There is no specific volume that a player must be at when playing at a forte level, or a mezzo forte. It's up to the creative interpretation; it's up to the conductor and the musicians.
A piano is not always the same. If you're playing a violin concerto, your piano might be a soft but carrying whisper, as opposed to if you're playing an ostinato in a wind band (ugh, alto saxophone parts). This is part of what makes music so extraordinary. There are surely right and wrong ways to do things; an Eb will never be an E, but how you play, your expression, is entirely up to you.
