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For a 1000 Watt amplifier (total combined power for both channels) this works out to about 16 cfm for a 30% duty cycle and a 5° F temperature rise. For six amplifiers in a rack, the cooling requirements would be on the order of 100 cfm. It should be noted that the temperature rise is that of the air in the room, not necessarily that of the amplifiers. The amplifiers may be at a different temperature depending on the local heat transfer within the racks and the point of delivery of the refrigerated air, which depends on fans in the rack or in the amplifiers themselves.

Time Coincidence

When two sound sources are used to cover the same receiver, any physical separation between them yields a difference in arrival time and a pattern of cancellation at certain frequencies, just as it did with an image source discussed in Chapt. 7. As more sources are added, the interference pattern becomes more complex and fills in the gaps in the spectrum created by the original pair. Using this line of reasoning, Davis and Davis (1987) argue for more loudspeakers covering a given area as long as the time delays between individual loudspeakers are not excessive. Comb filtering is seldom a problem in distributed loudspeaker systems, where multiple sources cover the same area, since it is a steady-state phenomenon. Speech varies in time so rapidly that comb filtering is rarely audible.

If a cluster is used, only one or two loudspeakers will cover a given area. Arrival time differences due to loudspeaker displacements of a few inches can be perceived as a lack of speech clarity. Here it is important that the sounds from adjacent units arrive at the listener at approximately the same time, since small misalignments are more audible than large ones. For a system such as that pictured in Fig. 18.6, time coincidence can be assured on axis by aligning the drivers. If the driver diaphragms of each loudspeaker are physically aligned then the wavefronts will be coincident along the centerline. In home hi-fi systems, where the principal listener is located on the centerline, correct alignment results in a marked improvement in imaging and clarity.

An off-axis listener does not receive the same benefit from this technique since the sound paths are of different lengths. Though seldom a problem in home systems, it is an important design parameter in sound-reinforcement systems. With speech-reinforcement systems, particularly those that include horns, the physical alignment of the drivers is inconvenient and not sufficient to guarantee time alignment, because the path length difference at an off-axis receiver is not the same as that for an on-axis receiver. In these cases the faces of the individual cone loudspeakers and horns should be aligned and an electronic delay should be used to ensure arrival time coincidence, as illustrated in Fig. 18.7. Although this scheme is an excellent technique, time coincidence cannot be guaranteed for every direction, since the off-axis path lengths still vary somewhat for each component. In a two-way system where

Figure 18.6 Two-Way Loudspeaker with Aligned Diaphragms

- High frequency driver diaphragm

Figure 18.6 Two-Way Loudspeaker with Aligned Diaphragms

- High frequency driver diaphragm

On-axis travel times are equal at the listener for each component

Low frequency driver diaphragm

On-axis travel times are equal at the listener for each component

Low frequency driver diaphragm

Figure 18.7 Two Component Loudspeaker System with Aligned Faces and an Electronic Delay

— High frequency loudspeaker face

Travel times are equal at the listener for each component

Figure 18.7 Two Component Loudspeaker System with Aligned Faces and an Electronic Delay

— High frequency loudspeaker face

Travel times are equal at the listener for each component

Delay distance

— Low frequency loudspeaker face

Delay time = delay distance / speed af sound

Delay distance

— Low frequency loudspeaker face

Delay time = delay distance / speed af sound time overlap is a concern only near the crossover frequency, differences in arrival time can change the character of the sound.

Sometimes timing delay differences are introduced on purpose to achieve directivity control. In the midrange, where cone loudspeakers are used, vertical stacking of components leads to a narrowing of the coverage angle in the vertical plane. This occurs even when trapezoidal boxes with splayed sides are arrayed in a line. Just because packaged enclosures point in different directions does not mean that they do not interact in the manner of a typical line source.

Imaging

In a well-designed audio system the sound appears to be coming from the talker. This is accomplished by using the law of the first arrival, which states that the sound that reaches a listener first fixes the perceived source direction unless its level is too low. An example is pictured in Fig. 18.8. When the first-arriving sound comes from the talker or from a loudspeaker placed near him, the illusion is maintained. Since our ears are in the horizontal plane we are more sensitive to differences in azimuth than in elevation. For example, a central cluster located in front of a proscenium arch above the stage can maintain the illusion that the sound is coming from a performer on stage if the performer's voice is strong enough

Figure 18.8 Delay Settings for Cluster Systems

Figure 18.8 Delay Settings for Cluster Systems

Delay far loudspeaker 1 in milliseconds

[CD - D() /O.34J + 5 Dimensions in meters No delay for cluster 2 since D2 > D

to provide the zero delay signal. Small loudspeakers located along the front of the stage can help pull the image down but they may have to be turned off when the pit orchestra is miked. The audio signal is fed into the main cluster, which may be delayed so that it arrives 5 to 10 msec later than the live sound. In the illustration, the cluster is located in front of the talker so that no additional delay is required. The actual delay setting depends on the position of the performer on stage and is a compromise since there is a range of performer locations.

In theme parks, where a live show might be combined with on-stage effects, point-source loudspeakers are positioned near an animatronic character or effect to generate the first arrival sound. This maintains the overall level and frequency balance between the live and recorded tracks and provides the physical illusion. Point-source loudspeakers do not need to have the full frequency range to preserve this imaging and can be small, as long as they produce an adequate level. If point sources are used with live microphones, the live mics must be muted during the effects to prevent feedback. In theme parks, this is done by using a show control computer to duck or gate the live mics. In live theater the ducking can be controlled either manually or automatically.

If a distributed system is used, the signal feeding the overhead loudspeakers is progressively delayed so that the illusion is maintained. Some source, either a live talker or a centrally located loudspeaker, must be used to produce the time-base-zero signal. The number of delay zones required for any given system depends on the details of the design; loudspeakers, which are no more than 10 msec apart in time delay, can be grouped into a zone. It is preferable in these systems to have only a few loudspeakers covering a given area. Thus this technique is most effective in low (< 6 m) ceiling rooms where the loudspeakers are close to the receivers. The overhead loudspeakers in the zones close to the talker help maintain the illusion for the zones farther away.

Figure 18.9 Delay Settings for a Lawn System

Figure 18.9 Delay Settings for a Lawn System

Delay tor loudspeaker 2 In milliseconds [p / 1.13 - 1 o] Dimensions In feet [p / ©.34 - 1©] Dimensions In meters

Outdoor amphitheaters often have a sound system with loudspeakers flown above a stage, with a series of loudspeakers located on poles around the rear of the fixed seating. These systems are designed to allow flexibility in servicing audiences of different sizes, with overflow patrons seated on a lawn behind the fixed seats. Setting time delays for a multiple-cluster system is difficult, particularly when the delayed cluster is elevated. In the configuration illustrated in Fig. 18.9, there are different delay times for listeners located under and behind the delayed loudspeaker. Normally the delays are set so that the time-base-zero loudspeakers lead the delayed loudspeakers by about 5-10 msec so that the illusion that the sound is coming from the stage is preserved. In this example the delayed loudspeakers are located on a tower 20 feet (6 m) in the air. If the time delay is picked to be 10 msec after the arrival of the time-base-zero signal, the sound heard at the base of the tower will lag the sound from the stage by about 30 msec and create a noticeable upward image shift. In tower systems the arrival time for the delayed loudspeakers should be set so as to lead the stage loudspeakers by about 10 msec. Then at the base of the tower the overhead sound lags the stage sound by 10 msec and the illusion is preserved. Farther back on the lawn the patrons are in line with the tower loudspeakers and even though they now lead the stage loudspeakers, the directional illusion still is preserved.

Feedback

The control of feedback and the achievement of adequate gain before the feedback becomes unstable are probably the most difficult aspects of sound system design. Figure 18.10 shows the gain structure of a sound reinforcement system. Note that gain and loss are used interchangeably. The open-loop system gain Zs = 20 log zs is defined as the difference between the level produced by the loudspeaker at the listener and the level produced by the talker at the microphone. The multiplier factor is 20 rather than 10 because zs is a voltage gain. Clearly the gain must be high enough to produce an adequate level in the audience.

When there is a path for the amplified sound to travel back to the microphone, it has a transfer gain (or loss) Gs = 20 log gs, which characterizes the feedback loop. In electrical engineering terms any closed loop produces feedback, which can be stable or unstable. The transfer function for the signal moving through the entire closed loop system (with feedback)

Figure 18.10 Sound System Gain Block Diagrams

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