A GA PLT'S FIRST ENCOUNTER WITH A LARGE MIL ACFT IN CLOSE PROX ON A DIFFERENT FREQ CAUSES HIM CONCERN.

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I WAS CRUISING AT 6500 FT IN CONTACT WITH ATLANTA APCH IN VFR CONDITIONS. TFC WAS GIVEN AT 4-5 O'CLOCK POS; 6000 FT. I NOTIFIED THE CTLR I HAD TFC IN SIGHT. AS I WATCHED THE TFC AND IT GOT CLOSER; IT APPEARED TO BE CLBING. IT WAS APCHING QUICKLY AND I KNOW I COULD NOT OUT CLB THE TFC. I THEREFORE DISENGAGED MY AUTOPLT AND DSNDED TO 5500 FT. AT THIS TIME; THE TFC TOOK EVASIVE ACTION ALSO BY TURNING TO THE L AND AWAY FROM ME. THE TFC PASSED BEHIND ME AFTER THE ACTION WAS TAKEN. THE TFC WAS A LARGE MIL PLANE. I COULD HEAR ONLY THE CTLR'S SIDE OF THE CONVERSATION WITH THE MIL PLANE. I HEARD THE CTLR SAY TO THE MIL PLANE (I DO NOT KNOW WHY HE DID THAT); WHICH I FIGURE WAS RELATING TO MY CHANGING OF ALTS. THE CTLR THEN ASKED ME WHOM I FILED MY FLT PLAN WITH. I TOLD HIM I HAD NOT FILED A FLT PLAN; BUT ASKED FOR FLT FOLLOWING WITH ZJX AND WAS HANDED OFF TO HIM BY ZJX. HE THEN ASKED WHERE MY HOME BASE WAS; AND I TOLD HIM. I FEEL BEING UNABLE TO HEAR THE CONVERSATION BTWN THE CTLR AND THE MIL PLANE CREATED A VERY UNEASY SIT. I HAVE NEVER HAD A PLANE THAT BIG FLY UNDER ME AT 500 FT BTWN PLANES. I DID NOT KNOW IF THE MIL PLANE HAD ME IN SIGHT BECAUSE OF THE DIFFERENT COM FREQ. I FEEL THE MIL PLANE COULD HAVE CHANGED COURSE ABOUT 20 DEGS TO THE L AND PASSED BEHIND ME WITH NO PROB.