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Size Matters: Observations On Loudspeaker Directivity
Physics hasn’t changed.... When it comes to pattern control, size still matters!
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Matter Of Control
Remember that the low frequency driver’s only means of controlling the dispersion of the sound wave in a front-loaded loudspeaker are its cone diameter, and to a lesser extent, some boundary effects (we’ll discuss that later).

At 100 Hz, the driver is physically small in comparison to the 10-foot wavelength and provides almost no directivity (Figure 1).

If we increase the frequency gradually, the 12-inch driver does not suddenly exert pattern control over the sound wave when it reaches 1,000 Hz (1 foot), and is the same size as the driver itself.

Rather, it has more and more effect as the frequency gets higher and the wavelengths get shorter. (Figures 2 & 3)

Fig 1: Horizontal directivity balloon of a 12-inch 2-way loudspeaker at 100 Hz (box facing left)

In this frequency range (800 Hz as shown in Figure 3), the cone driver is actually providing approximately 90-degree horizontal dispersion.

But also realize that since this pattern is conical (the driver is round), it is not producing the specified 60-degree vertical pattern.

As the frequency increases the driver exerts more and more control until it begins to “beam” at higher frequencies.

But by the time it narrows that much, it’s above the crossover frequency.

This particular loudspeaker crosses over about a half-octave above the balloon in Figure 3.

Fig 2: Horizontal directivity balloon of a 12-inch 2-way loudspeaker at 500 Hz (box facing left)

This has an overriding effect on the polar behavior of the box, especially in the vertical domain, so we will discuss the range from 1,000 Hz to 1,500 Hz when we discuss the crossover. Now, on to the horn.

Dominate The Wavelength
There are multiple elements in a horn’s design that contribute to its ability to achieve pattern control at a given frequency.

Some of them are throat geometry, length and flare rate.

But the most obvious factor is the size of the horn mouth. The same rules apply here as to the cone driver. Size matters.

The horn mouth must be large enough to dominate the wavelength in question in order to provide complete directivity at that frequency.

So if a horn mouth is 6 inches wide by 3 inches tall it will be somewhat omnidirectional at 1,000 Hz.

Fig 3: Horizontal directivity balloon of a 12-inch, 2-way loudspeaker at 800 Hz (box facing left)

It will not dominate the sound wave until the frequency reaches about 2,000 Hz in the horizontal plane and 3,000 Hz in the vertical plane.

It may provide a 90-degree by 60-degree pattern above 3,000 Hz, but almost certainly not at lower frequencies.

Cone drivers and horns by themselves are fairly predictable devices. But combining the two in close physical proximity can be quite challenging.

The first problem is physical offset. In a typical 2-way box, the devices are located one above the other ,and may also be at different depths.

Even if we use delay to correct the time alignment between the drivers on axis, any other vertical angle will skew the time arrivals from the horn and the cone driver.

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