ᐅ Downspout outside the upper floor exterior wall but within the corner of the ground floor – sound insulation

Hello everyone,

I have a question regarding the design of a detached house (pagoda-style) with a recessed upper floor (set back by 85 cm (33 inches) on each side).

The bathroom waste pipe on the upper floor was planned to be located in the corner wall of the kitchen on the ground floor. Because the upper floor is recessed, this waste pipe will be situated under the first (intermediate) roof, meaning outside the actual exterior wall. This should cause a significant amount of sound transmission from outside, since a roof does not effectively reduce noise, right?

For the double-wall construction, calcium silicate blocks were specifically chosen for the interior layer to improve sound insulation. With this opening in the exposed area (just under the intermediate roof) where the waste pipe passes through, the sound insulation is basically compromised, isn’t it? Is there any way to fix this situation? The shell construction is already at the stage where the floor slab has been poured...

View of the ground floor (left) and upper floor (right):

House cross-section: