panel to vibrate, but with minimal resonances. Speakers using NXT techniques can reproduce sound with a wide directivity pattern (paradoxically somewhat like a point source) and have been used in some computer speaker designs and a few small 'shelf systems' from such manufacturers as TEAC and Philips.

Heil air motion transducers

Dr. Oskar Heil invented this design in the 1960s. ESS, a California manufacturer, licensed it, employed Dr. Heil, and produced a range of speaker systems using them as tweeters during the 1970s and 1980s. Radio Shack, a large US retail store chain, also sold speaker systems using them as tweeters for a time.

In this approach, a pleated diaphragm is mounted in a magnetic field and forced to close and open under control of a music signal. Air is forced from between the pleats in accordance with the imposed signal, generating sound. The drivers are less fragile than ribbons and considerably more efficient (and able to produce higher absolute output levels) than ribbon, electrostatic, or planar magnetic tweeter designs. At present, there are two manufacturers of these drivers, both in Germany, one of which produces a range of high end professional speakers using tweeters and midrange drivers based on the technology.

Plasma arc speakers

Plasma arc loudspeakers use electrical plasma as a driver. Since plasma has minimal mass, but is charged and therefore can be manipulated by an electric field, the result is a very linear output at frequencies far higher than the audible range. Problems of maintenance and reliability for this approach tend to make it unsuitable for mass market use. In 1978 Dr. Alan Hill of the Los Alamos National Laboratory designed the Hill Plasmatronics, an $8000 monster whose plasma was generated from compressed helium gas.^[6] This avoided the ozone and nitrous oxide produced by RF decomposition of air in an earlier generation of plasma tweeters made by the pioneering DuKane Corporation, who produced the Ionovac (marketed as the Ionofane in the UK) during the 1950s. Currently, there remain a few manufacturers, all in Germany it seems, and a do it yourself design has been published.

A less expensive variation on this theme is the use of a flame for the driver, as flames contain ionized (electrically charged) gases.^[7]

Digital speakers

Digital speakers are an impractical but venerable technology, having been the subject of experiments by Bell Labs as far back as the 1920s. The design is simple; each bit drives an independent speaker driver. Increasingly significant bits drive speakers of twice the area of the previous (often in a ring around the previous driver). A value of "1" causes that driver to be driven to full amplitude; a value of "0" causes it to be completely shut off.

There are two problems with this design which have led to it being abandoned as impractical for the present. First, for a reasonable number of bits (required for adequate sound reproduction quality), the size of the system becomes very large. Secondly, due to analog digital conversion, the effect of aliasing is unavoidable, so that the audio output is "reflected" at equal amplitude in the frequency domain, on the other side of the sampling frequency, causing an unacceptably high level of ultrasonics to accompany the desired output.

The term "digital" or "digital-ready" is often used for marketing purposes on speakers or headphones, but these systems are not digital in the sense described above. Rather, this is a somewhat deceptive marketing tactic, in which the manufacturer is trying to capitalize on the popularity of digital sound recordings and equipment.

References

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