After doing some extensive googling:
Questions:
It's only when you open a faucet?
Same pitch and intensity regardless of flow rate and duration of flow?
It's a steady "whining" and not hissing, chirping or other sound?
Doesn't matter what the water source is?
Zero difference between gas or electric, or both simultaneously?
Hot water temp. appears to remain relatively the same?
Water temp. seems okay and not too high?
Is electric left on all the time with propane switched on?
What it's not or unlikely to be:
Can sometimes be the ignitor but you say it happens on electric and gas so rule that out.
Water chemistry can sometimes cause this but if it happens everywhere you go, rule that out.
Sediment can cause noises but you have a new TT so likely not that out.
Does not sound like the high pressure relief valve.
Does not sound like a check valve, but don't rule that out 100%.
Suggestions:
- Remove anode rod and empty the tank completely and re-establish the air pocket at top of tank. Air pocket is needed for expansion.
- Get a "real" regulator like a Watts 560 series and not an inline regulator and set to 50 psi.
- Check inside tank for any possible scale or sediment.
- Remove electric element and anode rod and inspect.
- Hot water temp. could be getting a bit too high or might help to reduce temp. a little. Remove non-adjustable type and install adjustable.
- Open/close relief valve a few times.
Caution - if opening relief valve or removing anode rod, make sure the water is cold enough.
