A common phrase in pro audio is “I need a P.A. that has enough throw to cover the audience.” Of course, loudspeakers do not lob sound like a baseball, but instead set up sound waves in the air that then travel to the ears of the audience, which then detect the sound as it passes them. Regardless of the questionable terminology, the concepts behind “throw” are an important to the audio industry.
The ability to cover patrons at increasing distances from the sound system opens doors to bid on larger events and ultimately get the show to the ears of more paying customers. Let’s examine the acoustic factors behind throw, the limitations loudspeakers impose on throw and some practical tips for getting the most coverage out of your sound system.
Sound Spreading in Air
Loudspeakers convert electrical signals into the mechanical motion of air molecules. Because air has elasticity, rather than simply pushing the molecules out of the way, a wave is set up in the air that travels through it. This wave influences each little area of air molecules as it passes through. Let’s look at how that occurs:
• As the sound wave moves by a group of air molecules, first the molecules are pressed tighter together (compression) and then pulled farther apart (rarefaction).
• During the period of compression, the local pressure is higher, and the inverse is true during rarefaction. The pressure oscillates first slightly above atmospheric, and then slightly below.
• The alternating high and low pressure moves the eardrum, and we perceive this oscillation as sound.
Because of the above, sound pressure (i.e., SPL) makes a convenient means to characterize what is perceived by the audience members’ ears. Pressure is defined as (force/area). The surface area of geometrical surfaces (e.g., square, rectangle and sphere) increases in a defined manner with distance from a source. Thus, for a given starting pressure (force/area), the final pressure will decrease as the original force is “diluted” over a larger surface area.
This dilution of the original starting sound over an ever increasing audience area is the first concept behind the decrease in SPL at distances far from the sound system. A second concept is that air takes away some of the sound wave’s energy as the wave travels along. This effect is known as absorption. Sound absorption depends on the factors of temperature, humidity and pressure. Then factor in human sound perception versus distance, and there are plenty of challenges to keep an experienced system tech busy. Because of the complex interplay of these factors, and from confusion about how sound travels (especially away from vertical array systems); there is plenty of incorrect “common sense” floating about in the industry at present. Let’s reduce the confusion with an overview of typical audience coverage requirements.
The Pyramid of (Sound) Needs
Fig. 1 (at beginning of this article) presents what I have dubbed the “sound pyramid.” It is a hypothetical representation of how the coverage of the loudspeaker system should ideally vary from the front of an audience to the back for typical audience areas. The sound pyramid represents several effects simultaneously:
• Due to the audience geometry, coverage should be narrower for the back of the audience than the front.
• Levels near the stage need to be lower to insure consistent volume from front to back of the venue due to absorption.
• Sound aimed at the back of the venue requires additional high frequency energy, because air preferentially absorbs high frequencies.
What can we learn from the sound pyramid? First, most loudspeaker systems can provide too much horizontal coverage for the farthest audience areas. As a result, the output from the loudspeaker drivers is dispersed over a wider area than the audience coverage area. This effect, combined with the absorption of sound at distance, reduces the volume for the more distant patrons. Second, for the typical full-range loudspeaker, the HF driver section is the limiting factor in terms of ultimate audience throw, due to the extra high frequency output required to overcome the preferential absorption of high frequencies.
Necessary Compromises
Two things drive coverage away from the idealized sound pyramid. Loudspeakers cannot always assume they will only be covering the cheap seats, and therefore have to provide sufficiently wide horizontal coverage for closer audience members. Further, physics dictates that extremely narrow coverage patterns usually require very large horn flares if they are to maintain the coverage pattern to a reasonably low frequency (see Keele Horn Equation sidebar, page 43).
It would be tempting to dramatically increase the output capabilities of individual drivers, especially high frequency compression drivers, even more than we have seen the last 15 years. But here too, physics forces a compromise. If the sound pressure becomes sufficiently intense, it causes enough heating and cooling of the air to briefly change the speed of sound a meaningful amount. This change in the speed of sound then distorts the sound’s waveform and introduces distortion. This distortion occurs in the region where the pressure levels are the highest, which would be at the compression driver’s phase plug and the throat of the horn. The onset of such distortion limits the output levels that individual compression drivers will be able to achieve.
The alternative to using higher output drivers, of course, is to use more drivers in concert with each other. Getting multiple drivers, and multiple boxes, to play well together is no trivial task. The last decade’s move towards vertical arrays that seek to play together has created a marked improvement towards this goal, but multiple speakers projecting on the same audience area is never without compromises.
Ironically, getting speakers to play well together at a long distance is the easiest, as the arrival times of all the drivers are very similar when the listener is far away. It is only when the listener is close to a multitude of drivers, all arriving at different times due to the loudspeaker array geometry, that things get the most messy (see p. 42 sidebar on “line” sources). Also, the behavior of sound absorption is very complex (see Fig. 2) and this often requires the high frequency shaping of the sound system to change throughout the course of an event as temperature, humidity and pressure change in the audience area.
Practical Tips on Throw
So, if physics limits individual driver output, and complicates getting multiple speakers to play together, what is the end user to do in an attempt to cover a larger audience area with their existing audio equipment? Here are some practical tips you can use to help cover the venue at your next event:
• Get the loudspeakers in the air, and pointed at the audience. The less the audience absorbs the sound as it travels, the more sound that remains for the cheap seats.
• Segment your audience vertically. By covering the far audience with the top of the array, and the near people with the bottom, you can change the processing of each array section to complement their area of the audience in terms of level and high frequency boost.
• Use front fills. Don’t force the main speakers to cover the whole audience. Focus the mains instead on the farther patrons, and use front fill or infill speakers to cover folks up close.
• Don’t expect too much from compression drivers. Beyond about 150 feet (50m) the amounts of high frequency boost needed to combat absorption get very demanding for all but the best compression drivers. Rather than trying to extend the system response to 15 kHz at these distances, better to focus instead on having good balance from 12 kHz on down.
• Realize that subwoofers often have the least directivity of all speakers, and as a result they project sound in many directions. This results in needing more subwoofer output than you might expect, as the energy from the subs can be “lost” to areas with no audience (e.g., behind the stage or into the sky above audience).
• Understand that the human brain expects the high frequencies to roll off as visual distance increases. We humans have spent our whole lives dealing with high frequency absorption, and if the highs are still quite bright a long way from the array, the brain experiences a degree of cognitive dissonance. It is appropriate to taper the high frequencies to be somewhat duller far from the array.
Some Final Advice
As a final point of advice, it is typical and expected for the spectral balance of the sound system to change throughout the day, especially outdoors. It is appropriate to play an active role in re-balancing the system’s output as environmental conditions dictate. It also makes sure that a high frequency boost appropriate for dry morning air isn’t overbearing for the humid mid-day festivities. Actively managing the P.A. throughout the day insures the best experience for band engineers and patrons alike.
Some Thoughts on “Line” Sources
Since the introduction of V-DOSC in the early 1990s, much ink has been penned about the behavior of line arrays, and how they produce more consistent sound levels with distance. As a result, one of the things that has become commonly, and incorrectly, understood is that these arrays are not subject to the inverse square law, and therefore throw sound farther. While this is great for marketing, it unfortunately doesn’t reflect physics.
The reality of a vertical “line” array (or any finite array configuration) is that once you get far enough away from the array, it behaves like a point source. A good practical example outside of audio is the Sun in our solar system. If you were standing on the planet Mercury, the sun would fill almost your entire field of view, like a very tall array. Here on Earth the Sun is a large dot in the sky, and at the far reaches of our solar system the Sun is just a tiny bright speck visually. In a similar way, if you walk far enough away from even a large sound system array, it will begin to look visually small.
Acoustically, when you are far away from a large line array, the visual smallness of the array correlates to the output from all adrivers arriving at your ear at essentially the same time. This is because the large distance from the array has minimized the effects of the array’s physical geometry. As a result, the array acts acoustically like a point source and is subject to the inverse square law. Conversely, when you are near a large array, the inter-driver distances become appreciable, and the drivers all arrive at your ear at slightly different times. It is this incoherent addition of the sound from all the drivers that causes the SPL to be more consistent near the array. The scrambling of the arrivals drives the improved uniformity in levels front to back.
Line arrays do not “break” the inverse square law by somehow having different wave properties, but instead have more even coverage by exhibiting less coherency as you get closer to the array. In the far field, they behave just like a point source, and therefore show no fundamental throw advantage over the classic point source.
This is not to say that the modern vertical line array doesn’t have substantial advantages. They typically have many (2x to 4x) more compression drivers than the classic trap array. They also tend to have smaller spacing between cabinets and drivers. Most have carefully designed waveguides, aiming software and the ability to process the top and bottom of the array differently. All of these things are advantages over the classic trap array that have real world benefits. None of these benefits, though, are a result of some “special” method of wave propagation, regardless of the marketing department.
The Keele Horn Equation
Don Keele, in his landmark 1975 Audio Engineering Society (AES) paper “What’s So Sacred about Exponential Horns?” introduced an empirical relationship that is now known as the Keele horn equation. The equation tells the approximate frequency to which you can expect a horn to provide consistent directional control:
Minimum frequency of constant coverage = 23500 / (coverage angle in degrees * horn mouth width in meters)
Plug in the horn coverage angle, and the dimension of the horn in the direction of coverage, and the Keele horn equation provides a reasonable estimate of the lowest frequency that will yield consistent directional control from a horn. The key thing to realize from the equation is that coverage angle and mouth dimension are inversely related. For a given frequency of constant coverage, the mouth dimension must increase as the coverage angle decreases. Very narrow coverage angles therefore result in large horns.
