Page 28 - Winter 2008

loudspeakers of different types, with different gains, distances become awkward to use. Under these conditions, the simple form of the articulation loss equation can no longer be used.
Fortunately %ALcons can also be expressed in terms of a signal to noise energy ratio, or rather the noise to signal ener- gy ratio times the reverberation time (Bistafa and Bradley, 2000). This allows us to apply it to complex sound systems.
(4)
There are more complex versions of this relationship that include extraneous noise and extend the formula to long dis- tances, but for our purposes this will suffice.
Another approach is to use raw signal to noise ratios in several octave bands. For our purposes the signal is the com- bined direct field level from all loudspeakers and the noise is the combined reverberant field level from all loudspeakers. With these assumptions
(5)
In this metric the signal and the noise are expressed as energies, both of which are steady state values. There is no consideration of when the signals arrive or how they have reflected. We rely on the relative levels to sort this out. Loudspeakers contribute to the useful energy only to the extent that the levels they produce affect the direct field level at a particular receiver.
Table 1 (Long, 2006) shows a chart of steady state signal- to-noise ratios which can be used to judge how intelligible a system will be. The comparisons are made in three octave bands centered at 500, 1k, and 2k Hz.
In almost all locations in a room the calculated reverber- ant field levels are higher than the direct field levels, but even in these areas, good intelligibility can be achieved. By com- paring signal to noise ratios in several octave bands we have a useful tool for sound system design.
As part of the computer modeling the reverberation times and the signal to noise ratios were calculated at Mount Saint Mary’s Chapel. In the existing church in the empty condition, the mid frequency reverberation times were around 4 seconds, much too high for optimal results. Even with the distributed loudspeakers, the signal-to-noise ratios were about -10 dB, which yielded only fair intelligi- bility. As a result it was decided to add some absorption to the room. Normally it is best to do this in the high ceiling areas, where surfaces do not provide useful reflections for envelopment or intelligibility. In this room those surfaces were not available, so panels were designed to fit into the niches of the side walls, as shown in Fig. 4. These reduced the calculated reverberation times to about 1.7 seconds and the signal to noise ratio to -6 to -7 dB, both satisfactory val-
Maxfield and Albersheim, (1947) wrote about the Liveness in terms of the ratio of the reverberant-to-direct energy densi- ties times the reverberation time for a source having a direc- tivity of one.
(1)
The familiar reverberation time in metric units is defined in the usual way as
(2)
Intelligibility—Articulation loss
In 1971 Peutz published a formula similar to that previ- ously found, for the percentage articulation loss of conso- nants or %ALcons. In metric units an equation can be writ- ten in terms of the properties of a room for a single source, having a directivity of 1.
(3)
It is intuitive that when the receiving room is highly reverberant, speech is more difficult to understand. The standard practice is to use the 2000 Hz octave band to calcu- late the articulation loss of consonants. Values less than 5–10% are considered good.
Intelligibility—Signal to noise ratio
While there are many ways of measuring intelligibility, they are all based on some sort of signal-to-noise ratio. Different metrics use different definitions of what constitutes the signal and what constitutes the noise. The consensus is that the direct signal (or most of it) is good for intelligibility and the reverberant noise (or most of it) is bad for intelligi- bility, and a ratio of the two is a measure of how good or bad the intelligibility is.
Notice that noise, other than the reverberant field, is left out of this discussion to make things easier, even though it, too, is bad.
The articulation loss formula is relatively easy when there is only one source. Early pioneers converted levels into dis- tances to make the comparison easier. When there are multiple
26 Acoustics Today, January 2008