Now that you've physically attached the microphones to the actors, and gotten a clean RF signal back to the receivers, it is time to mix and process the sound and get it out to the audience.
We're going to assume for the sake of this essay that you have a sound system to use, and it sounds decent. That will not always be the case! Often a major stop on the road to getting the wireless mics to sound good is optimizing the sound system. Even in places where the sound system works well for playback of music or effects, it may not be optimized for wireless mics.
In the big houses, the wireless mics are on an independent system; they have their own amps and their own speakers. This physical placement of the sound source helps the listener to sort out voices from orchestration and sound effects; without raising the volume, the voices become easier to hear (exactly the same principle that is at work when you "focus in" on the speech of the person in front of you during a party or in some other crowded place).
In the really nice houses, vocal reinforcement actually comes from multiple sets of speakers; actors are cross-assigned so when two people are on stage, each is actually on a different set of speakers. Most of us will not have access to a system like this!
Other details; humans perceive height of sound sources less acutely then horizontal position. Thus it is better to have speakers high and centered rather than low and out at the proscenium. Feedback (or as the British so descriptively call it, "Howl-round") is often an issue with the kinds of levels necessary to get over modern music. Thus, speakers that are forward of the acting areas are a bonus.
A critical issue in the playback system and environment is intelligibility. Sheer volume will not make up for time smear, an overly "live" space, or flawed playback that emphasizes out-of-band frequencies at the expense of those frequencies that carry vocal consonant information. As little as a twenty millisecond mismatch between two sources reaching the same audience member can compromise their ability to pick out and understand the words.
Because, really, the Broadway musical is not a bel canto opera. It is utterly dependent on clear understanding of the lyrics. The loveliest vowel production must take second place to being able to understand the words. When the audience complains "they can't hear," it is never because they couldn't hear sound coming from the singer; it is because they couldn't understand the words.
Intelligibility, unfortunately, is too big a subject to go into in this essay. Just let it be said that there are formula, and there are ways to understand and enhance vocal intelligibility within a specific playback situation. In general placement, emphasis of the important frequencies, and control of reflections/reverb are the tools to achieve this.
Back to the mics. You have to mix them. You really have to have a human operator, sitting where they can hear what the audience hears (what we call the "Front-of-House" position; the best version is a sound board actually set up among the seats of the audience.)
The majority of musicals are incompatible with having all the microphones on all the time. Actors leave the stage. They change costumes. They also kiss, crawl into wardrobes, get buckets put on their heads, and otherwise do things that can sound distracting on a microphone. At the very least, you need to have a way to turn microphones on and off.
The traditional solution is to have a sound operator for the show, seated in front of a mixing board. They can work off a script, but more normally will learn the show by watching it until they have memorized all the entrances and exits, as well as any other moments that might require turning off a microphone.
Actors aren't always consistent, from moment to moment, song to dialog, or night to night. They get colds. They have problems with their mics. They follow screaming dialog with a murmured solo. Although just turning the mics on and off may be sufficient, actively adjusting levels is better.
Again, it is possible to automate this, or put it in the form of called cues, but there is no replacement for a live pair of ears. A good mic mixer really jumps a show up to a new level; that mic mixer can adjust vocal blends, adjust for softer dialog, push the singer up above a full orchestral tutti and ride the levels to nuance the natural dynamics of the song and of the show.
So assume you've got a mixing board, it is set up where you can hear the show, and you've found the cable to get all the receivers connected to it. Here's a few simple defaults I've found work most of the time:
Roll off the bottom. Even though the fundamental of a male voice may be down as low as 125 Hz, the definition of vowel sounds is closer to 1,000 Hz. Everything, really, below 400 Hz will thicken and muddy the vocal sound. And everything below 100 Hz is junk, as far as vocal reinforcement goes. Very few voices, in very few situations, benefit from what is down there.
My simple default is a shelving filter set somewhere between 100 and 200 Hz. For some reason digital boards have a very gentle slope on their shelving EQ; the stop-gap is to add another filter right at the cut-off to "fill in" the slope and make it more like a brick wall.
A trick borrowed from the movies is to gently boost 2 to 4 dB centered on 6 KHz. This is the range where consonants are defined, and adds brightness and sweetness to the vocal sound.
The sibilants live higher, starting at 8 KHz and running up through 12 KHz. Although you can try rolling off the high end (and you may need to, to control feedback; it is usually these higher frequencies that will get you in trouble), a better solution to sibilance is to use a faster attack on your compression.
Compression on every single mic channel is the last of my basic defaults. I default to 2:1 with an attack of around 40 ms, with a soft knee, with the threshold set above the average speaking level.
For many shows you can slide between vocal and dialog levels (many actors, unfortunately, sing at a softer level than they speak their dialog). The old Broadway standards are well-organized for this; five minutes of dialog, a musical introduction over dialog that allows you to gently bring up the microphone level, and then a song for five minutes. During the applause peak you sneak the mic back down.
For more modern shows things move too quickly, slipping in and out of song, dialog, underscore and fanfare. For those you may need to keep the compressor up high and live with the lack off fully optimal levels for some moments.
My last default is delay; I set a delay of about 10 ms between the moment the primary impulse of sound from the actor's mouth hits the ears of the audience, and the first impulse from the speaker carrying the wireless mic sends. As a rule of thumb, sound travels a foot per millisecond, meaning a ten foot difference in path length between ear-to-speaker and ear-to-mouth is already around 10 ms. So you add the two, and then give the result a good listen. In the geometry of a real space different seats will be a different sum of distances, so whatever delay you set will be a compromise anyhow.
The reason to introduce this delay? First, it helps control feedback. Second, though, and more importantly, by introducing a delay you leverage the Precedence Effect, also known as the Haas Effect. What is this? Most of our lives are spent in reflective environments, where over half of the sound energy reaching your ears is indirect. Thus, our brains have evolved to focus perceptually on the direction the first impulse came from. After all. you want to look towards the bear, not the reflection of his snarl off a cave wall! This perceptual effect is so hard-wired is that a delayed source will actually "vanish" -- even if it is several dB louder than the original.
Used correctly, then, this trick helps to fool the ears of the audience into thinking the sound is coming from the actors instead of from the speakers hung over their heads. It's effectiveness, and the exact parameters, depend on the acoustics of the actual performance and space.
The modern digital board simplifies many of these steps and gives you more options as well. On a traditional mixing deck, your on-board equalization is limited to high shelving, low shelving, and a movable mid-range with a fixed Q value (aka width). You can tailor the overall mic sound with a graphic equalizer -- this can help you to notch out feedback and room nodes, but it also colors the sound.
The digital board has parametric EQ; each available filter can be set to frequency, depth, and width or Q Factor. There is also often EQ on the outputs or group busses as well, allowing you to make global tailoring of the sound.
The digital boards also generally have compressors available on every channel. On an older board you need to hook up rack-mount compressors via insert cables -- it makes the mixing position rather more complicated-looking and crowded. In addition (DSP is cheap!) they will usually have several different reverbs that can be flexibly assigned. As well as, of course, delay that can be set on any output bus.
Both still allow you other tailoring tricks. Flanging or ring modulator for a scary artificial effect (think Dalek voice -- but I've used a similar effect for Man of La Mancha"s THE KNIGHT OF THE MIRRORS.) Octave doubling for an even more monstrous effect (I did this for THE LARGE AND TERRIBLE FROG from Frog and Toad.) Guitar amp distortion -- I love this trick for a live telephone effect on stage, or (in smaller doses) for a period microphone. Reverb, of course, but also slap-back delay and reverse reverb algorithms (the only thing digital boards don't do as well is give you access to a tap-tempo button).
I have found a small amount of reverb helps to "seat" a voice more in the space, making it sound more natural, and also gives the voice a little more body that can help it cut through orchestration.
And those are the basics. The rest is tailoring for the voices and for the show. For some reason that only makes sense to me I tend to boost heroic male characters in the manly 400-600 range, and give romantic leading ladies a little extra sweetness at 1-3 KHz. I play with the compression for "wild" voices, or to zero in on the balance between bite and sibilance. Many voices, many characters, will have characteristic timbres a little careful EQ can bring out. On the other hand, there are those problem voices; like actors with poor enunciation, but also, those peculiar fuzzy buzzing voices that just don't seem to have a nice sound you can bring out.
During the dial-in process you will be tweaking all of these settings. You will also be shifting microphones around, or trading elements. Sometimes something as simple as a shift of a centimeter on an actor's cheek will help to really zone in on a voice. Just like with mic'ing orchestral instruments, it starts with having the right mic in the right place. All the tweaking of EQ can't save a bad mic position.
But as I said, every performance is different. During the run of the show, things will change. Elements die; I have become familiar with a variety of specific sounds made by several brands of dying microphone. Countryman mics get a cloudy, fuzzy sound as the filters clog. A broken wire leads to sharp crackly sounds with sounds like electric sparking. The Shure WL93's die in a wonderfully musical way; they begin to emit soft chimes as the voice slowly fades away completely under them.
This is why during the run you really want two people. One is the ears of the show; she is on the board, listening, tweaking levels and settings from night to night, moment to moment. Hers is also the responsibility to creatively problem-solve; making the tough choices to deal with a bad mic on an important solo, or helping an actor through a sudden frog. There are times you lose a mic and end up trying to "chase" a solo through the mics of the actors standing close to him. There are times you have a loose wire and you can't afford to lose the mic...so you dial up the compression to make a limiter, EQ out the hum, and sweat it out until the end of the song.
The other person is the hands of the show. A good mic wrangler is worth the bucks; they are not only standing by on headset, but they are using their own ears and their own smarts; standing by through every quick-change with extra tape and spare batteries in their hands just in case. A good wrangler will catch dead mics and swap them out for you without you even having to pick up a headset.
And between the two of you, you might just get through a performance without having any problems the audience can hear.