There are two types of ceilings.  There are the simple acoustical tile ceilings that surround the lighting fixtures, duct outlets, etc., and conceal unsightly ductwork, piping and electrical work.  The acoustical tile reduces the reflected noise within the room, but does virtually nothing to reduce sound transmission from above.  It does not prevent noise within the room traveling upward or over partition walls that are not floor to structural ceiling. A sound barrier ceiling is entirely different.  Originally, they were all plaster on lathe and still are occasionally for curved or artistic finishes. 

In many situations there is a barrier ceiling and a mechanical ceiling below it.  Piping, ducting and electrical services are usually located between the two, because it is both costly and difficult to break through the gypsum