SMA X HAD NMAC WITH ACFT Y IN TFC PATTERN ON FINAL APCH TO RWY. SEE AND AVOID.

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I AM A STUDENT PLT; AND WAS ON MY FOURTH SOLO XCOUNTRY FLT. I HAD TO CALL WAUKESHA TWR 2 OR 3 TIMES BEFORE GETTING A RESPONSE. I WAS TOLD TO RPT R BASE FOR RWY 10. ON BASE; I AGAIN HAD TO CALL TWR 2 OR 3 TIMES BEFORE BEING ANSWERED. I THOUGHT MY RADIO WAS INTERMITTENT. I WAS CLRED TO LAND. ON 1/2 MI FINAL; ANOTHER ACFT Y WAS ABOUT 300 FT OFF MY L WING. IT LOOKED LIKE HE WAS ALSO ON FINAL; BUT I WASN'T SURE. TWR THEN CLRED THE OTHER ACFT Y TO LAND; AND TOLD ME TO TURN L ON FIRST TXWY; TAXI TO RAMP.' THE REAL ACFT ON THE GND CORRECTED THE TWR; WHO THEN TOLD ME TO MAKE A L 270 DEG TURN FOR FINAL. I RESPONDED THAT I WAS ON FINAL; WOULD DO A LEFT 360 DEG BACK TO FINAL. EVENTUALLY; EVERYBODY LANDED SAFELY. THINGS COULD HAVE TURNED OUT A LOT WORSE. WHILE DOING MY L 360 I WAS LOW AND SLOW. MY AIRSPD WAS DROPPING WHEN I REMEMBERED TO ADD PWR AND RETRACT FLAPS. CONTRIBUTING FACTORS: 1) I LATER LEARNED THAT A SINGLE CTLR WAS WORKING TWR; GND AND CLRNC DELIVERY. HE COULDN'T KEEP UP; AND DID NOT KNOW WHERE ACFT WERE IN THE PATTERN. I THOUGHT MY RADIO WAS BROKEN; BUT ATC SIMPLY DIDN'T HAVE TIME TO TALK. 2) I SHOULD HAVE BEEN MORE AWARE OF THE TFC IN THE PATTERN. I WAS PUTTING ALL MY FAITH IN ATC. 3) I SHOULD NOT HAVE DONE THE 360. I SHOULD HAVE GONE AROUND INSTEAD (AS I HAVE BEEN TRAINED TO DO). I DON'T KNOW WHY I DIDN'T.