Throw & coverage

High sensitivity and controlled coverage are the reasons horns are used to throw sound over a distance. This sheet answers the two practical questions: how loud is it at the back row, and how wide a strip of audience does one horn cover there?

Level

Outdoors, or indoors before the room takes over, the level from a single horn falls by 6 dB for every doubling of distance. Power adds 3 dB per doubling:

with $P$ in watts and $d$ in metres. Turning the equation around gives the reach for a target level, $d = 10^{(L_1 - L_{target})/20}$, where $L_1$ is the level at one metre at the chosen power.

Width

A horn with nominal horizontal coverage $\alpha$ illuminates, at distance $d$, a strip of width

The level at the edges of that strip is 6 dB below the axis by definition of the coverage angle, less a little because the edge seats are also slightly farther away.

What to keep in mind

• Ten times the power buys only 10 dB. A horn 3 dB more sensitive saves half the amplifier.
• Air absorbs high frequencies: roughly 2 to 4 dB per 100 m at 4 kHz and several times that at 10 kHz, depending on humidity. Long throws sound dull unless equalised.
• Indoors, beyond the critical distance the reverberant field holds the level up and the inverse-square law no longer applies.
• The amplifier figure should be the driver's rated continuous power or less. Compression drivers are easily destroyed by more.