Weird. I'm really not a plumber, so I feel silly offering my opinion, but what the heck, it's the internet, right?
If there's no vibration that you can feel then it's probably alright. Flutes don't fall apart from their own sound. But we're talking about your plumbing here, where a failure can be expensive and inconvenient, so "probably" isn't that reassuring. It's just not supposed to be doing that.
> We just replaced the tank, and the sound began after that. The plumber insisted it was unrelated.
It's not impossible (that they're unrelated) but that sounds to me like the obvious culprit, eh?
