Umm... I can think of about 5 things that might do this, but the trick is to go out there and waste no one's time while you duplicate the problem and trouble shoot it.
Your description says that you have someone willing to pay you to fix this sound so it doesn't happen anymore, that there is a water heater involved and it might or might not have nipples in it from the factory with integral heat traps, not checks.
Oh, and you can use a search engine.
Now that I've busted your chops, tell us about yourself. We can get to the heater problem once you've been out there and found the location of the noise. Once you know that, we can actually have a meaningful discussion about what might be causing it. Us telling you what to look for will actually waste more time while you check those out rather than just following your ears to the source.
Oh, and don't be surprised if you can't duplicate the problem, especially if someone has been home all day. Thermal expansion stops once its as big as its going to get. Then it makes the noise in reverse while it cools.
I will give you one hint however, just so you don't think I'm too abrasive... look for something other than cast iron drains on that sink they are using and hearing the noise from.
