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Despite its small size filed W output power, will consult with all I have just bought a samsung stylish room cinema system However, when the room is fully occupied, a increases to 0. We calculate the critical distance for the unaided talker directivity index of 3 dB to be 2 meters in an empty room and 3. The room is provided with a sound system diagrammed in Figure Forty loudspeakers are mounted in the ceiling on 1.

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. 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.

A moderate-size lecture room Figure Sound system in a medium-size lecture room Sound System Design Reference Manual 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 listener's 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.

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. Below Hz the response of the system can be gradually shelved, or attenuated, without seriously degrading the quality of speech.

Above 4 kHz sound systems tend to take care of themselves, due to the increase in overall acoustical sound absorption. At very high frequencies, most environments are substantially absorptive, the air itself contributes considerable acoustical absorption and loudspeaker systems tend to become directional. These factors make it highly unusual to encounter feedback frequencies much above Hz. To make sure that a sound reinforcement system will successfully amplify speech, it is a good idea to make gain calculations in at least two frequency bands.

In a well-designed system, if calculations are made for the regions centered at 1 kHz and 4 kHz, chances are that no unforeseen problems in achieving desired system gain will be encountered. However, the region below Hz cannot simply be ignored.

The room constant and the directivities of the loudspeaker system and the microphone should be checked in the - Hz range to make sure that there are not substantial deviations from the calculations made at 1 and 4 kHz. If the room has very little absorption below 1 kHz, and if the loudspeaker system becomes nondirectional in this region, it may be impossible to achieve satisfactory system gain without severely attenuating the mid-bass region.

The result is the all too familiar system which provides satisfactory speech intelligibility, but which sounds like an amplified telephone. The Indoor Gain Equation From the foregoing discussions, we can appreciate the complexity of indoor system gain analysis and the need for accurately calculating the attenuation of sound along a given path, from either talker or loudspeaker, noting when we leave the direct field and make the transition into the reverberant field.

If we were to attempt to establish a general system gain equation, we would have a very difficult task. However, in the special case where the microphone is in the talker's direct field, and both microphone and listener are in the loudspeaker's reverberant field, then the system gain equation simplifies considerably.

Let us consider such an indoor system, first with the system turned off, as shown in Figure If the talker produces a level L at the microphone, then the level produced at the listener will be: System Gain vs. Frequency Response In the preceding examples we have not defined the frequency range in which gain calculations are to be made.

In most sound systems the main reason for worrying about system gain is to make sure that the voice of a person talking can be amplified sufficiently to reach a comfortable listening level in all parts of the seating area. Therefore, the most important frequency band for calculating gain is that which contributes primarily to speech intelligibility: the region between and Hz.

The assumption made here is that the level at the listener is entirely made up of the talker's reverberant field and that that level will be equal to the inverse square component at Dct. Now, the system is turned on, and the gain is advanced until the loudspeaker produces a level L at the microphone.

At the same time, the loudspeaker will produce the same level L at the listener, since both microphone and listener are in the loudspeaker's reverberant field. Of course there are many systems in which the microphone may be placed in the transition zone between the talker's direct and reverberant fields, or where the listener is located in the transition region between the loudspeaker's direct and reverberant fields.

In these more complicated cases, the foregoing equation does not apply, and the designer must analyze the system, both on and off, pretty much as we went stepwise through the three examples at the start of this chapter. Measuring Sound System Gain Measuring the gain of a sound system in the field is usually done over a single band of frequencies. It is normally specified that system gain shall be measured over the octave-wide band centered at 1 kHz. Another common technique is to use pink noise which is then measured with the A-weighted scale.

A typical specification for sound system gain might read as follows: "The lectern microphone shall be used in its normal position. A small loudspeaker shall be mounted on a stand to simulate a person talking approximately. The response of this test loudspeaker shall be reasonably flat over the range from - Hz. This level shall be measured with a precision sound level meter, using the "A" scale, with its microphone immediately adjacent to the sound system microphone.

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The amplified sound level shall be measured with the same sound level meter in the central part of the auditorium. Details of the measurements are shown in Figure Conditions for the indoor system gain equation Sound System Design Reference Manual 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.

Reverberation time. Speech syllables occur three or four times per second. For reverberation times of 1. Direct-to-reverberant ratio. For reverberation times in excess of 1. 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. As would be expected, the researchers found wide variations in both talkers and listeners. 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.

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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 dB. Figure 1. Measurement of sound system gain and delta D Sound System Design Reference Manual The last point is illustrated graphically in Figure , 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 dB. This agrees with other published information on intelligibility. For example, Rettinger points out that in rooms having a reverberation time of 1. 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.

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 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.

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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.

Probable articulation loss of consonants vs.

Such localized dead spots or zones of interference may not be discovered until the sound system is installed. In large reverberant spaces, sufficient flexibility should always be built into the sound system design to allow for such surprises. The effect of masking by unwanted background noise has been touched on only briefly in this section. Such unwanted noise may be produced by sound from the outside environment, by noisy air handling equipment, by noisy backstage mechanical equipment or by the audience itself.

For good listening conditions, the level of ambient noise as measured on the "A" scale should be at least 10 dB below the desired signal.

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Since the optimum level for reproduced speech in the absence of strong background noise is 65 - 70 dB A this means that background noise with a full audience should not exceed 55 dB A.

In auditoriums and concert halls, acoustical designers normally attempt to reduce background noise in an empty house to a level not exceeding 25 dB A. In a church or meeting hall, the maximum tolerable background noise for an empty room is about 40 dB A.

A sound reinforcement system cannot be turned up indefinitely. In many situations it is difficult enough to achieve a useful operating level of 60 - 65 dB A without feedback.

It is easy to see, therefore, that the presence of excessive background noise can render an otherwise good sound reinforcement system unsatisfactory. As an example of how the Peutz analysis can dictate the type of sound system to be used, let us consider a reinforcement system to be used in a large reverberant church.

Details are shown in Figure Let us assume that the reverberation time is 4 seconds at mid-frequencies and that the designer's first choice is a single-point loudspeaker array to be placed high above the chancel. What we wish to calculate is the direct-toreverberant ratio at selected points in the audience area to determine if the Peutz criteria for acceptable intelligibility can be met.

The most direct way of doing this is to calculate the total reverberant level in the room for a given power input to each horn and compare it with the direct sound coverage provided by each horn over its coverage angle. Probable intelligibility as a function of reverberation time and direct-to-reverberant sound ratio Sound System Design Reference Manual The analysis shown in Figure indicates that when each of the two horns is powered by one watt, the reverberant field in the room read directly from Figure is 94 dB-SPL.

The direct field level provided by each horn over its coverage angle is about 85 dB-SPL. This produces a direct-toreverberant ratio of -9 dB, and an inspection of Figure tells us that the system will have marginal intelligibility. Note that for 4 seconds of reverberation time, the direct-to-reverberant ratio should be no less than about -7 dB if acceptable intelligibility is to be expected.

This simple analysis has told us that, on paper, we have designed a sound system which will likely fail to satisfy the customer. Had the system consisted of a single horn, knowledge of its on-axis DI and Q could have led quickly to a determination of critical distance, and the direct-to-reverberant ratio could have been scaled from DC. However, for the composite array analyzed here, there is no single value of DI or Q which can be used, and a direct calculation of the overall reverberant level, using what we know about the efficiency of the transducers, and making a comparison with the direct field, based on the sensitivities of the transducers, is the quickest way to solve the problem.

But the question remains: What kind of system will work in this large resonant room? Clearly, a distributed system is called for. In such a system, a number of lower-powered loudspeakers are placed on columns on each side of the church, each loudspeaker covering a distance of perhaps no more than 5 or 6 meters. In this way, the direct-toreverberant ratio can be kept high.

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If such a system is further zoned into appropriate time delays, the effect will be quite natural, with subjective source localization remaining toward the front of the listening space. Details of this are shown in Figure Again, we calculate the total reverberant level and compare it with the longest throw each loudspeaker will be called upon to handle. There are 14 loudspeakers, 7 on each side.

Let us assume that the efficiency of these loudspeakers is 1. Feeding one watt into each loudspeaker results in a total acoustical power of 14 x. The longest throw each loudspeaker has to cover is, say, 4 meters. Since the 1-watt, 1-meter sensitivity is 95 dB, the direct field for each loudspeaker will be 12 dB lower, or 83 dB.

Analysis of intelligibility criteria Sound System Design Reference Manual Thus, the direct-to-reverberant ratio will be , or -9 dB. This is still not good enough, but we must remember that more than half the listeners will be closer to a loudspeaker than 4 meters. Another very important point we have not yet considered is the fact that the distributed loudspeakers are aimed almost totally into the audience, with its absorption coefficient considerably greater than a of.

This is the appropriate time to use R' instead of R in our calculations. Calculating R' based upon an a' of. Will the reverberant level really be only 80 dB? In actuality, we might observe something a little higher than 80 dB, but not enough to alter our analysis significantly. 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. Let us round this off and call it 1. 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.

A distributed system in a large church Sound System Design Reference Manual 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 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.

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 E 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. Fugure The Haas, or precedence, effect Sound System Design Reference Manual System Equalization and Power Response of Loudspeakers It is customary to equalize all professional sound reinforcement systems for two reasons: overall response shaping and control of feedback.

The overall response may be made smoother for a more natural effect through the use of broadband equalization and through the proper choice of drive components themselves. Where high system gain is required, narrow-band notch filters may successfully remove the tendency of the system to "ring" at certain frequencies.

We will examine the requirements of broad-band equalization first. A sound system is equalized by feeding pink noise equal power per octave into the system and adjusting the system's response to fit a preferred contour at some point in the middle of the house. This procedure is shown in Figure A. The response contour most often used today is shown at B. At the point in the house where the measurement is made, the reverberant field predominates, and what we are shaping with the equalizer is actually the power response of the loudspeaker as influenced by boundary absorption in the room.

If the loudspeaker's power response is smooth to begin with, then all is well. However, if, as in some older designs, the system's power response is irregular, then equalization will usually make things worse, as shown in Figure Sound system equalization procedure Figure Systemequalization Sound System Design Reference Manual At A, we see the on-axis solid curve and power dotted curve response of a 2-way system making use of a ported LF horn unit and an older type HF radial horn.

When such a system is equalized for smooth power response, as in the case of the standard mid-house equalization procedure, then the on-axis, or direct field response of the system will have a couple of "bumps" in its response.

This will have the effect of making both speech and music sound unnatural. Now let us examine the case at B. Note that the power response and on-axis response very nearly lie over each other. Thus, the adjustment of the system out in the house will result in both reverberant field response power response and direct field response on-axis response tracking each other closely.

Such a system can often be broad-band-equalized merely through the proper choice of components, dividing network and transducer drive levels, requiring little, if any, added electronic equalization. The graph shown in Figure shows this clearly. Here, we have plotted the variation in R over the frequency range for a large auditorium. When we calculate the room constant as a function of frequency and plot it, along with the sound level that would be produced by one acoustic watt in the room, we see that the total variation in SPL is only about 3 dB.

The importance of this observation is that, if we had a loudspeaker system exhibiting flat power response, then it would produce a reverberant SPL in this auditorium that would vary no more than the inverse of the curve shown in Figure Obviously, the smoother the power response of a loudspeaker, the less equalization it will require and the more natural it will sound on all types of program. Another use of equalization is in controlling feedback.

As we have stated many times, a sound reinforcement system should be operated at least 6 dB below the point of feedback if it is to be stable. Through careful and selective use of narrow-band notch filters, the first several ring modes of a sound system can be minimized, and the overall system gain can be increased perhaps 3 or 4 dB.

The practice of narrow-band equalization is complex, and it is best left to those who have been trained in it. V ariation in R and reverberant level with frequency Sound System Design Reference Manual System Design Overview There is a rational approach to indoor sound reinforcement system design, and it can be broken down into the following steps: 1. Lay out the coverage requirements, generally starting with a central array.

Determine the drive requirements for each element in the array. Calculate both direct field and reverberant field levels at various parts of the audience area, and then determine if their ratios, in combination with the reverberation time of the room, will result in adequate intelligibility. These calculations are most important in the 1 kHz range, but they should also be made in the Hz and 4 kHz ranges as well.

Determine the requirements for adequate gain, noting the value of DS that will be required in normal operation. If the intelligibility criteria are met, then the system can be completed. If the intelligibility criteria indicate an inadequate direct-to-reverberant ratio, consider the possibility of increasing R through the addition of acoustical absorption in the room. In existing rooms, this may not be possible; however, for rooms still in the design phase, it may be possible to increase the amount of absorption.

If a recalculation of the room parameters indicates that a central array will work, then the design can be completed. If not, the next step is to determine the nature of a distributed system that will satisfy the requirements of intelligibility. A central array can often be designed to cover just the front part of a room, with delayed loudspeakers covering the rear of the room. In marginal cases, this is likely to be more satisfactory than an all-out distributed system. The entire process described above has been reduced to the flow chart shown in Figure Flow diagram for system design Sound System Design Reference Manual Sound System Design Reference Manual Chapter 7: System Architecture and Layout Introduction 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. The system is to be used primarily for speech reinforcement.

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.

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.

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 Sound System Design Reference Manual will simplify things by considering only a single microphone path through the system to a single loudspeaker.

For the moment, let us consider only the abbreviated console flow diagram shown in the upper part of Figure A. Microphone ratings in use today state the unloaded output voltage when the unit is placed in a sound field of 94 dB SPL.

Normal speech level at an operating distance of. With the input and output faders at their nominal "zero" markings, set the microphone's input trim control for a console output of 0. Alternatively, a stable sound pressure level of 72 dB may be generated at the microphone, and the microphone trim setting adjusted for 0.

Vrms output. In making this setting, the trim potentiometer marker will normally be somewhere between 10 o'clock and 2 o'clock. Typical operating levels are as shown in the lower portion of Figure A. The level diagram shown in Figure B shows that, at the power amplifier's output, the noise level of the microphone is about 3 dB greater than the noise contributed by the power amplifier. Both of these noise sources will be swamped out by the acoustical noise level in the acoustical space, however.

The electrical noise floor is transformed over to an equivalent noise level of -2 dB A at a distance of 20 meters, some 25 dB lower than the acoustical noise floor of a typical space. With this calibration procedure, the maximum output level possible in the house is limited by the dynamic range and nominal operating point established for the DSC If more output level is desired, the nominal operating points must be reset accordingly.

Figure A. Let us further assume that the reverberation time in the room is no greater than 1. 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. In the biamplification mode the HF section will require considerably less than 0.

Following this, increase the level of the HF section to reach the same value. Details here are shown in Figure 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 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. Let us assume that the wire run is 80 meters and that AWG 10 wire is used.

For systems that will be stressed with full amplifier output for long periods of time, we recommend that the amplifier's continuous output rating be chosen to be equal to the loudspeaker's input power rating. Situations of this sort occur primarily in music reinforcement, where a constant, wide-band signal predominates.

For applications, such as speech reinforcement, where there is an operator who controls levels carefully, we can confidently recommend an amplifier with output capability that is twice 3 dB greater than the loudspeaker's continuous rating. The rational here is that peak power requirements, often slightly in excess of the loudspeaker's continuous rating, can be handled with no problem, and it makes sense to provide amplification accordingly.

For certain critical monitoring applications, as in recording studios or film postproduction environments, amplifiers may be chosen that can deliver four-times 6 dB greater power than the loudspeaker can withstand on a long-term continuous basis. The rational here is that the loudspeakers can ordinarily handle midrange and high frequency peaks of short duration that are much higher in instantaneous power than the long-term continuous rating of the loudspeaker.

In most speech reinforcement applications, condition 2 above will apply. Note however that there is no absolute necessity to use the larger amplifier unless high acoustical peak levels are anticipated. As given here, the loss consists of two terms: the actual loss generated in the wire run and the added loss incurred due to the impedance mismatch between the intended load and the actual load. Good engineering practice dictates that losses at the load be held to 0.

Calculation of resistance in wire runs Constant Voltage Distribution Systems volt lines Many distribution systems in the United States make use of the volt line for powering multiloudspeaker paging systems. In Europe the volt line is common. In either system, the full output power of the driving amplifier is available at a line voltage of 70 Vrms or Vrms, respectively.

In placing loads across the line, the design engineer simply keeps a running count of the number of watts of power drawn from the line. There is no need to calculate the aggregate load impedance at any point in the process.

When the total number of watts drawn from the line is equal to the power rating of the amplifier, then the line is fully loaded and properly matched. Figure shows details of a volt distribution system. The maximum load on the amplifier is transformed so that the applied voltage will be 70 Vrms. Individual loads are placed across the amplifier in parallel using line-to-loudspeaker distribution transformers that have a volt primary and a tapped secondary designated in watts.

The system 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 volt distribution is to laboriously keep track of combined load impedances in parallel, a big task. Details of a volt transformer are shown in Figure In Europe, a 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. In using this equation, we assume that the space is fairly reverberant at very low frequencies and that the value of absorption coefficient at 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 A shows the Figure Details of a volt transmission system Figure Details of a typical volt distribution transformer Sound System Design Reference Manual 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.Figure A.

Determine the power allocation for each loudspeaker. It describes a method of calculating potential sound system gain, and that method has since become a fundamental part of modern sound system design. 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.

We have calculated that the unaided talker produces a level at the listener's position of

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