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Realistic Goals
Taking a closer look at the reality of what it actually takes to achieve rider-specified concert sound pressure levels.
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Courtesy of Merlijn van Veen.

Why does a specification like “We need a sound system capable of delivering full range 103 dB(A) of clear and undistorted sound at the front of house position” make me scratch my head?

Because, typically the mix doesn’t exhibit an A-weighted spectrum.

Even as a precautionary measure to make sure the sound system is capable of handling the show, this remains a questionable specification. Never mind that it doesn’t mention an integration time (average) e.g. 1 second, 5 minutes or 2 hours or how long that desired level should be maintained? What makes specifications like these questionable, is the full range A-weighting specification.

Figure 1

Figure 1 shows various spectra (absolute SPL) in an unweighted (Zero) and weighted (A) fashion. All these spectra read 103 dB(A) with pink noise on a sound level meter using A-weighting. The weighting curves (figure 2) are derived from the Fletcher-Munson curves which predate WWII. Specifically at lower frequencies our ears are less sensitive to pressure.

A-weighting is used to mimic our ear’s non-linear loudness perception over frequency at low levels. According to today’s Equal Loudness Contours it represents 60 phon i.e. conversational speech or background music which is quite peculiar given the levels of concerts. The B-weighting in contrast, represents the ear’s behavior at high SPL (100-110 phon).

Figure 2

The black line in the right hand chart of figure 1, shows a flat A-weighted spectrum of 103 dB. If we look at the unweighted or Z-weighted values in the left hand chart of figure 1, we can see this would require 140 dB of SPL at 40 Hz. So how many subwoofers would it require to deliver that much pressure at FOH?

When we move towards FOH, we lose 6 dB of pressure for each doubling in distance (inverse square law) and the only way to counter this (delay subs excluded) is by increasing the number of subwoofers.

Figure 3 shows 6 different models of dual 18-inch subwoofers by 6 different manufacturers, producing continuous pink noise under half space (ground stacking) conditions, with a crest factor of 4:1 or a dynamic range of 12 dB if you will.

Figure 3

Imagine a pile of subwoofers on the floor, spaced closely together in an attempt to achieve maximum coupling and therefor efficiency which in practice won’t succeed because their physical size prevents this.

Notice in figure 3 how most manufacturers would require 24 to 32 subwoofers to produce levels around 140 dB (103 dB(A) @ 40 Hz) at merely 8 meters (26 feet). That’s a lot of subwoofers and we haven’t even left the penalty area of a soccer pitch!

DISCLAIMER: These tables are based directly on manufacturer published specification sheets. Please handle them with caution. The criteria that constitute peak output and how gracious the speakers go about it, are unknown.

Even with really long (line) arrays of subwoofers, the cylindrical waves that drop at only 3 dB per doubling distance would have limited merit as is shown in the bottom left table of figure 3. This table shows the line length (number of loudspeakers times spacing) required to extent the cylindrical wave behavior up to a certain distance, until it falls back to spherical wave behavior with 6 dB per doubling distance (inverse square law).

The sheer number of subwoofers required to achieve full range 103 dB(A) of sound pressure, is what makes the A-weighted specification questionable which raises the question if we need that much pressure?

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