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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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Trap boxes and line arrays get all the attention. And that’s no surprise - they’re big and loud, and dare I say it, glamorous.

But the truck rarely rolls without a complement of two-way loudspeakers sporting a 12-inch or 15-inch woofer and a horn.

Whether its monitor wedges, drum fill, front fill or just “speakers on sticks,” small 2-way boxes do many of the everyday jobs that make up a typical sound reinforcement day.

We take the performance of these boxes for granted, but they can be used to better effect if we really understand their directivity characteristics and what makes them perform the way they do. They’re often described as a 90 by 60 box or some other dubious reference.

But 90 degrees by 60 degrees at what frequency? Certainly not from DC to light.

There are four principle ingredients that govern the dispersion pattern of these loudspeakers, including the cone driver, horn, crossover and cabinet.

Let’s look at these one at a time and assess their contributions. Before we go through our list, though, let’s review some basics.

The amount of directivity any device can exert on a sound wave is directly related to the proportional sizes of the device and the sound wave.

To understand this relationship it is important to have a good grasp of how big or small a sine wave is at a given frequency.

Sound at sea level at 72 degrees Fahrenheit travels at approximately 1,130 feet per second. We express frequency or cycles (sine waves) per second as Hertz.

So if the frequency of a wave is 1 Hz, the wave is 1,130 feet long. Logically, a 10 Hz wave is 113 feet long, a 100 Hz wave is 11.3 feet long, and a 1,000 Hz wave is 1.13 feet long, etc.

While it’s not overly difficult to do the math to determine the wavelength of any given frequency, there is an old “cheat” called the rule of 5-2-1:

20 Hz = 50 feet
50 Hz = 20 feet
100 Hz = 10 feet
200 Hz = 5 feet
500 Hz = 2 feet
1,000 Hz = 1 foot
2,000 Hz = .5 foot
5,000 Hz = .2 foot
10,000 Hz = .1 foot

While not perfectly accurate, it fills the bill for “quick and dirty” calculations. Physics dictates that a source be physically large in comparison to a wavelength to exert directional control over it.

So let’s look at the low frequency directivity of a 12-inch driver in a 2-way loudspeaker with a 90-degree by 60-degree horn.

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