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Working with loud speaker systems

The theatre is putting on a new musical and they are changing from traditional rifle microphones to radio microphone system. The theatre has some concerns over doing this, they are: transmitter operation with regard to power supplies, inter-modulation problems and choice of transmitter frequency band and output power.

Please can you help me with this problem. I have a list of equipment below if it helps you.

equipment
15 SK 50 VHF pocket transmitters (5 additional SK for instruments)
5 MKE 2 clip-on mics
3 EM 1046 systems
Mikroport system
1 Cadac J-type mixing console (72-inputs, 12 matrix and 24 matrix outputs)
41 loudspeaker system.

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There are four basic configurations of wireless microphone systems, related to the mobility of the transmitter and receiver components, as required for different applications. But we will focus on systems consisting of a portable transmitter and a stationary receiver. The transmitter is usually carried by the user, who is free to move about, while the receiver is located in a fixed position. The input source in this setup is normally a microphone or an electronic musical instrument. The receiver output is typically sent to a sound system, recording equipment, or a broadcast system. This is the configuration of the standard "wireless microphone" and is the arrangement most widely used in entertainment, public address, and broadcast applications.
Diversity
Fixed receivers are offered in two basic external configurations: diversity and non-diversity. Non-diversity receivers are equipped with a single antenna while diversity receivers generally have two antennas. Both systems may offer otherwise similar outward features: units may be free standing or rack-mountable; outputs may include balanced/unbalanced microphone or line level as well as headphones; indicators for power and audio/radio signal level may be present; controls for power and permanently attached.
Though diversity receivers tend to include more features than non-diversity types, the choice of a diversity vs. a non-diversity receiver is usually dictated by performance and reliability considerations. Diversity receivers can significantly improve both qualities by minimizing the effect of variations in radio signal strength in a given reception area.
The net received signal strength at any location is the sum of the direct and reflected waves. These waves can reinforce or interfere with each other depending on their relative amplitude and phase. The result is substantial variation in average signal strength throughout an area. This creates the possibility of degradation or loss of the radio signal at certain points in space, even when the transmitter is at a relatively short distance from the receiver. Cancellation of the signal can occur when the direct and indirect waves are similar in amplitude and opposite in phase.
The audible effects of such signal strength variation range from a slight swishing sound ("noise-up"), to severe noises ("hits"), to complete loss of audio ("dropout").
Diversity refers to the general principle of using multiple (usually two) antennas to take advantage of the very low probability of simultaneous dropouts at two different antenna locations. "Different" means that the signals are substantially independent at each location. This is also sometimes called "space diversity", referring to the space between the antennas. In most cases, at least 1/4 wavelength separation between antennas is necessary for significant diversity effect, though increased benefit may be had by greater separation.
General rules concerning setup and use of receiver antennas:
First, maintain line-of-sight between the transmitter and receiver antennas as much as possible. Avoid metal objects, walls, and large numbers of people between the receiving antenna and its associated transmitter. Ideally, this means that receiving antennas should be in the same room as the transmitters and elevated above the audience or other obstructions.
Second, keep the receiver antenna at a reasonable distance to the transmitter. The maximum distance is not constant but is limited by transmitter power, intervening objects, interference, and receiver sensitivity. Closer is preferable to farther but a minimum distance of about 10 feet is recommended to avoid potential intermodulation products in the receiver. Ideally, it is better to have the antenna/receiver combination near the transmitter (and run a long audio cable) than to run a long antenna cable or to transmit over long distances.
Third, use the proper type of receiver antenna. A 1/4-wave antenna can be used if it is mounted directly to the receiver, to an antenna distribution device or to another panel which acts as a ground-plane. If the antenna is to be located at a distance from the receiver a 1/2-wave antenna is recommended. This type has somewhat increased sensitivity over the 1/4-wave and does not require a ground-plane. For installations requiring more distant antenna placement or in cases of strong interfering sources it may be necessary to use a directional (Yagi or log-periodic) antenna suitably aimed.
Fourth, select the correctly tuned receiver antenna(s). Most ...

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Solution with all explanations for working with loud speaker systems and mathematical steps are provided.

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