walls
I live in a two story house build in the 60s. The lower floor(half buried) is only under half of the ground floor so I think there is a possibility that there is an extra room beside a wall in the lower floor. When I knock on the wall it emits a hollow sound.
Any ideas on how I could find out if there is a room behind the wall without drilling through it or knocking it down?
What is on the other side of the wall? Cutting a hole in the drywall on the other side would be the preferred method. If the 2" diameter hole is not large enough for both flex-lines, the you might need to enlarge it, or drill a 2nd hole through the tile and backerboard with an appropriate bit and lots of muscle.
Though.... if the contractor abandoned the job the tile job probably wasn't done right either and will leak meaning you will need to rip it down anyway.
Oooo! That's a challenging problem.
An idea that springs to mind is try renting a pneumatic gopher: variously called a hole hog, underground pneumatic piercing tool, air hog, etc.
There is a (crummy) Wikipedia article about them.
Those bore in a straight line, so I expect starting it some distance back from the wall and point it downward at about 45° to miss the bottom of the wall. You'd then have to dig a hole to find the borer.
Here I show digging a big hole at the left for device access. Bore a hole for the new connecting pipe (magenta). Dig a hole at the lower right to intercept the bore and provide access to connect to the lower line. (I should have erased your red line.)
Best Answer
Sure there are other ways, you could spend tens of thousands of dollars to have it x-rayed (they do this in commercial buildings), but realistically, drilling a small hole and using an inspection camera is the simplest and cheapest route.
You might also try contacting your cities building department to see if they have any plans on-file - this might show you what is there.