A PVT PLT; DEPARTING RDU; WAS GIVEN AMENDED DEP INSTRUCTIONS WHICH WERE 'STEPPED ON' DURING HIS INITIAL CLB. FOLLOWING HIS ORIGINAL CLRNC; THE RPTR EXPERIENCE AN NMAC WITH A DC9.

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I WAS DEPARTING ON A SHORT PLEASURE FLT WITH MY SON IN ONE OF OUR CLB RENTAL ACFT; A PIPER ARCHER. GIVEN A DEP FROM RWY 5L AT RDU IMMEDIATELY BEHIND A DEPARTING FOKKER 100. INSTRUCTIONS WERE 'NXYZ; CLRED TO DEPART RWY 5L; HDG 090 DEGS.' AFTER TKOF; I PARALLELED RWY 5L (SLIGHT R SHIFT TO AVOID WAKE TURB). AFTER PASSING THE CTL TWR; I TURNED ON TO 090 DEGS AND CONTINUED TO CLB. I HEARD A BRIEF TWR INTERCHANGE WITH A COMMERCIAL FLT; THEN A SHORT; 'STEPPED ON' XMISSION. AS I CLBED OUT; XING THE PARALLEL RWY 5L; I LOOKED R TO CHK FOR TFC BUT SAW NONE. THE CTLR CALLED MY CALL SIGN AND I RESPONDED. HE SAID 'ARE YOU ON RWY HDG?' I REPLIED; 'YOU GAVE ME 090 DEGS; SIR.' HE CALLED BACK SORT OF HEATED; SAYING; 'BUT I CALLED YOU BACK WITH A CORRECTION TO RWY HDG.' AS HE WAS SAYING THIS; I BANKED L TO 050 DEGS; I REPLIED TO HIM THAT I HAD NOT HEARD ANY INSTRUCTIONS; BUT THAT PERHAPS THE 'STEPPED ON' CALL I HAD HEARD WAS HIS. HE DID NOT RESPOND TO THAT. AFTER A FEW SECONDS HE SAID (MORE RELAXED); 'OK; WE CAN EASE UP NOW; YOU CAN RESUME 090 DEGS AND CONTINUE CLB TO 2000 FT.' MY 11 YR OLD TOLD ME LATER THAT A DC9; IN WHAT HE DESCRIBED AS AN ACR'S COLORS; CAME 'REAL CLOSE; DAD.'