Sound System Design Reference Manual

Table of Contents

Preface..... Chapter 1: Wave Propagation.... Wavelength, Frequency, and Speed of Sound... Combining Sine Waves.... Combining Delayed Sine Waves.... Diffraction of Sound.... Effects of Temperature Gradients on Sound Propagation... Effects of Wind Velocity and Gradients on Sound Propagation... Effect of Humidity on Sound Propagation.... Chapter 2: The Decibel.... Introduction..... Power Relationships.... Voltage, Current, and Pressure Relationships.... Sound Pressure and Loudness Contours.... Inverse Square Relationships.... Adding Power Levels in dB.... Reference Levels.... Peak, Average, and RMS Signal Values... Chapter 3: Directivity and Angular Coverage of Loudspeakers.. Introduction..... Some Fundamentals.... A Comparison of Polar Plots, Beamwidth Plots, Directivity Plots, and Isobars.. Directivity of Circular Radiators.... The Importance of Flat Power Response.... Measurement of Directional Characteristics... Using Directivity Information.... Directional Characteristics of Combined Radiators... Chapter 4: An Outdoor Sound Reinforcement System... Introduction..... The Concept of Acoustical Gain... The Influence of Directional Microphones and Loudspeakers on System Maximum Gain. How Much Gain is Needed?.... Conclusion..... Chapter 5: Fundamentals of Room Acoustics.... Introduction..... Absorption and Reflection of Sound.... The Growth and Decay of a Sound Field in a Room.. Reverberation and Reverberation Time.... Direct and Reverberant Sound Fields.... Critical Distance..... The Room Constant.... Statistical Models and the Real World.... i 1-1 1-1 1-2 1-3 1-5 1-6 1-6 1-7 2-1 2-1 2-1 2-2 2-4 2-6 2-7 2-7 2-8 3-1 3-1 3-1 3-3 3-4 3-6 3-7 3-8 3-8 4-1 4-1 4-2 4-3 4-4 4-5 5-1 5-1 5-1 5-5 5-7 5-12 5-14 5-15 5-20
Table of Contents (cont.)
Chapter 6: Behavior of Sound Systems Indoors... Introduction..... Acoustical Feedback and Potential System Gain.... Sound Field Calculations for a Small Room... Calculations for a Medium-Size Room... Calculations for a Distributed Loudspeaker System... System Gain vs. Frequency Response.... The Indoor Gain Equation.... Measuring Sound System Gain.... General Requirements for Speech Intelligibility... The Role of Time Delay in Sound Reinforcement... System Equalization and Power Response of Loudspeakers... System Design Overview..... Chapter 7: System Architecture and Layout... Introduction..... Typical Signal Flow Diagram... Amplifier and Loudspeaker Power Ratings... Wire Gauges and Line Losses.... Constant Voltage Distribution Systems (70-volt lines)... Low Frequency AugmentationSubwoofers... Case Study A: A Speech and Music System for a Large Evangelical Church.. Case Study B: A Distributed Sound Reinforcement System for a Large Liturgical Church. Case Study C: Specifications for a Distributed Sound System Comprising a Ballroom, Small Meeting Space, and Social/Bar Area... Bibliography 6-1 6-1 6-2 6-2 6-5 6-8 6-9 6-9 6-10 6-11 6-16 6-17 6-19 7-1 7-1 7-1 7-5 7-5 7-6 7-6 7-9 7-12 7-16
Preface to the 1999 Edition:
This third edition of JBL Professionals Sound System Design Reference Manual is presented in a new graphic format that makes for easier reading and study. Like its predecessors, it presents in virtually their original 1977 form George Augspurgers intuitive and illuminating explanations of sound and sound system behavior in enclosed spaces. The section on systems and case studies has been expanded, and references to JBL components have been updated. The fundamentals of acoustics and sound system design do not change, but system implementation improves in its effectiveness with ongoing developments in signal processing, transducer refinement, and front-end flexibility in signal routing and control. As stated in the Preface to the 1986 edition: The technical competence of professional dealers and sound contractors is much higher today than it was when the Sound Workshop manual was originally introduced. It is JBLs feeling that the serious contractor or professional dealer of today is ready to move away from simply plugging numbers into equations. Instead, the designer is eager to learn what the equations really mean, and is intent on learning how loudspeakers and rooms interact, however complex that may be. It is for the student with such an outlook that this manual is intended. John Eargle January 1999

Effects of Wind Velocity and Gradients on Sound Propagation
Figure 1-9 shows the effect wind velocity gradients on sound propagation. The actual velocity of sound in this case is the velocity of sound in still air plus the velocity of the wind itself. Figure 1-10 shows the effect of a cross breeze on the apparent direction of a sound source. The effects shown in these two figures may be evident at large rock concerts, where the distances covered may be in the 200 - 300 m (600 - 900 ft) range.
Figure 1-8. Effects of temperature gradients on sound propagation
Figure 1-9. Effect of wind velocity gradients on sound propagation
Effects of Humidity on Sound Propagation
Contrary to what most people believe, there is more sound attenuation in dry air than in damp air. The effect is a complex one, and it is shown in Figure 1-11. Note that the effect is significant only at frequencies above 2 kHz. This means that high frequencies will be attenuated more with distance than low frequencies will be, and that the attenuation will be greatest when the relative humidity is 20 percent or less.
Figure 1-10. Effect of cross breeze on apparent direction of sound
Figure 1-1 1. Absorption of sound in air vs. relative humidity

Chapter 2: The Decibel

Introduction
In all phases of audio technology the decibel is used to express signal levels and level differences in sound pressure, power, voltage, and current. The reason the decibel is such a useful measure is that it enables us to use a comparatively small range of numbers to express large and often unwieldy quantities. The decibel also makes sense from a psychoacoustical point of view in that it relates directly to the effect of most sensory stimuli. signal. The convenience of using decibels is apparent; each of these power ratios can be expressed by the same level, 10 dB. Any 10 dB level difference, regardless of the actual powers involved, will represent a 2-to-1 difference in subjective loudness. We will now expand our power decibel table: P1 (watts) 1.25 1.60 2.5 3.15 6.Level in dB 8 10

Power Relationships

Fundamentally, the bel is defined as the common logarithm of a power ratio: bel = log (P1/P0) For convenience, we use the decibel, which is simply one-tenth bel. Thus:
Level in decibels (dB) = 10 log (P1/P0)
The following tabulation illustrates the usefulness of the concept. Letting P0 = 1 watt: P1 (watts) 10,000 20,000 Level in dB 40 43
This table is worth memorizing. Knowing it, you can almost immediately do mental calculations, arriving at power levels in dB above, or below, one watt. Here are some examples: 1. What power level is represented by 80 watts? First, locate 8 watts in the left column and note that the corresponding level is 9 dB. Then, note that 80 is 10 times 8, giving another 10 dB. Thus: 9 + 10 = 19 dB 2. What power level is represented by 1 milliwatt? 0.1 watt represents a level of minus 10 dB, and 0.01 represents a level 10 dB lower. Finally, 0.001 represents an additional level decrease of 10 dB. Thus:

closely approach an ideal free field, but we still must take into account the factors of finite source size and non-uniform radiation patterns. Consider a horn-type loudspeaker having a rated sensitivity of 100 dB, 1 watt at 1 meter. One meter from where? Do we measure from the mouth of the horn, the throat of the horn, the driver diaphragm, or some indeterminate point in between? Even if the measurement position is specified, the information may be useless. Sound from a finite source does not behave according to inverse square law at distances close to that source. Measurements made in the near field cannot be used to estimate performance at greater distances. This being so, one may well wonder why loudspeakers are rated at a distance of only 1 meter. The method of rating and the accepted methods of measuring the devices are two different things. The manufacturer is expected to make a number of measurements at various distances under free field conditions. From these he can establish
Figure 2-5. Inverse square relationships
Figure 2-6. Nomograph for determining inverse square losses
that the measuring microphone is far enough away from the device to be in its far field, and he can also calculate the imaginary point from which sound waves diverge, according to inverse square law. This point is called the acoustic center of the device. After accurate field measurements have been made, the results are converted to an equivalent one meter rating. The rated sensitivity at one meter is that SPL which would be measured if the inverse square relationship were actually maintained that close to the device. Let us work a few exercises using the nomograph of Figure 2-6: 1. A JBL model 2360 horn with a 2446 HF driver produces an output of 113 dB, 1 watt at 1 meter. What SPL will be produced by 1 watt at 30 meters? We can solve this by inspection of the nomograph. Simply read the difference in dB between 1 meter and 30 meters: 29.5 dB. Now, subtracting this from 113 dB: 113 29.5 = 83.5 dB 2. The nominal power rating of the JBL model 2446 driver is 100 watts. What maximum SPL will be produced at a distance of 120 meters in a free field when this driver is mounted on a JBL model 2366 horn? There are three simple steps in solving this problem. First, determine the inverse square loss from Figure 2-6; it is approximately 42 dB. Next, determine the level difference between one watt and 100 watts. From Figure 2-1 we observe this to be 20 dB. Finally, note that the horn-driver sensitivity is 118 dB, 1 watt at 1 meter. Adding these values: + 20 = 96 dB-SPL Calculations such as these are very commonplace in sound reinforcement work, and qualified sound contractors should be able to make them easily.

Adding Power Levels in dB
Quite often, a sound contractor will have to add power levels expressed in dB. Let us assume that two sound fields, each 94 dB-SPL, are combined. What is the resulting level? If we simply add the levels numerically, we get 188 dB-SPL, clearly an absurd answer! What we must do in effect is convert the levels back to their actual powers, add them, and then recalculate the level in dB. Where two levels are involved, we can accomplish this easily with the data of Figure 2-7. Let D be the difference in dB between the two levels, and determine the value N corresponding to this difference. Now, add N to the higher of the two original values. As an exercise, let us add two sound fields, 90 dB-SPL and 84 dB-SPL. Using Figure 2-7, a D of 6 dB corresponds to an N of about 1 dB. Therefore, the new level will be 91 dB-SPL. Note that when two levels differ by more than about 10 dB, the resulting summation will be substantially the same as the higher of the two values. The effect of the lower level will be negligible.

Reference Levels

Although we have discussed some of the common reference levels already, we will list here all of those that a sound contractor is likely to encounter. In acoustical measurements, SPL is always measured relative to 20 x 10-6 Pa. An equivalent expression of this is.0002 dynes/cm2. In broadcast transmission work, power is often expressed relative to 1 milliwatt (.001 watt), and such levels are expressed in dBm. The designation dBW refers to levels relative to one watt. Thus, 0 dBW = 30 dBm. In signal transmission diagrams, the designation dBu indicates voltage levels referred to.775 volts.
Figure 2-7. Nomograph for adding levels expressed in dB. Summing sound level output of two sound sources where D is their output difference in dB. N is added to the higher to derive the total level.
In other voltage measurements, dBV refers to levels relative to 1 volt. Rarely encountered by the sound contractor will be acoustical power levels. These are designated dB-PWL, and the reference power is 10-12 watts. This is a very small power indeed. It is used in acoustical measurements because such small amounts of power are normally encountered in acoustics.

The Concept of Acoustical Gain
Boner (4) quantified the concept of acoustical gain, and we will now present its simple but elegant derivation. Acoustical gain is defined as the increase in level that a given listener in the audience perceives with the system turned on, as compared to the level the listener hears directly from the talker when the system is off. Referring to Figure 4-3, let us assume that both the loudspeaker and microphone are omnidirectional; that is, DI = 0 dB and Q = 1. Then by inverse square loss, the level at the listener will be: 70 dB - 20 log (7/1) = 70 - 17 = 53 dB
If the loudspeaker produces a level of 70 dB at the microphone, it will produce a level at the listener of: 70 - 20 log (6/4) = 70 - 3.5 = 66.5 dB With no safety margin, the maximum gain this system can produce is: 66.5 - 53 = 13.5 dB Rewriting our equations: Maximum gain = 70 - 20 log (D2/D1) - 70 - 20 log (D0/Ds) This simplifies to:
Now, we turn the system on and advance the gain until we are just at the onset of feedback. This will occur when the loudspeaker, along the D1 path, produces a level at the microphone equal to that of the talker, 70 dB.
Maximum gain = 20 log D0 - 20 log Ds + 20 log D1 - 20 log D2
Figure 4-3. System gain calculations, loudspeaker and microphone both omnidirectional
Adding a 6 dB safety factor gives us the usual form of the equation: Maximum gain = 20 log D0 - 20 log Ds + 20 log D1 - 20 log D2 - 6 In this form, the gain equation tells us several things, some of them intuitively obvious: 1. That gain is independent of the level of the talker 2. That decreasing Ds will increase gain 3. That increasing D1 will increase gain.
The Influence of Directional Microphones and Loudspeakers on System Maximum Gain
Let us rework the example of Figure 4-3, this time making use of a directional loudspeaker whose midband polar characteristics are as shown in Figure 4-4A. It is obvious from looking at Figure 4-4A that sound arriving at the microphone along the D1 direction will be reduced 6 dB relative to the omnidirectional loudspeaker. This 6 dB results directly in added gain potential for the system.
The same holds for directional microphones, as shown in Figure 4-5A. In Figure 4-5B, we show a system using an omnidirectional loudspeaker and a cardioid microphone with its -6 dB axis facing toward the loudspeaker. This system is equivalent to the one shown in Figure 4-4B; both exhibit a 6 dB increase in maximum gain over the earlier case where both microphone and loudspeaker were omnidirectional. Finally, we can use both directional loudspeakers and microphones to pick up additional gain. We simply calculate the maximum gain using omnidirectional elements, and then add to that value the off-axis pattern advantage in dB for both loudspeaker and microphone. As a practical matter, however, it is not wise to rely too heavily on directional microphones and loudspeakers to make a significant increase in system gain. Most designers are content to realize no more than 4-to-6 dB overall added gain from the use of directional elements. The reason for this is that microphone and loudspeaker directional patterns are not constant with frequency. Most directional loudspeakers will, at low frequencies, appear to be nearly omnidirectional. If more gain is called for, the most straightforward way to get it is to reduce Ds or increase D1.

Figure 4-6. Concept of Effective
Acoustical Dustance (EAD)
As we saw in an earlier example, our system only has 7.5 dB of maximum gain available with a 6 dB safety factor. By going to both a directional microphone and a directional loudspeaker, we can increase this by about 6 dB, yielding a maximum gain of 13.5 dB still some 16 dB short of what we actually need. The solution is obvious; a hand-held microphone will be necessary in order to achieve the required gain. For 16 dB of added gain, Ds will have to be reduced to the value calculated below: 16 = 20 log (1/x) 16/20 = log (1/x) 10.8 = 1/x Therefore: x = 1/10.8 = 0.16 meter (6) Of course, the problem with a hand-held microphone is that it is difficult for the user to maintain a fixed distance between the microphone and his mouth. As a result, the gain of the system will vary considerably with only small changes in the performer-microphone operating distance. It is always better to use some kind of personal microphone, one worn by the user. In this case, a swivel type microphone attached to a headpiece would be best, since it provides the minimum value of DS. This type of microphone is now becoming very popular on-stage, largely because a number of major pop and country artists have adopted it. In other cases a simple tietack microphone may be sufficient.

Conclusion

In this chapter, we have presented the rudiments of gain calculation for sound systems, and the methods of analysis form the basis for the study of indoor systems, which we will cover in a later chapter.
Chapter 5: Fundamentals of Room Acoustics
Most sound reinforcement systems are located indoors, and the acoustical properties of the enclosed space have a profound effect on the systems requirements and its performance. Our study begins with a discussion of sound absorption and reflection, the growth and decay of sound fields in a room, reverberation, direct and reverberant sound fields, critical distance, and room constant. If analyzed in detail, any enclosed space is quite complex acoustically. We will make many simplifications as we construct statistical models of rooms, our aim being to keep our calculations to a minimum, while maintaining accuracy on the order of 10%, or 1 dB.
Absorption and Reflection of Sound

Sound tends to bend around non-porous, small obstacles. However, large surfaces such as the boundaries of rooms are typically partially flexible and partially porous. As a result, when sound strikes such a surface, some of its energy is reflected, some is absorbed, and some is transmitted through the boundary and again propagated as sound waves on the other side. See Figure 5-1. All three effects may vary with frequency and with the angle of incidence. In typical situations, they do not vary with sound intensity. Over the range of sound pressures commonly encountered in audio work, most construction materials have the same characteristics of reflection, absorption and transmission whether struck by very weak or very strong sound waves.
Figure 5-1. Sound impinging on a large boundary surface
When dealing with the behavior of sound in an enclosed space, we must be able to estimate how much sound energy will be lost each time a sound wave strikes one of the boundary surfaces or one of the objects inside the room. Tables of absorption coefficients for common building materials as well as special acoustical materials can be found in any architectural acoustics textbook or in data sheets supplied by manufacturers of construction materiaIs. Unless otherwise specified, published sound absorption coefficients represent average absorption over all possible angles of incidence. This is desirable from a practical standpoint since the random incidence coefficient fits the situation that exists in a typical enclosed space where sound waves rebound many times from each boundary surface in virtually all possible directions. Absorption ratings normally are given for a number of different frequency bands. Typically, each band of frequencies is one octave wide, and standard center frequencies of 125 Hz, 250 Hz, 500 Hz, 1 kHz, etc., are used. In sound system design, it usually is sufficient to know absorption characteristics of materials in three or four frequency ranges. In this handbook, we make use of absorption ratings in the bands centered at 125 Hz, 1 kHz and 4 kHz. The effects of mounting geometry are included in standardized absorption ratings by specifying the types of mounting according to an accepted numbering system. In our work, familiarity with at least three of these standard mountings is important.
Acoustical tile or other interior material cemented directly to a solid, non-absorptive surface is called No. 1 mounting (see Figure 5-2). To obtain greater absorption, especially at lower frequencies, the material may be spaced out on nominal two-inch thick furring strips and the cavity behind loosely filled with fiberglass blanket. This type of mounting is called out as No. 2. No. 7 mounting is the familiary suspended T-bar ceiling system. Here the material is spaced at least 0.6 meter (2) away from a solid structural boundary. Absorption coefficients fall within a scale from zero to one following the concept established by Sabine, the pioneer of modern architectural acoustics. Sabine suggested that an open window be considered a perfect absorber (since no sound is reflected) and that its sound absorption coefficient must therefore be 100 percent, or unity. At the other end of the scale, a material which reflects all sound and absorbs none has an absorption coefficient of zero. In older charts and textbooks, the total absorption in a room may be given in sabins. The sabin is a unit of absorption named after Sabine and is the equivalent of one square foot of open window. For example, suppose a given material has an absorption coefficient of 0.1 at 1 kHz. One hundred square feet of this material in a room has a total absorption of 10 sabins. (Note: When using SI units, the metric sabin is equal to one square meter of totally absorptive surface.)

Figure 5-2.

ASTM types of mounting (used in conducting sound absorption tests)
More recent publications usually express the absorption in an enclosed space in terms of the average absorption coefficient. For example, if a room has a total surface area of 1000 square meters consisting of 200 square meters of material with an absorption coefficient of.8 and 800 square meters of material with an absorption coefficient of.1, the average absorption coefficient for the entire internal surface area of the room is said to be.24: Area: 1000 a Coefficient: x 0.8 x 0.1 Sabins: = 160 = 80 240

= 240 = 0.24 1000

Although we commonly use published absorption coefficients without questioning their accuracy and perform simple arithmetic averaging to compute the average absorption coefficient of a room, the numbers themselves and the procedures we use are only approximations. While this does not upset the reliability of our calculations to a large degree, it is important to realize that the limit of confidence when working with published absorption coefficients is probably somewhere in the neighborhood of 10%. How does the absorption coefficient of the material relate to the intensity of the reflected sound wave? An absorption coefficient of 0.2 at some specified frequency and angle of incidence means that 20% of the sound energy will be absorbed and the remaining 80% reflected. The conversion to decibels is a simple 10 log function: 10 log10 0.8 = -0.97 dB In the example given, the ratio of reflected to direct sound energy is about -1 dB. In other words, the reflected wave is 1 dB weaker than it would have been if the surface were 100% reflective. See the table in Figure 5-3. Thinking in terms of decibels can be of real help in a practical situation. Suppose we want to improve the acoustics of a small auditorium which has a pronounced slap off the rear wall. To reduce the intensity of the slap by only 3 dB, the wall must be surfaced with some material having an absorption coefficient of 0.5! To make the slap half as loud (a reduction of 10 dB) requires acoustical treatment of the rear wall to increase its absorption coefficient to 0.9. The difficulty is heightened by the fact that most materials absorb substantially less sound energy from a wave striking head-on than their random incidence coefficients would indicate. Most acoustic materials are porous. They belong to the class which acousticians elegantly label fuzz. Sound is absorbed by offering resistance to the flow of air through the material and thereby changing some of the energy to heat. But when porous material is affixed directly to solid concrete or some other rigid non-absorptive surface, it is obvious that there can be no air motion and therefore no absorption at the boundary of the two materials.

The use of the average absorption coefficient a has the advantage that it is not tied to any particular system of measurement. An average absorption coefficient of 0.15 is exactly the same whether the surfaces of the room are measured in square feet, square yards, or square meters. It also turns out that the use of an average absorption coefficient facilitates solving reverberation time, direct-toreverberant sound ratio, and steady-state sound pressure.
Figure 5-3. Reflection coefficient in decibels as a function of absorption coefficient
Figure 5-4. Interference pattern of sound reflected from a solid boundary
Figure 5-5. Reflectivity of thin plywood panels
Consider a sound wave striking such a boundary at normal incidence, shown in Figure 5-4. The reflected energy leaves the boundary in the opposite direction from which it entered and combines with subsequent sound waves to form a classic standing wave pattern. Particle velocity is very small (theoretically zero) at the boundary of the two materials and also at a distance 1/2 wavelength away from the boundary. Air particle velocity is at a maximum at 1/4 wavelength from the boundary. From this simple physical relationship it seems obvious that unless the thickness of the absorptive material is appreciable in comparison with a quarter wavelength, its effect will be minimal. This physical model also explains the dramatic increase in absorption obtained when a porous material is spaced away from a boundary surface. By spacing the layer of absorptive material exactly one-quarter wavelength away from the wall, where particle velocity is greatest, its effective absorption is multiplied many times. The situation is complicated by the necessity of considering sound waves arriving from all possible directions. However, the basic effect remains the same: porous materials can be made more effective by making them thicker or by spacing them away from non-absorptive boundary surfaces. A thin panel of wood or other material also absorbs sound, but it must be free to vibrate. As it vibrates in response to sound pressure, frictional losses change some of the energy into heat and sound is thus absorbed. Diaphragm absorbers tend to resonate at a particular band of frequencies, as any other tuned circuit, and they must be used with care. Their great advantage is the fact that low frequency absorption can be obtained in less depth than would be required for porous materials. See Figure 5-5. A second type of tuned absorber occasionally used in acoustical work is the Helmholtz resonator: a reflex enclosure without a loudspeaker. (A patented construction material making use of this type of absorption is called Soundblox. These masonry blocks containing sound absorptive cavities can be used in gymnasiums, swimming pools, and other locations in which porous materials cannot be employed.)

Figure 5-8. Calculating reverberation time
Figure 5-9. Reverberation time equations
by a single number, a. Only one step remains to complete our model. Since sound travels at a known rate of speed, the mean free path is equivalent to a certain mean free time between bounces. Now imagine what must happen if we apply our model to the situation that exists in a room immediately after a uniformly emitting sound source has been turned off. The sound waves continue to travel for a distance equal to the mean free path. At this point they encounter a boundary surface having an absorption coefficient of a and a certain percentage of the energy is lost. The remaining energy is reflected back into the room and again travels a distance equal to the mean free path before encountering another boundary with absorption coefficient a. Each time sound is bounced off a new surface, its energy is decreased by a proportion determined by the average absorption coefficient a. If we know the proportion of energy lost with each bounce and the length of time between bounces, we can calculate the average rate of decay and the reverberation time for a particular room. Example: Consider a room 5m x 6m x 3m, as diagrammed in Figure 5-8. Let us calculate the decay rate and reverberation time for the octave band centered at 1 kHz. The volume of the room is 90 cubic meters, and its total surface area is 126 square meters; therefore,
the MFP works out to be about 3 meters. The next step is to list individually the areas and absorption coefficient of the various materials used on room surfaces. The total surface area is 126 square meters; the total absorption (Sa) adds up to 24.9 absorption units. Therefore, the average absorption coefficient (a) is 24.9 divided by 126, or.2. If each reflection results in a decrease in energy of 0.2, the reflected wave must have an equivalent energy of 0.8. A ratio of 0.8 to 1 is equivalent to a loss of 0.97 decibel per reflection. For simplicity, let us call it 1 dB per reflection. Since the MFP is 2.9 meters, the mean free time must be about 0.008 seconds (2.9/334 = 0.008). We now know that the rate of decay is equivalent to 1 dB per 0.008 seconds. The time for sound to decay 60 dB must, therefore, be: 60 x 0.008 = 0.48 seconds. The Eyring equation in its standard form is shown in Figure 5-9. If this equation is used to calculate the reverberation of our hypothetical room, the answer comes out 0.482 seconds. If the Sabine formula is used to calculate the reverberation time of this room, it provides an answer of 0.535 seconds or a discrepancy of a little more than 10%.

Figure 5-10. Reverberation time chart, SI units
Figure 5-1 1. Reverberation time chart, English units
Figure 5-12. Approximate absorption coefficients of common material (averaged and rounded-off from published data)
Rather than go through the calculations, it is much faster to use a simple chart. Charts calculated from the Eyring formula are given in Figures 5-10 and 5-11. Using the chart as a reference and again checking our hypothetical example, we find that a room having a mean free path just a little less than 3 meters and an average absorption coefficient of.2 must have a reverberation time of just a little less than.5 seconds. Since reverberation time is directly proportional to the mean free path, it is desirable to calculate the latter as accurately as possible. However, this is not the only area of uncertainty in these equations. There is argument among acousticians as to whether published absorption coefficients, such as those of Figure 5-12, really correspond to the random incidence absorption implicit in the Eyring equation. There also is argument over the method used to find the average absorption coefficient for a room. In our example, we performed a simple arithmetic calculation to find the average absorption coefficient. It has been pointed out that this is an unwarranted simplification that the actual state of affairs requires neither an arithmetic average nor a geometric mean, but some relation considerably more complicated than either.
Another source of uncertainty lies in determining the absorption coefficients of materials in situations other than those used to establish the rating. We know, for example, that the total absorption of a single large patch of material is less than if the same amount of material is spread over a number of separated, smaller patches. At higher frequencies, air absorption reduces reverberation time. Figure 5-13 can be used to estimate such deviations above 2 kHz. A final source of uncertainty is inherent in the statistical nature of the model itself. We know from experience that reverberation time in a large concert hall may be different in the seating area than if measured out near the center of the enclosed space. With all of these uncertainties, it is a wonder that the standard equations work as well as they do. The confidence limit of the statistical model is probably of the order of 10% in terms of time or decay rate, or 1 dB in terms of sound pressure level. Therefore, carrying out calculations to 3 or 4 decimal places, or to fractions of decibels, is not only unnecessary but mathematically irrelevant. Reverberation is only one of the characteristics that help our ears identify the acoustical signature of an enclosed space. Some acousticians separate acoustical qualities into three categories: the direct sound, early reflections, and the late-arriving reverberant field.

Figure 5-22. Room constant vs. surface area and
room constant with some confidence, then we can estimate the sound pressure level that will be produced in the reverberant field of the room for a given acoustical power output. Figure 5-22 enables us to determine by inspection the room constant if we know both a and the total surface area. This chart can be used with either SI or English units. If both room constant and directivity factor of a radiator are known, the critical distance can be solved directly from the following equation:

DC =.14 QR

This equation may be used with either SI or English units, and a graphical solution for it is shown in Figure 5-23. It is helpful to remember that the relationship between directivity index and critical distance is in a way very similar to the inverse square law: an increase of 6 dB in directivity (or a timesfour increase in Q) corresponds to a doubling of the critical distance. One might think of this as the direct square law. A second useful factor to keep in mind is that the directivity index of a person talking, taken in the
1 kHz range along the major axis, is about 3 dB. For convenience in sound system calculations, we normally assume the Q of the talker to be 2. These two facts can be used to make reasonably accurate acoustical surveys of existing rooms without equipment. All that is needed is the cooperation of a second person and a little experience. Have your assistant repeat a word or count slowly in as even a level as possible. While he is doing this, walk directly away from him while carefully listening to the intensity and quality of his voice. With a little practice, it is easy to detect the zone in which the transition is made from the direct field to the reverberant field. Repeat the experiment by starting at a considerable distance away from the talker, well into the reverberant field, and walking toward him. Again, try to zero in on the transition zone. After two or three such tries you may decide, for example, that the critical distance from the talker in that particular room is about 4 meters. You know that a loudspeaker having a directivity index of 3 dB will also exhibit a critical distance of 4 meters along its major axis in that room. To extend the critical distance to 8 meters, the loudspeaker must have a directivity index of 9 dB.
Figure 5-23. Critical distance as a function of room constant and directivity index or directivity factor

Once the critical distance is known, the ratio of direct to reverberant sound at any distance along that axis can be calculated. For example, if the critical distance for a talker is 4 meters, the ratio of direct to reverberant sound at that distance is unity. At a distance of 8 meters from the talker, the direct sound field will decrease by 6 dB by virtue of inverse square law, whereas the reverberant field will be unchanged. At twice critical distance, therefore, we know that the ratio of direct to reverberant sound must be -6 dB. At four times DC, the direct-to-reverberant ratio will obviously be -12 dB.
Figure 5-24. Peutz (9) has developed an empirical equation which will enable a designer to estimate the approximate slope of the attenuation curve beyond DC in rooms with relatively low ceilings and low reverberation times:

0.4 V dB h T60

Statistical Models vs. the Real World
We stated earlier that a confidence level of about 10% allowed us to simplify our room calculations significantly. For the most part, this is true; however, there are certain environments in which errors may be quite large if the statistical model is used. These are typically rooms which are acoustically dead and have low ceilings in relation to their length and width. Hotel ballrooms and large meeting rooms are examples of this. Even a large pop recording studio of more regular dimensions may be dead enough so that the ensemble of reflections needed to establish a diffuse reverberant field simply cannot exist. In general, if the average absorption coefficient in a room is more than about 0.2, then a diffuse reverberant field will not exist. What is usually observed in such rooms is data like that shown in
In this equation, D represents the additional falloff in level in dB per doubling of distance beyond DC. V is the volume in meters3, h is the ceiling height in meters, and T60 is the reverberation time in seconds. In English units (V in ft3 and h in feet), the equation is:

0.22 V dB h T60

As an example, assume we have a room whose height is 3 meters and whose length and width are 15 and 10 meters. Let us assume that the reverberation time is one second. Then:

0.= 2.8 dB 3 (1)

Thus, beyond DC we would observe an additional fall-off of level of about 3 dB per doubling of distance.

Figure 5-24.

Attentuation with distance in a relatively dead room

Sound System Design Reference Manual
Chapter 6: Behavior of Sound Systems Indoors

Introduction

The preceding five chapters have provided the groundwork on which this chapter is built. The fine art and science of sound reinforcement now begins to take shape, and many readers who have patiently worked their way through the earlier chapters will soon begin to appreciate the disciplines which have been stressed. The date at which sound reinforcement grew from public address by guesswork to a methodical process in which performance specifications are worked out in advance was marked by the publication in 1969 of a paper titled The Gain of a Sound System, by C. P. and R. E. Boner (4). It describes a method of calculating potential sound system gain, and that method has since become a fundamental part of modern sound system design. The following discussion is based on the Boner paper. Certain points are expanded, and examples are given that require calculations more complicated than those in the original study. Also discussed is the relation between theoretically achievable system gain and practical operating parameters of typical indoor sound systems.
Figure 6-1. An indoor sound system
Acoustical Feedback and Potential System Gain
Just as in the outdoor case studied earlier, if we have a microphone/amplifier/loudspeaker combination in the same room and gradually turn up the gain of the amplifier to a point approaching sustained feedback, the electrical frequency response of the system changes with the gain setting. The effect results from an acoustic feedback path between the loudspeaker and the microphone. As a person talks into the microphone, the microphone hears not only the direct sound from the talker, but the reverberant field produced by the loudspeaker as well. The purpose of using high-quality loudspeakers and microphones having smooth response characteristics, and sound system equalization (apart from achieving the desired tonal response) is to smooth out all of the potential feedback points so that they are evenly distributed across the audible frequency range. When this has been done, there should be as many negative feedback points as positive feedback points, and the positive feedback points should all reach the level of instability at about the same system gain. We might expect this to average out in such a way that the level produced by the loudspeaker reaching the microphone can never be greater than that produced by the talker without causing sustained oscillation. In other words, we assume that the extra gain supplied by all the positive feedback spikes is just balanced out by the loss caused by all the negative feedback dips. If the Boner criteria for optimum system geometry are followed, the microphone will be close to the talker so that it hears mostly direct sound from the talker. It will be far enough from the loudspeaker to be well into the reverberant field of the loudspeaker, so that direct sound from the loudspeaker is not an appreciable factor in triggering system feedback. Assuming that listeners are also in the reverberant field of the loudspeaker, it follows that the sound level in the listening area with the system turned on cannot be greater than that of the unaided talker at the microphone position with the system turned off. Using the Boner concept of system delta, the situation at maximum gain corresponds to a delta of unity. (Delta is defined as the difference in decibels between sound level at the system microphone with system off and the level in the audience area with system on. See Figure 6-1). Although we have described these as conditions of maximum potential system gain, it is possible in practice to achieve a delta greater than unity. For example, if a directional microphone is used it can discriminate against the reverberant field 6-2

and allow another 3 to 4 dB of system gain. Another possibility is to place the listener in the direct field of the loudspeaker, allowing a further increase in system gain. If the level of the reverberant field is lower in the performing area than in the listening area, additional system gain also results. This situation is described by the Boners as a room constant in the microphone area different from that in the seating area. Similar results may be noted in rooms having large floor areas, relatively low ceilings, and substantial sound absorption. In such rooms, as we have seen, sound from a point source tends to dwindle off beyond DC at a rate of 2 or 3 dB for each doubling of distance rather than remaining constant in level. Still another way to increase gain is to electrically suppress the positive feedback frequencies individually with very narrow bandwidth filters. If one could channel all energy into the negative feedback frequencies, the potential system gain would theoretically become infinite! Unfortunately, the acoustic feedback path is not stable enough to permit this degree of narrow-band equalization. In all other situations, a gain setting is reached at which sustained oscillation occurs. By definition, maximum system gain is reached just below this point. However, the system cannot be operated satisfactorily at a point just below oscillation because of its unpleasant comb-filter response and the prolonged ringing caused by positive feedback peaks. To get back to reasonably flat electrical response and freedom from audible ringing, it usually is recommended that a properly equalized system be operated about 6 dB below its maximum gain point. Even an elaborately tuned system using narrowband filters can seldom be operated at gains greater than 3 dB below sustained oscillation.
Sound Field Calculations for a Small Room
Consider the room shown in Figure 6-2. This is a typical small meeting room or classroom having a volume less than 80 m3. The average absorption coefficient a is 0.2. Total surface area is 111 m2. The room constant, therefore, is 28 m2. From the previous chapter, we know how to calculate the critical distance for a person talking (nominal directivity index of 3 dB). In the example given, DC for a source having a directivity index of 3 dB is 1 meter. The figure also shows geometrical relationships among a talker, a listener, the talkers microphone and a simple wall-mounted loudspeaker having a directivity index of 6 dB along the axis pointed at the listener. The microphone is assumed to be omnidirectional.

Step 1: Calculate relative sound levels produced by the talker at microphone and listener. We begin with the sound system off. Although the calculations can be performed using only relative levels, we will insert typical numbers to get a better feel for the process involved. The microphone is.6 meter from the talker, and at this distance, the direct sound produces a level of about 70 dB. Since DC for the unaided talker is only 1 meter, the microphone distance of.6 meter lies in the transition zone between the direct field and the reverberant field of the talker. By referring to Figure 6-3, we note that the combined sound levels of the reverberant field and the direct field at a distance of.6 meter must be about 1 dB greater than the direct field alone. Therefore, since we have assumed a level of 70 dB for the direct field only, the total sound level at the microphone must be 71 dB. Next, we use a similar procedure to calculate the sound level at the listeners position produced by an unaided talker: The listener is located 4.2 meters from the talker, more than 3 times the critical distance of 1 meter, and therefore, well into the reverberant field of the talker. We know that the sound level anywhere in the reverberant field is equal to that produced by the direct field alone at the critical distance. If the level produced by direct sound is 70 dB at a distance of.6
meter, it must be 4.6 dB less at a distance of 1 meter, or 65.4 dB, and the level of the reverberant field must also be 65.4 dB. The sound level produced by the unaided talker, at the listeners position, therefore is 65.4 dB. At this point, let us consider two things about the process we are using. First, the definition of critical distance implies that sound level is to be measured with a random-incidence microphone. (For example, we have chosen a non-directional system microphone so that it indeed will hear the same sound field as that indicated by our calculations). Second, we have worked with fractions of decibels to avoid confusion, but it is important to remember that the confidence limits of our equations do not extend beyond whole decibel values, and that we must round off the answer at the end of our calculations. Step 2:The sound field produced by the loudspeaker alone. Now let us go back to our example and calculate the sound field produced by the loudspeaker. Our system microphone is still turned off and we are using an imaginary test signal for the calculations. We can save time by assuming that the test signal produces a sound level at the microphone of 71 dB the same previously assumed for the unaided talker.
Figure 6-2. Indoor sound system gain calculations
The loudspeaker is mounted at the intersection of wall and ceiling. Its directivity index, therefore, is assumed to be 6 dB. In this room, the critical distance for the loudspeaker is 1.4 meters. This is almost the same as the distance from the loudspeaker to the microphone. Since the microphone is located at the loudspeakers critical distance, and since we have assumed a level of 71 dB for the total sound field at this point, the direct field at the microphone must equal 71 dB minus 3 dB, or 68 dB. The listener is 4.8 meters from the loudspeaker (more than 3 times the critical distance) and therefore, well into the reverberant field of the loudspeaker. We know that the level in the reverberant field must equal the level of the direct field alone at the critical distance. The sound level at the listeners position produced by the loudspeaker must, therefore, be 68 dB. Step 3: Potential acoustic gain is now considered. Since we deliberately set up the example to represent the condition of maximum theoretical gain for a properly equalized system, we can use these same figures to calculate the difference in level at the listeners position between the unaided talker and the talker operating with the system turned on. We have calculated that the unaided talker produces a level at the listeners position of 65.4 dB. We have also calculated that the level produced by the loudspeaker at the listeners position is 68 dB. The

The third step is to make similar calculations for the loudspeaker alone. The listener is located on the major axis of the loudspeaker and is more than 3 times the critical distance of 4.2 meters. The microphone is located at a vertical angle of 60 degrees from the loudspeakers major axis, and also is more than 3 times the critical distance (at this angle) of 1 meter. Both the listener and the microphone are located in the reverberant field of the loudspeaker. If the sound level produced by the loudspeaker at the microphone can be no greater than 70 dB (the same level as the talker) then the level produced by the loudspeaker at the listeners position must also be 70 dB, since both are in the reverberant field. Having established these relationships we know that the talker produces a level at the listeners position of 60 dB with the sound system off and 70 dB with the sound system on, or a maximum potential gain of 10 dB. Allowing 6 dB headroom in a properly equalized system, we still realize 4 dB gain at the listeners position, and the sound system can be said to provide a small but perceptible increase in sound level.
Figure 6-6. Critical distance as a function of room constant and directivity index or directivity factor
However, all of the preceding calculations have assumed that the microphone is an omnidirectional unit. What happens if we substitute a directional microphone? Figure 6-7 shows the additional geometrical relationships needed to calculate the increase in gain produced by a directional microphone. Note that the distance from talker to microphone is still.6 meters and that the talker is assumed to be located along the major axis of the microphone. The loudspeaker is located 5.4 meters from the microphone along an angle of 75 from the major axis. Figure 6-7 also shows a typical cardioid pattern for a directional microphone. The directivity index of such a microphone along its major axis is about 5 dB. Since the talker is located on the major axis of the microphone, it hears his signal 5 dB louder than the random incidence reverberant field. In theory this should increase potential system gain by a factor of 5 dB. But we must also consider the microphones directional characteristics with relation to the loudspeaker. If the directivity index of the microphone at 0 is 5 dB, the polar pattern indicates that its directivity index at 75 must be about 3 dB. This tells
us that even though the loudspeaker is 75 off the major axis of the microphone, it still provides 3 dB of discrimination in favor of the direct sound from the loudspeaker. We know that the loudspeakers directivity index is -3 dB along the axis between the loudspeaker and the microphone. We also know that the microphones directivity index along this axis is +3 dB. The combined directivity indices along this axis must therefore, be 0 dB and we can find the equivalent critical distance from Figure 6-6. The combined critical distance of loudspeaker and microphone along their common axis is about 1.3 meters. Since the distance between the two is more than 3 times this figure, the microphone still lies within the reverberant field of the loudspeaker. Using the directional microphone should therefore allow an increase in potential system gain before feedback of about 5 dB. (In practice, little more than 3 or 4 dB of additional gain can be achieved.)

Figure 6-7. Characteristics of a cardioid microphone
Calculations for a Distributed Loudspeaker System
Figure 6-8 shows a moderate-size meeting room or lecture room. Its volume is 485 m3, surface area is about 440 m2, and a is 0.2 when the room is empty. For an unaided talker in the empty room, R is 110 m2. However, when the room is fully occupied, a increases to 0.4 and the corresponding room constant is 293 m2. We calculate the critical distance for the unaided talker (directivity index of 3 dB) to be 2 meters in an empty room and 3.4 meters when the room is full. The room is provided with a sound system diagrammed in Figure 6-9. Forty loudspeakers are mounted in the ceiling on 1.5 meter centers to give smooth pattern overlap up into the 4 kHz region. Coverage at ear level varies only 2 or 3 dB through the entire floor area.
The usual definitions of critical distance and direct-to-reverberant ratio are ambiguous for this kind of loudspeaker array. Here, however, we are interested only in potential acoustic gain, and the ambiguities can be ignored. We already have stated that the loudspeaker array lays down a uniform blanket of sound across the room. The relative directional and temporal components of the sound field do not enter into gain calculations. An omnidirectional microphone is located.6 meters from the talker, less than 1/3 DC. No matter how many people are present, the microphone is in the direct field of the talker. The farthest listener is 9 meters from the talker, more than three times DC when the room is empty, and just about three times DC when the room is full. If the unaided talker produces 70 dB sound level at the microphone with the system off, and if the amplified sound level can be no greater than 70 dB at the microphone with the system on, then the maximum level is 70 dB everywhere in the room.

Figure 6-8.

A moderate-size lecture room
Figure 6-9. Sound system in a medium-size lecture room
From our calculations of critical distances, we see that the unaided talker will produce a sound level at the listener of 59 dB in an empty room and about 55 dB with a full audience. For a usable working delta of -6 dB, the calculated acoustic gain at the listeners position is about 5 dB in an empty room and about 9 dB when full. Can we get more gain by turning off the loudspeaker directly over the microphone? Not in a densely packed array such as this. The loudspeakers are mounted close together to produce a uniform sound field at ear level. As a result, the contribution of any one loudspeaker is relatively small. However, by turning off all the loudspeakers in the performing area and covering only the audience, some increase in system gain may be realized. In the example just given, each loudspeaker is assumed to have a directivity index in the speech frequency region of +6 dB at 0, +3 dB at 45, and 0 dB at 60. Suppose we use only the 25 loudspeakers over the audience and turn off the 15 loudspeakers in the front of the room. In theory, the increase in potential gain is only 1 dB with a single listener or 2 dB when the audience area is filled. Even if we allow for the probability that most of the direct sound will be absorbed by the audience, it is unlikely that the gain increase will be more than 3 dB. The calculations required to arrive at these conclusions are tedious but not difficult. The relative direct sound contribution from each of the loudspeakers at microphone and listener locations is calculated from knowledge of polar patterns and distances. By setting an arbitrary acoustic output per loudspeaker, it is then possible to estimate the sound level produced throughout the room by generally reflected sound (reverberant field) and that produced by reflected plus quasi-direct sound.

Figure 6-10. Conditions for the indoor system gain equation
General Requirements for Speech Intelligibility
The requirements for speech intelligibility are basically the same for unamplified as for amplified speech. The most important factors are: 1. Speech level versus ambient noise level. Every effort should be made to minimize noise due to air handling systems and outside interferences. In general, the noise level should be 25 dB or greater below the lowest speech levels which are expected. However, for quite high levels of reinforced speech, as may be encountered outdoors, a noise level 10 to 15 dB below speech levels may be tolerated. 2. Reverberation time. Speech syllables occur three or four times per second. For reverberation times of 1.5 seconds or less, the effect of reverberant overhang on the clarity of speech will be minimal. 3. Direct-to-reverberant ratio. For reverberation times in excess of 1.5 seconds, the clarity of speech is a function of both reverberation time and the ratio of direct-to-reverberant sound. In an important paper (8), Peutz set forth a method of estimating speech intelligibility which has found considerable application in sound system design. The Peutz findings were compiled on the basis of data gathered over a period of years. The data and the method used to arrive at the published conclusion are clearly set forth in the paper itself. The conclusions can be summarized as follows:
1. In practice, the articulation loss of consonants can be used as a single indicator of intelligibility. Although the original research of Peutz was in Dutch speech, the findings seem to be equally applicable to English. 2. As would be expected, the researchers found wide variations in both talkers and listeners. However, a 15% articulation loss of consonants seems to be the maximum allowable for acceptable speech intelligibility. In other words, if articulation loss of consonants exceeds 15% for the majority of listeners, most of those people will find the intelligibility of speech to be unacceptable. 3. Articulation loss of consonants can be estimated for typical rooms. Articulation loss of consonants is a function of reverberation time and the direct-to-reverberant sound ratio. 4. As a listener moves farther from a talker (decreasing the direct-to-reverberant sound ratio) articulation loss of consonants increases. That is, intelligibility becomes less as the direct-toreverberant ratio decreases. However, this relationship is maintained only to a certain distance, beyond which no further change takes place. The boundary corresponds to a direct-to-reverberant ratio of -10 dB.

Figure 6-1 1. Measurement of sound system gain and delta (
The last point is illustrated graphically in Figure 6-12, adapted from the Peutz paper. Each of the diagonal lines corresponds to a particular reverberation time. Each shelves at a point corresponding to a direct-to-reverberant sound ratio of -10 dB. Note that the shelf may lie above or below the 15% figure depending upon the reverberation time of the room. This agrees with other published information on intelligibility. For example, Rettinger points out that in rooms having a reverberation time of 1.25 seconds or less, direct sound and early reflections always make up the greater portion of the total sound field. Intelligibility in such rooms is good regardless of the direct-to-reverberant sound ratio at any given listening position. Conversely, anyone who has worked in extremely large reverberant spaces such as swimming pools or gymnasiums knows that intelligibility deteriorates rapidly at any point much beyond the critical distance. According to the chart, a 15% articulation loss of consonants in a room having a reverberation time of 5 seconds corresponds to a direct-to-reverberant sound ratio of only - 5.5 dB. Problems associated with speech intelligibility in enclosed spaces have received a great deal of attention prior to the publication of the Peutz paper. The virtue of Peutz method for estimating speech intelligibility is its simplicity. It must be remembered, however, that a number of contributing factors are
ignored in this one simple calculation. The chart assumes that satisfactory loudness can be achieved and that there is no problem with interference from ambient noise. It also postulates a single source of sound and a well behaved, diffuse reverberant sound field. The data from the Peutz paper have been recharted in a form more convenient for the sound contractor in Figure 6-13. Here we have arbitrarily labeled the estimated intelligibility of a talker or a sound system as satisfactory, good, or excellent, depending upon the calculated articulation loss of consonants. There often is a dramatic difference in the acoustical properties of a room depending upon the size of the audience. Calculations should be made on the basis of the worst case condition. In some highly reverberant churches particularly, it may turn out that there is no practical way to achieve good intelligibility through the entire seating area when the church is almost empty. The solution may involve acoustical treatment to lessen the difference between a full and an empty church, or it may involve a fairly sophisticated sound system design in which reinforced sound is delivered only to the forward pews when the congregation is small (presuming that a small congregation can be coaxed into the forward pews).
Figure 6-12. Probable articulation loss of consonants vs. reverberation time & direct-to-reverberant sound ratio

We can also ask the question of whether our analysis using R would have materially affected the performance of the central array system. A rigorous analysis would be a little tedious, but we can make a simplifying assumption. Let us assume that half of the direct sound from the central array was incident on the audience with its.95 absorption coefficient. Let us round this off and call it 1.0 instead, resulting in no sound at all being reflected from the audience. This would only lower the reverberant level in the room by 3 dB, hardly enough to make the direct-toreverberant ratio workable. More than any other we have carried out in this chapter, this analysis points up the multi-dimensional complexity of sound system design. Again, we state that there are no easy solutions or simple equations. Instead, there is only informed rational analysis and thoughtful balancing of many factors.

Figure 6-15.

A distributed system in a large church
The Role of Time Delay in Sound Reinforcement
The preceding example mentioned time delay as a means of preserving naturalness in a distributed system. This comes about by way of the Haas (or precedence) effect (5), which is illustrated in Figure 6-16. If two loudspeakers are fed the same signal, a listener mid-way between them will localize the source of sound directly ahead (A). At B, we have introduced a delay in one of the otherwise identical channels, and the listener will clearly localize toward the earlier loudspeaker. At C. the leading signal has been reduced in level, resulting in an effect of equal loudness at both loudspeakers. This has the approximate effect of restoring the apparent localization to the center. While this tradeoff is not an exact one, the values shown in the graph at D indicate the approximate trading value between level and delay for equal loudness at both loudspeakers.
Figure 6-16E shows how delay is typically implemented in sound reinforcement. Here, that portion of the audience seated under the balcony does not get adequate coverage from the central array. Small loudspeakers placed in the balcony soffit can provide proper coverage only if they are delayed so that the sound arrives at the listeners in step with that from the central array. In this way, the listener tends to localize the source of sound at the central array not at the soffit loudspeakers. If the soffit loudspeakers are not delayed, listeners under the balcony would localize sound directly overhead, and those listeners just in front of the balcony would be disturbed by the undelayed sound. In practice, the delay is usually set for an additional 20 msec in order to minimize comb filtering in the overlap zone between direct and delayed sound fields. The ready availability of solid state digital delay units has made time delay an indispensable element in sound system design.

Figure 6-20. Flow diagram for system design
Chapter 7: System Architecture and Layout
Just as the building architect interprets a set of requirements into flexible and efficient living or working spaces, the designer of a sound reinforcement system similarly interprets a set of requirements, laying out all aspects of the system in an orderly fashion. A full sound system specification will detail almost everything, including all equipment choices and alternatives, rack space requirements, wire gauges and markings, and nominal signal operating levels. In addition, the electroacoustical aspects of the system will have been worked out well ahead of time so that there will be few surprises when the system is turned on for the first time. The consultant or design engineer lays out the broad system parameters, but it is the sound contractor who is responsible for all component layout and orderly completion of the system, along with documentation for usage as well as maintenance. System architecture also addresses signal flow and nominal operating levels, consistent with the requirements of the system. The best designs are usually the simplest and most straightforward ones. In this chapter we will cover several design projects, beginning with basic design goals and fundamental performance specifications. We will then move on to system descriptions and layout, suggesting ways that the specification can be met. We will concentrate on the electroacoustical problems that are fundamental to each case study. By way of review, we will first discuss a few basic audio engineering subjects, beginning with an abbreviated signal flow diagram for a relatively simple speech reinforcement system.
Typical Signal Flow Diagram
Assume that we have the following requirements: 1. Up to ten microphones may be needed at different locations. 2. The system is to be used primarily for speech reinforcement. 3. The system shall be able to produce peak levels up to 85 dB-SPL in all parts of the house under all speech input conditions, including weak talkers. The room noise level is about 25 dB(A). The most basic interpretation of these requirements tells us the following: 1. A small Soundcraft or Spirit console should suffice for all input configurations and routing control. 2. A single central array is the preferred system type, based on the desire for most natural speech reproduction. The array may be specified using individual HF and LF components; alternatively, an appropriate full-range system with integral rigging capability may be specified, as we will show here. 3. Both biamplification and system response equalization are recommended, and this suggests that a digital loudspeaker controller be used for frequency division, time alignment, and system response equalization. Note that there are many points in the system where we can set or change gain. There is always considerable gain overlap in the electronic devices used in sound system work. The purpose of this is to allow for a great variety of input conditions as well as to allow the equipment to be configured in different ways, as required. It is critical that the designer specify a nominal setting of each gain control, locking off, when possible, those controls that will not or should not be altered during normal system use. This important setting of gain relationships should be based on the absolute requirement that the input noise floor of the system should not be degraded later in the chain, and that no early stage of amplification should overload before the output power amplifier overloads. In our exercise here, we 7-1

Figure 7-1A. Signal flow diagram for a simple reinforcement system
Figure 7-1B. detailed level diagram showing noise levels, nominal operating levels, and maximum output levels of each device
Step Two: We now have to determine what the nominal operating level of the system should be for the farthest listeners, which we will assume are some 20 meters away from the loudspeaker. Let us further assume that the reverberation time in the room is no greater than 1.5 seconds in the range from 250 Hz to 2 kHz and that the average noise level room is in the range of 25 dB(A). Referring to Figure 7-2, we can
see that for an ambient noise level in the 25 dB(A) range, the EAD for a lowered voice would be about 2 meters, or a speech level of about 60 dB SPL. For a direct field level of 60 dB at a distance of 20 meters, the LF section of the loudspeaker will require a signal input of 0.1 watts (into 8 ohms). In the biamplification mode the HF section will require considerably less than 0.1 watt input in order to reach the desired level at a distance of 20 meters.

Figure 7-2. EAD versus

A-weighted noise levels
Step Three: For a simulated microphone input of 72 dB SPL, adjust the HF and LF outputs of the DSC260 for nominal levels of 0.4 Vrms. Then, advance the LF gain control on the MPX600 amplifier until a reference level of 60 dB SPL has been reached at a distance of 20 meters. Following this, increase the level of the HF section to reach the same value. Details here are shown in Figure 7-1. Set up in this manner, there will be adequate headroom, in the console, controller, and power amplifier to handle nominal speech levels as well as levels up to 25 dB higher, should this ever be deemed necessary.
Wire Gauges and Line Losses
In modern sound system engineering it is standard practice to locate power amplifiers as close to the loudspeaker loads as is possible so that line losses become negligible. However, in some applications this is not possible, and the designer must consider line losses, choosing wire gauges that will keep to an acceptable minimum. Figure 7-3 shows the fundamental calculations. Note that there are actually two sources of loss: the loss in the wire itself and the loss due to the impedance mismatch that the long wire run can cause. For example, let us assume an input signal of 8 volts into a nominal load of 8 ohms. With no line losses the power dissipated in the load would be 8 watts (E2/RL). Let us assume that the wire run is 80 meters and that AWG #10 wire is used. Using the table, we can see that the wire resistance in one leg will be: R = 80/300 =.26 ohms and the total round trip resistance in the wire run will be twice that value. The voltage across the 8-ohm load will then be: EL = 8/[8 + (2 x.26)] x 8 = 7.5 volts, and the power dissipated in the load will be: PL = (7.5)2/8 = 7 watts The power loss is then: Loss (dB) = 10 log (7/8) = 0.58 dB The general equation for the loss in dB is:

designer (or installer) merely has to keep a running tally of watts drawn from the line, and when the number of watts equals the continuous output power rating of the amplifier, then the system is fully loaded. Ordinarily, no additional loads will be placed across the line, but there is some leeway here. The alternative to 70-volt distribution is to laboriously keep track of combined load impedances in parallel, a big task. Details of a 70-volt transformer are shown in Figure 7-5. In Europe, a 100-volt transmission system, derived in a similar manner, is used.
Low Frequency Augmentation Subwoofers
Whether in the cinema or in open spaces, LF augmentation systems are becoming popular for special effects. For indoor applications many acoustical engineers calculate the reverberant sound pressure level that can be produced by a transducer, or group of transducers, operating continuously over an assigned low frequency band, normally from 25 Hz to about 80 Hz. The equation for determining the reverberant level is:
LREV = 126 + 10 log WA - 10 log R, where WA is the continuous acoustical power output from the transducer and R is the room constant in m2. In using this equation, we assume that the space is fairly reverberant at very low frequencies and that the value of absorption coefficient at 125 Hz (the lowest value normally stated for materials) will be adequate for our purposes.
Some design engineers prefer to make actual direct field calculations for one or more subwoofer units at a distance, say, of two-thirds the length of the enclosed space. In large motion picture spaces, both sets of assumptions yield results that are usually within 5 dB of each other. The phenomenon of mutual coupling always comes to our aid in increasing the power output of combined subwoofer units. Figure 7-6A shows the
Figure 7-4. Details of a 70-volt transmission system
Figure 7-5. Details of a typical 70-volt distribution transformer
transmission coefficient for a direct radiator as a function of cone diameter. The solid curve is for a single unit, and the dotted curve is for two units positioned very close to each other. In addition to the double power handling capability afforded by the two units, the dotted curve shows a 3 dB increase in transmission coefficient at low frequencies. This is due basically to the tendency for the two drivers to behave as a single unit with a larger cone diameter, and hence higher efficiency. Thus, at B, we see the relative response of a single woofer (solid curve) compared to two such radiators (dashed curve). Note that the upper frequency transition point for the pair is 0.7 that of the single unit. The more such units we combine, the lower the effective cut-off frequency below which mutual coupling is operant. As an example, let us pick a large cinema with the following physical parameters: V = 14,000 m3 S = 3700 m2 T60 = 1.2 seconds R = 2500 m2 We will use the JBL 2242H LF transducer. Taking into account its power rating and its dynamic compression at full power, we note that its power output in acoustic watts will be:

3. Delay Zoning: Suggested delay settings are: Zone 1. Loudspeakers 2, 3, 6, and 7 Zone 2. Loudspeakers 1, 4, 5, and 8 Zone 3. Loudspeakers 9 and 10 Zone 4. Loudspeakers 11 and 12 Zone 5. Loudspeakers 13 and 14 Zone 6. Loudspeakers 15 and 16 Zone 7. Loudspeakers 17 and msec 22 msec 40 msec 55 msec 70 msec 85 msec 100 msec
4. General comments: The system described in this section emphasizes the complex inter-relations between acoustics and electroacoustics that are inherent in basic sound reinforcement design in large, live spaces. We strongly urge that all of the basic relationships presented here be carefully studied and understood. The fundamental principles we would like to stress are: 1. Whenever possible, use distributed loudspeakers that cover the intended seating area, but that have rapid cutoff beyond their nominal coverage angles; in other words, keep the on-axis DI as high as possible consistent with required coverage. 2. Try to minimize the longest throw distance within a given loudspeaker zone. Loudspeakers have been placed in overhead chandeliers in the attempt to do this. Pewback systems take this approach to the limit. 3. Seat the congregation toward the front of the room and turn off unnecessary loudspeakers. 4. Many large spaces were designed during a time when few people cared about speech intelligibility, and many liturgical spaces are simply too live for modern requirements. A careful assessment should be made here, and no live liturgical space should be altered acoustically without the advice and counsel of an experienced acoustical consultant.
Case Study C: Specifications for a Distributed Sound System Comprising a Ballroom, Small Meeting Space, and Social/Bar Area.
1. General Information and Basic Performance Specifications: 1.1 Ballroom Description: The size of the space is 33 meters long, 22 meters wide, and 8 meters high. A stage is located at the center of one short side, and the room may be used for banquets, displays, and social events such as dancing. A distributed (ceiling) system will be used for general speech/music purposes, as well as amplification of stage events. For this purpose the system should be zoned for delay. Reinforced levels up to 100 dB SPL will be expected, and coverage should be uniform within 1.5 dB up to a frequency of 2 kHz. The space is normally carpeted, except for dancing. Reverberation time is minimal. 1.2 Meeting Space Description: This space is typical of many that will be found in convention and meeting areas. The size is 8 meters by 5 meters and 3 meters high. A distributed ceiling system is to be designed, uniform within 1.5 dB up to 2 kHz. Normal maximum levels are expected to be 85 dB SPL.

1.3 Social Area: This space is of irregular shape, as shown in the diagram. A foreground stereo music system is to be specified for this space; no paging will be required. The system should be capable of producing levels of 85 dB SPL. There is also a disco/dance floor area, and a fourloudspeaker installation should provide levels of 105 dB at the center of the dance floor. 2. Exercises: Study the attached figures that detail the layout of distributed systems in general, and pick either the square or hexagonal layout. 2.1 Ballroom System: 1. Determine quantity and placement of ceiling loudspeakers that will meet the specification. 2. Determine the power allocation for each loudspeaker and describe the power distribution system (70-volt or low-Z). 3. Determine the minimum number of workable zones for signal delay for stage events. 2.2 Meeting Space System: 1. Determine the model loudspeaker required and the spacing density in the ceiling.
Figure 7-13. Ballroom layout. Plan view (A); side section view (B).
2. Determine the power allocation for each loudspeaker. 2.3 Social Area System: 1. Suggest a stereo layout of loudspeakers that will provide all patrons with satisfactory sound. 2. Determine power requirements and distribution method. 3. Specify disco components that will produce a level of 115 SPL dB in the middle of the dance floor.
3. Answers to Exercises: 3.1 Ballroom System: 1. Use the square array, with center-to-center overlap. Reasons: results in easier zoning requirements and fits the rectilinear design of the room better. Designing for seated ear height (1 meter) results in 12 loudspeakers. 2. Use JBL 2155 coaxial loudspeakers. With sensitivity of 102 dB and power rating of 150 watts, a
Figure 7-14. Ballroom system, signal flow diagram.
Figure 7-15. Meeting space layout. Plan view (A); side section view (B)
Figure 7-16. Meeting space system, signal flow diagram.
single loudspeaker will, at a distance of 7 meters, produce a level of 105 dB. The added contribution of the eight neighboring loudspeakers will increase this by 3 dB, making a maximum level capability of 108 dB. Level variations will be 1.4 dB. Because of the wide-band capability of the loudspeakers and relatively high power required, a low impedance distribution system should be used. Each 8-ohm loudspeaker should be driven from a section of a JBL MPX 300 amplifier, making a total of 6 amplifiers. This will provide 200 watt capability into each loudspeaker, which will more than exceed the specification. JBL Professional provides a program for determining layout density for distributed ceiling loudspeakers. It is called Distributed System Design, version 1.1, and runs on Windows 95 and is available from JBL Professional. 3. Zoning requirements: Measure the average distance from center stage to a center listening position directly under each zone. Subtract from that the value of 7 meters. For each meter difference, calculate 3 milliseconds of delay: Zone Difference negligible 12 meters 20 meters 26 meters Delay 0 msec 36 msec 60 msec 78 msec