A BE76 AND A CHEROKEE HAVE AN NMAC WHILE BOTH ACFT ARE APCHING RWY 21L AT PRC; AZ.

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UPON CONTACTING TWR; WE WERE TOLD TO RPT A 2 MI R 45 DEG ENTRY FOR RWY 21. NEITHER THE STUDENT NOR I RECALL HEARING THE L OR R RWY (PRC HAS RWY 21L&R SEPARATED BY 700 FT). WE ENTERED A WIDE R DOWNWIND PER TWR INSTRUCTIONS. I HAD FAILED ONE OF THE ENGS (SIMULATED) BY REDUCING THE THROTTLE TO IDLE AT ABOUT 4 MI FROM THE ARPT. WE ADVISED TWR THAT WE HAD TFC OFF OUR R WING IN SIGHT ON A CLOSER DOWNWIND AND THEY GAVE US LNDG CLRNC. I RECALL READING BACK 'CLRED TO LAND RWY 21L.' WE LOST SIGHT OF OUR TFC TO FOLLOW WHEN ON BASE LEG AFTER WE EXTENDED THE DOWNWIND LEG A COUPLE OF MI. I ADVISED THE TWR AND ASKED FOR AN UPDATE ON OUR TFC'S POS. THEY NEVER GOT BACK TO ME. UNKNOWN TO ME AT THE TIME; THERE WAS A BONANZA RPTING SMOKE IN THE COCKPIT NEARBY THAT HAD DECLARED AN EMER. THE TWR FREQ WAS SATURATED. SEVERAL ACFT WERE INSTRUCTED TO CIRCLE AT VARIOUS POINTS AROUND THE PATTERN. JUST AS I WAS ABOUT TO KEY THE MIKE TO CONFIRM LNDG CLRNC; WE NOTICED ANOTHER ACFT TO OUR L; HIGH. WE WERE GOING FASTER THAN THE OTHER AIRPLANE AND WERE SLIGHTLY AHEAD OF THEM. THIS WAS ON ABOUT A 1 MI FINAL. I TOOK THE CTLS FROM THE STUDENT AND APPLIED FULL PWR. AT THE SAME TIME; I INCREASED OUR RATE OF DSCNT TO INCREASE OUR LATERAL AND VERT DISTANCE FROM THE OTHER ACFT. THE OTHER ACFT DID NOT APPEAR TO BE TAKING ANY EVASIVE ACTION. WE WERE IN THEIR BLIND SPOT. IT IS WORTH NOTING THAT THE TWR WAS USING 2 FREQS AT THE TIME. WE WERE ON THE FREQ FOR ACFT ARRIVING FROM THE SW. THE OTHER ACFT WAS ON THE OTHER FREQ. AFTER WE WERE WELL AHEAD OF THE OTHER ACFT; I INITIATED A GAR. AT THAT TIME; THE TWR ASKED US WHICH RWY WE WERE LINED UP FOR. I TOLD THEM RWY 21L. THEY THEN INSTRUCTED US TO GO AROUND. I ADVISED THEM THAT WE WERE ALREADY DOING THAT. I BELIEVE THIS SIT OCCURRED BECAUSE OF LACK OF ADEQUATE COMS REGARDING PATTERN ENTRY AND LNDG CLRNC. SATURATION OF THE PATTERN; AN EMER IN PROGRESS AND LACK OF QUESTIONING OF ATC INSTRUCTIONS EARLIER CONTRIBUTED. A SIMILAR SIT COULD BE PREVENTED BY BEING MORE AWARE OF POTENTIAL MISCOM IN THE FUTURE ON THE PART OF THE CTLR AND THE PLT.