@Jeff Handy - That's it! A ghost!
The older I get, the more I hear.
@JamieRI - Yes, just like the sound a 2-foot flute makes when blown with all the stops closed.
@TomFOhio and CT18 - I think that's probably it. I had to cut off a 1/2-inch length of copper pipe when I was plumbing it. The piece dropped onto the top of the heater, bounced once, and jumped into the flue. I wasn't about to move the tank back off of its 2-foot pedestal, turn it upside down, hope that the piece would fall out, and then oink the tank up up into position.
@Mitchell-DIY-Guy - I installed a new gas valve and a new flex hose between the heater and the gas pipe, so I don't think that's the problem. The sound level is pretty much constant as I move my ear up and down the tank.
@Stout Mechanical - Here's a photo:
So I think I'll just live with it. The heater is in the garage and so it is rare that I'm there when it fires up.
I really appreciate all of your replies!