Speaker system size and directivity relationship

At present, the technology of small Speaker output and fidelity has been improved rapidly, but the physical properties have not changed. When covering mode control, the speaker size is still a problem.

In applications, inverted speakers and line arrays have received much attention. This is not surprising - because they are big and loud, they are also very attractive. However, this type of device does not work without a two-way speaker system. The two-way speaker system can consist of a 12-inch or 15-inch woofer and a horn. The small two-way speaker can be used for main sound reinforcement in daily work, whether it is stage monitoring, drum sound filling, front area filling or filling on the bracket.

Users take advantage of the characteristics of these speakers, but if you can really understand their pointing characteristics and how they work, then you will get better results.


1 decide the factors that cover the pattern allocation

The directivity of small speakers is often labeled as 90° x 60° or other uncertain parameters. But what is the directivity of 90° × 60°? Of course not from DC (0Hz) to 20kHz. There are four main factors that determine the coverage mode assignment of these speaker systems, namely the cone drive, the treble horn, the crossover, and the cabinet.

Let's analyze these factors in turn and evaluate their respective roles. Before enumerating these factors, review some basic knowledge.

The influence of the directivity of any device on sound waves is directly proportional to the size of the device and the length of the sound wave. To understand this relationship, it is important to have an in-depth understanding of the sine wave size for a given frequency.

At 72 degrees Celsius, sea level sound waves travel at approximately 1130 feet per second. Hertz is used to represent the circumference (sine wave) produced by the frequency per second. If the wave has a frequency of 1 Hz and a wavelength of 1130 ft, it is logically calculated that the 10 Hz wave frequency has a wavelength of 113 ft, the 100 Hz wave frequency has a wavelength of 11.3 ft, the 1000 Hz wave frequency has a wavelength of 1.13 ft, and so on.

It is not difficult to calculate the wavelength as long as the frequency is given. There is an old-fashioned "secret" called "5-2-1 rule":

20HZ = 50 feet, 50HZ = 20 feet, 100HZ = 10 feet, 200HZ = 5 feet, 500HZ = 2 feet, 1000HZ = 1 foot, 2000HZ = 0.5 feet, 5000HZ = 0.2 feet, 10000HZ = 0.1 feet.

This means that although not completely accurate, it is suitable for calculations in emergency situations. Physics shows that a sound source is larger than the wavelength, in order to control its directivity during the enhancement period.


2 control problems

Note that for a front-guided speaker system, the only way the low-frequency drive unit controls the distribution of the sound waves is the cone drive diameter (less of which is controlled by the boundary effect).

At 100 Hz, the driver size is small relative to a 10-inch wavelength and there is little directivity.

If the frequency is gradually increased, reaching 1000HZ, the 12-inch driver will not suddenly affect the radiation angle control mode of the sound wave, but will be the same size as the driver itself. However, as the frequency becomes higher and higher, the wavelength becomes shorter and shorter, and its influence becomes more and more obvious.

At this frequency point, the cone driver actually produces a horizontal directivity of approximately 90 degrees. But because the radiation pattern is conical (the drive is round), it does not produce a specific vertical angle of 60 degrees.

As the frequency increases, the drive's influence on the radiation pattern is increasing, until the high-band acoustic radiation begins to appear in a "beam" shape. When the beam is narrow to a certain extent, it will be above the crossover point.

This mainly affects the pole figure characteristics of the cabinet, especially in the vertical area. Therefore, the frequency division point discussed here refers to the frequency band from 1000HZ to 1500HZ.


3 factors determining the wavelength

There are several factors in the horn design that enable it to achieve radiation pattern control at a given frequency point. Some of these factors include the geometry, length, and opening ratio of the throat. But the most significant factor is the size of the bell mouth (the same as the influencing factor of the tapered drive).

The bell mouth size must be large enough to determine the wavelength at which point the full directivity is provided. If the horn of a horn is 6 inches wide and 3 inches high, it is close to omnidirectional at 1000 Hz.

Only when the horizontal frequency reaches 2000HZ and the vertical frequency reaches 3000HZ will affect the sound wave. The radiation angle above 3000HZ is 90 degrees * 60 degrees, but the low frequency band has almost no directivity.

Conical drives and horns are just old-fashioned devices and are not new. But combining the two is challenging. First designed to the physical offset problem. In a typical 2-way box, the drive unit is located one above the other and the longitudinal distances of the two units may be different.

Although time delays can be used to time align the two drive units on the axis, other vertical angles can deviate from the arrival times of the horn and the tapered drive. Because the vertical distribution pattern of the bandpass and the driver overlaps in the crossover point area, it is possible to hear the sound of the two drivers inverting at any vertical angle outside the axis. This means that lobes and nulls must be generated.

Based on driver cancellation mode control, crossover slope, superposition, and delay distribution settings, the direction and sensitivity of these lobes will vary, but only in the multi-drive enclosure, and these sources are separated from each other.

If you put a speaker on its side, the phenomenon in the horizontal direction is the same. What about the ground monitor speakers?

There is only one reason for recurrence in coaxial speakers.

Because there is no vertical offset between the sources, the user can only correct the amount of depth variation between the source of the cone driver and the horn driver, and this distance remains constant with the off-axis listening position. The trade-off is that multiple coaxial designs use a conical drive unit as the horn to generate high frequencies. It may be possible to monitor speakers or near-field places, but if sound is amplified, more precise coverage angle control is often required.


4 baffles, borders

The last factor in the problem of directivity is the box itself and the boundary effects created by the cabinet installation. When the space is reduced, the fractional space load is generated when the speaker radiates inside. The low frequency is omnidirectional, so the low frequency radiation space is effectively reduced by half when the speaker is placed on the floor. This produces an additional 3DB output on the hemisphere.

At a given frequency point, if the baffle on the speaker cabinet is large enough, it can be bordered to create half a space load. Sometimes this is called the "baffle effect." In today's cabinets, the baffles are often not as large as the drives installed inside them, because the weight, the brackets, and the hanging hardware are the first considerations.

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