Editing Loudspeaker (section)

==Listening environment==
{{Main|Room acoustics}}
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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 (e.g. from [[resonant room modes]]), thus changing the timbre and character of the sound at the listener's ears. The human brain is sensitive to small variations in reflected sound, 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 (acoustics)|absorption]] and [[Diffusion (acoustics)|diffusion]] present in the environment. Clapping one's hands in a typical empty room, without draperies or carpet, produces a zippy, fluttery echo due to a lack of absorption and diffusion.

===Placement===
In a typical rectangular listening room, the hard, parallel surfaces of the walls, floor and ceiling cause primary [[acoustic resonance]] nodes in each of the three dimensions: left–right, up–down and forward–backward.<ref>{{cite book |last=Beranek |first=Leo |date=1954 |title=Acoustics |chapter=10 |publisher=McGraw Hill }}</ref> Furthermore, there are more complex resonance modes involving up to all six boundary surfaces combining to create [[standing wave]]s. This is called speaker boundary interference response (SBIR).<ref>{{cite web |url=https://arqen.com/acoustics-101/speaker-placement-boundary-interference/ |title=Is Speaker–Boundary Interference Killing Your Bass? |date=November 11, 2014 |access-date=February 15, 2022 }}</ref> Low frequencies excite these modes the most, since long wavelengths are not much affected by furniture compositions or placement. The mode spacing is critical, especially in small and medium-sized rooms like recording studios, home theaters and broadcast studios. The proximity of the loudspeakers to room boundaries affects how strongly the resonances are excited as well as affecting the relative strength at each frequency. The location of the listener is critical, too, as a position near a boundary can have a great effect on the perceived balance of frequencies. This is because standing-wave patterns are most easily heard in these locations and at lower frequencies, below the [[Schroeder frequency]], depending on room size.{{Citation needed|date=April 2024}}

===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]]. 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.

Any object radiating sound, including a loudspeaker system, can be thought of as being composed of combinations of such simple point sources. The radiation pattern of a combination of point sources is not the same as for a single source but depends on the distance and orientation between the sources, the position relative to them from which the listener hears the combination, and the frequency of the sound involved. Using mathematics, some 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 [[Dipole speaker|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 that connects the two sources and minimum output to the sides when the observing point is equidistant from the two sources{{snd}}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 point sources or dipoles. If mounted on a finite baffle, and these out-of-phase waves are allowed to interact, peaks and nulls in the frequency response result. When the rear radiation is absorbed or trapped in a box, the diaphragm becomes an approximate point-source radiator. Bipolar speakers, made by mounting in-phase drivers (both moving out of or into the box in unison) on opposite sides of a box, are a method of approaching omnidirectional radiation patterns.

[[File:Bosch 36W column loudspeaker polar pattern.png|thumb|Polar plots of a four-driver industrial columnar [[public address]] loudspeaker taken at six frequencies. Note how the pattern is nearly omnidirectional at low frequencies, converging to a wide fan-shaped pattern at {{nowrap|1 kHz}}, then separating into lobes and getting weaker at higher frequencies<ref>Polar pattern File: Speaker is a [[Robert Bosch GmbH|Bosch]] 36 watt [http://www.boschcommunications.us/ProductFamily/Plena%20Public%20Address%20Systems/ProductType/Loudspeakers%20-%20Column/ LA1-UW36-x columnar model] {{webarchive|url=https://web.archive.org/web/20080918082043/http://www.boschcommunications.us/ProductFamily/Plena%20Public%20Address%20Systems/ProductType/Loudspeakers%20-%20Column/ |date=September 18, 2008 }} with four identical 4-inch drivers arranged vertically in an enclosure {{convert|841|mm|in|abbr=on}}ch) high. Polar prediction software is [http://www.clfgroup.org/viewer.htm CLF viewer]. Loudspeaker information was gathered by the manufacturer into a CF2 file.</ref>]]

In real life, individual drivers are complex 3D shapes such as cones and domes, and they are placed on a baffle for various reasons. Deriving a mathematical expression for the directivity of a complex shape, based on modeling combinations of point sources, is usually not possible, but in the far field, the directivity of a loudspeaker with a circular diaphragm is close to that of a flat circular piston, so it can be used as an illustrative simplification for discussion.

Far-field directivity of a flat circular piston in an infinite baffle is{{cn|date=March 2025}}

<math display="block">p(\theta) = \frac{p_0 J_1(k_a \sin \theta)}{k_a \sin \theta}</math>

where <math>k_a=\frac{2\pi a}{\lambda}</math>, <math>p_0</math> is the pressure on axis, <math>a</math> is the piston radius, <math>\lambda</math> is the wavelength (i.e. <math>\lambda = \frac{c}{f} = \frac{\text{speed of sound}}{\text{frequency}}</math>), <math>\theta</math> is the angle off axis and <math>J_1</math> is the [[Bessel function]] of the first kind.

A planar source such as this radiates sound uniformly for wavelengths longer than the dimensions of the planar source, and as frequency increases, the sound from such a source focuses 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 approximate 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. An example of the first is a room corner system with many small drivers on the surface of a 1/8 sphere. A system design of this type was patented and produced commercially as the [[Bose 2201]].<!--[[User:Kvng/RTH]]-->

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 and its contents. A very directive (sometimes termed ''beamy'') speaker (i.e. 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 well on axis (e.g. ''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.
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