  We consider a coupled $1D$ heat-wave system which serves as a simplified
fluid-structure interaction problem. The system is coupled in two different
ways: the first, when the interface does not have mass and the second, when the
interface does have mass. We prove an optimal regularity result in Sobolev
spaces for both cases. The main idea behind the proof is to reduce the coupled
problem to a single nonlocal equation on the interface by using Neummann to
Diriclet operator. Furthermore, we show that point mass coupling regularizes
the problem and quantify this regularization in the sense of Sobolev spaces.
