I recently saw a production of South Pacific that made me wonder—given that most Nellies are wearing microphones on their foreheads and a wig, how does the showering part of "Wash That Man" work from a sound/wig design standpoint? I saw footage of Kelli O'Hara doing it and it looks like she totally soaked the wig, but the mic was working just fine.
High-grade body microphones like those used on Broadway are waterproof. It protects not only against the use of water in a show, for example, but from actors who might excessively sweat during a performance.
I'll also add that it is standard practice to 'double mic' on Broadway, so there is always a "back-up" should anything happen to that primary mic (such as a leak in the waterproofing).
I would think waterproof mics are relatively new (this is speculation, not fact), because one of the problems with the original CARRIE production; every time they dropped the blood, it clogged the mic, so you couldn't hear the actress during the destruction sequence.
Excerpt of an interview with Broadway revival sound designer Scott Lehrer:
What kind of mics did you use on the actors? We’re basically using DPAs for everybody, except on Kelli we used Countryman lavs because they’re super water resistant, and it made the “I’m Gonna Wash That Man Right Outta My Hair” number easier because we just left the mics on her while she showered.
How did that scene work audio-wise? She actually had to move the transmitters around, but the mics are on her head. She’s wearing a wig, and the microphones themselves are under her wig. We couldn’t fit the transmitters in the wig because it was too small, so we put the transmitters on her body, and she moved them into her bikini top for that scene.
What did you place around the transmitters so that they wouldn’t get wet? We basically used Saran Wrap. They were tested once when she dropped them in the toilet and they stayed dry. We realized that they worked pretty well. She sheepishly came backstage and said, “I dropped one of my transmitters in the toilet.”