As advised, I called the local gas utility, PG&E and requested a service call.

The young service guy came, took a look and hearing my story, asked a few questions and said he would call his guru.

After his phone call, he said the guru noted that they had seen this problem lately with a few new water heaters and the cause was determined to be a misaligned gas orifice, which would work like a flute if it is aimed slightly off to the side instead of straight in. His belief is that the orifice may get accidentally knocked out of alignment a little bit during transportation/installation. Recommendation was to call the dealer and, as it is relatively new, have it replaced / repaired under warranty.

After his departure, we took a pliers to the (upon inspection) ever so slightly tilted metal "L" shaped pipe that feeds the orifice and pried it a little bit so it's lower portion appeared to be more parallel to the floor, and presumably, to move the orifice so it would be better aligned/more 'straight in.'

It worked. No more fog horn/train horn/deep hum.

Thank you all for your kind help!

PS: Expansion tank is now planned.