"How might you support a child who hates loud unexpected noises, especially high-pitched ones, but otherwise enjoys places where such noises tend to occur (e.g. swimming pool, playground)?"
Is it the sound or the surprise?
Headphones and an iPod or an old fashioned walkman? (That would be for the playground, not the swimming pool.)
Watching TV shows or movies that feature shrieking kids, and playing with the reality of such shocking and high pitched sound in a totally controlled environment?
Playing games with making loud unexpected noises – surprising each other, or tagging with sound, or pretend with stuffed animals or dolls?
Have some sort of “come back,” internal or external to the sound and the surprise of it? Maybe a song, a saying, a shudder, a shout… I’m imagining something grounding and assertive, like Gandalf stating “you shall not pass” to the Balrog… Or maybe comparing live shrieks to TV/movie shrieks? Or to sounds made by vehicles, animals, or musical instruments?
It also might help to have the parent playing official tour guide “that sound was made by the girl at the far end of the pool that got splashed right in the face. She’s laughing now, and splashing back, but she sure was surprised by her friend.” “That sound was made by the child that went down the slide. He’s having a lot of fun.” Providing the context, showing that the sounds are not intended to be painful or frightening.
Does this child ever make loud unexpected noises? Maybe even high-pitched ones? If so, it might be worthwhile to point ‘em out. And to notice if those sounds were alarming for anyone in the area. Not in any kind of shaming way, but just matter of fact. Surprising loud noises happen. I think it’s the interpretation of them as scary or bad that is causing the problems here, so figuring out how to reframe them might be really useful.
I hope something here helps.