Double bass array

A double bass array describes a specific spatial arrangement of several bass speakers in a cuboid listening room. Its purpose is to prevent unwanted resonances when playing music with a hi-fi or home theater system by avoiding standing waves , so that the playback can take place as unadulterated as possible and regardless of where the listener is.

General

At least two (the more, the greater the effective range) identical subwoofers are required, half of which are placed on the same side of the room as the normal front speakers as close to the wall as possible. The other half of the subwoofer is placed on the opposite wall and serves there to actively cancel out the reflected sound wave.

A double bass array has nothing to do with multichannel music reproduction (surround sound) with 5.1 or 7.1 channels as with Dolby Digital or DTS . The necessary electronics are usually not provided by playback devices that can handle the aforementioned codes. However, some top models offer two pre-amp outputs for subwoofers, which can be controlled with separate delay.

functionality

Grid arrangement

Frequently implemented grid arrangement with four woofers

By placing the woofers on the front and back of the room in a grid with a certain distance from one another, the modes between the side walls and the floor or ceiling are not stimulated. The woofers must be placed on the wall according to the following formulas:

${\displaystyle p_{x}{=}{\frac {(2\cdot n+1)\cdot w_{x}}{2\cdot a_{x}}}}$

${\displaystyle p_{y}{=}{\frac {(2\cdot n+1)\cdot w_{y}}{2\cdot a_{y}}}}$

${\displaystyle w_{x}}$: Width of the wall

${\displaystyle w_{y}}$: Height of the wall

${\displaystyle p_{x}}$: Distance from the wall horizontally (in the picture for n = 0) ${\displaystyle d_{x}/2}$

${\displaystyle p_{y}}$: Vertical distance from the ceiling (in the picture for n = 0) ${\displaystyle d_{y}/2}$

${\displaystyle a_{x}}$: Number of woofers horizontally

${\displaystyle a_{y}}$: Number of woofers vertically

with counter ${\displaystyle n={0,1,2,3,...,(a-1)}}$

Top view of a room with two sound sources in a grid arrangement. Together with the mirror sources, a flat wave front forms.

As a result of this placement in a grid arrangement, the reflections of the sound on the boundary surfaces act as mirror sound sources. The interference of the individual sound sources creates a flat wave front parallel to the front of the room, as would an infinitely extended sound source. The two dimensions are to be considered independently. This means that the number of woofers as well as the distance between them can be different horizontally and vertically. It also doesn't matter whether the number of woofers is odd or even.

The cutoff frequency up to which the constructive interference forms a plane wave front is calculated for one dimension ${\displaystyle f_{c}}$

${\displaystyle f_{c}{=}{\frac {c}{2\cdot d}}}$

with : speed of sound ${\displaystyle c}$

${\displaystyle d}$: Distance between the woofers

It is therefore clear that a larger number of woofers results in a better formation of the flat wave front. However, this depends strongly on the dimensions of the room and the frequency range in which the DBA is to be used. For smaller rooms or a deep separation of the bass system, a single woofer per grille may be sufficient, for example, so as not to excite the vertical and transverse modes.

Example: With a wall measuring 4 × 3 m, four woofers per grille (two per dimension) would result in non-excitation of the transverse modes up to approx. 86 Hz and the vertical modes up to approx. 114 Hz, which would be sufficient for home theater applications.

Active extinction

Schematic representation of the active cancellation. The transverse wave symbolizes the bass signal. The flat wavefront of the front is reflected by the back wall. At the same moment, the rear bass grille emits an inverted wave front. Both extinguish each other.

Due to the grid arrangement of the front woofers, only the longitudinal mode remains along the length of the room. This is maximally stimulated by the installation close to the wall. The DBA's trick is to attach another, identical grid arrangement of woofers to the back of the room and to control them inverted and with a time delay. The rear grille emits an inverted plane wave exactly when the plane wave emitted by the front subwoofers reaches the rear wall and is reflected by it. Thus the reflection and the inverted wave cancel each other out. In contrast to absorption , in which the sound wave is converted into thermal energy, with the DBA there is destructive interference. Since the sound waves of the two grids take the same path and are of the same nature, they extinguish each other to infinity. The time delay to be selected for the rear grille must be calculated according to the length of the room: ${\displaystyle t_{d}}$ ${\displaystyle l}$

${\displaystyle t_{d}{=}{\frac {l}{c}}}$

with : speed of sound ${\displaystyle c}$

To implement a real DBA, a frequency-independent delay element (delay) is required, as it is, for. B. offer most digital equalizers or digital active crossovers . An all-pass for phase rotation , as is the case with common pre-built subwoofers , is not suitable for this. The inversion can be carried out in a simple manner by reversing the polarity of the loudspeakers or the signal fed to the amplifier.

Active extinction does not only work in cuboid rooms, but can in principle be applied to any room that is symmetrical in the longitudinal direction. The functional principle can even be applied to L-shaped rooms by simulating the wave front of a cuboid room using additional sound sources. The additional sound sources complete the plane wave generated in one of the branches. This can then be deleted as usual on the rear wall. An additional delay channel is necessary for this arrangement. Active cancellation works even if the two grids have different numbers of drivers. So z. B. the rear grille can be made smaller without affecting the overall effect.

The interface reinforcement (pressure chamber effect) below the first spatial mode is also pronounced in a DBA.

Single Bass Array (SBA)

An arrangement without a rear bass grille is usually referred to as a single bass array (SBA) . Since the plane wave is not extinguished on the rear wall, it should be designed to be highly absorbent. Otherwise the longitudinal modes are excited to the maximum, which leads to strong, location-dependent distortions of the transfer function.

If the absorber on the rear wall is not sufficient to completely attenuate the longitudinal modes, a parametric equalizer can be used to linearize the transfer function . Both room modes and IIR filters have minimal phases , so that not only the amplitude response is linearized, but the decay is also reduced. If the grid density is sufficient, the transfer function set in this way is valid for a plane parallel to the low-frequency grid (e.g. a complete row of seats).

A single bass array is twice as efficient as a double bass array with an identical number of woofers. The costs for the woofer and amplifier are only half as high with the same grid density. The rear absorber usually requires more space for this. Furthermore, with a non-ideal absorber, the transfer function depends on the listening position in the direction of the length of the room. The more effective the absorber, the lower this dependency becomes.

advantages

• The sound pressure level is constant throughout the room.
• No room modes are stimulated (no unpleasant roar).
• Since the subwoofers are best mounted directly in or on the wall, a DBA can be integrated almost invisibly into the room.
• There are no large, passive absorbers required for the low frequency range.
• Relatively easy to build.

disadvantage

• There are never ideal conditions in the listening room, so no DBA works perfectly either. In addition, large pieces of furniture interfere with the flat wave front.
• The effect of the DBA depends on the number of woofers, which can easily assume double-digit values ​​with large walls.
• The installation is complex (measurements) and expensive, the efficiency is relatively poor.
• The absorption of long wavelengths (i.e. deep tones) is possible to a certain extent with conventional plate absorbers. Under certain circumstances, an SBA with damping on the rear wall is sufficient to also eliminate the longitudinal mode.
• When moving on the spatial axis, the plane wave front experiences less drop in level than a cylindrical wave of a line of sound or the spherical wave of a conventional loudspeaker. With the essential 100Hz-20kHz range, the sound balance therefore varies depending on the location.

Remarks

In principle, it is also possible to place a DBA on the side walls (or even on the floor or ceiling) of a room. However, since the front speakers are the focus of attention when it comes to cinema sound and music, it is advisable to also place the first wave front of the bass, which may be localized, on the front.

How well a DBA works in a real listening room depends on a number of factors.

• The room should ideally be cuboid, but at least symmetrical. Good results can e.g. B. can also be achieved in the loft.
• Reflective properties of the walls: the harder the material, the fewer losses there are at the edge of the plane wave front.
• It takes a few iterations to adjust the level and delay of the back grille. A measuring system with which the amplitude response and a waterfall diagram can be displayed is helpful for this.

literature

• Götz Schwamkrug: Loudspeaker boxes, construction, conversion, replica. 2nd edition. Elektor-Verlag, Aachen 1989. ISBN 3-921608-83-X

Web links

Commons : Double Bass Array  - collection of pictures, videos and audio files

• Original paper by Anselm Goertz (PDF file; 1.42 MB)
• Realization of a double bass array by Nubert (PDF file; 768 kB)
• Example of a realization with images and measurements
• English-language summary of the DBA concept with photos
• Visualization of the modes of any cuboid room