What is the purpose of thw music "Ave Maria" and what feeling does it evoke in the play?

It represents the pure and innocence of the play that Laura projects.

In Chapter Four, "Ave Maria" is symbolic of Amanda's role as a mother. This is evident to the audience by the way in which stage direction denotes the lighting to focus on Amanda, as her daughter heads for the fire escape. The music in itself is meant to be an ironic contrast between the unconditional love and devotion of Mary, as opposed to Amanda, who's devotion appears only when she needs it for her own purposes. Example, she doesn't want Tom to leave the family because she needs his support.