You can't mute the ambient sound unless you mute the master sound
The sound of the ocean, thunder, river, etc is only mutable if you mute all sound. It should go under ambiance. I'm not talking about the sounds of combat far away or leveling up units which probably should go under something else, just the ocean/thunder/river/critter stuff. I have tried muting everything but pings or the announcer, w/e and it stays still on.
It doesn't seem to bother too many people, but TFT is basically unplayable for me if I play w/ the volume I normally would play on. I can't help but focus on those sounds and it throws me off my game. Even if that wasn't the case I find them extremely annoying.
While I'm here I might as well note the sound it makes after you take something on the carousel and return to base is extremely loud for some reason.