Carpentry and Woodworking - Stair Construction Question

When I removed the plaster ceiling over my basement stairs, I exposed the bottom of the stairs that go up to the 2nd floor. There is a board nailed to the underside of these stairs that runs parallel to the stringers. It's clearly not structural since it doesn't run the entire length. Would this have been done just to support the ceiling below, or perhaps does this play a role in helping to silence the stairs above? There is no such board under the basement stairs and they do sound a bit ricketier.

Also, how might I go about making the stairs feel and sound more solid? I'm thinking of using construction adhesive (Liquid Nails) to glue cross pieces under the riser to tread joints while the underside is exposed.

TIA

Joel
Bayside, NY

Hi
You might nail an other stringer along the expose side to re inforce the stairs.
that would make the stair more stable and less flex in it.
using construction adhesive (Liquid Nails) glue cross pieces under the riser to tread joints to make the step less chance to squeek if exposed.


cheers

pgtek