NON TWR ARPT COMMUTER ON COMPANY UNICOM FREQ VERSUS LISTED CTAF.

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CAPT AND MYSELF (WE) WERE TAXIING OUT FOR DEPARTURE ON RWY 12 FORT DODGE. ANOTHER COMMUTER WAS ALSO TAXIING BACK ON RWY 6 FOR DEPARTURE. MY CAPT COMMENTED '...LETS HURRY WE CAN BEAT HIM (FOR TKOF)' (OR WORDS TO THAT EFFECT) SO HURRY WE DID RUSHING THROUGH CHKLIST. BEGINNING TKOF ROLL I ANNOUNCED OVER RADIO 'TAKING OFF RWY 12 FORT DODGE LEFT TURN DEPARTURE NORTHWEST BOUND.' DURING OUR TKOF ROLL OTHER A/C WAS STILL GETTING POSITIONED FOR TKOF ON RWY 6. WE DEPARTED TURNED LEFT NW BOUND (TIGHT TURN) AND AT THAT POINT OTHER A/C WAS ON THE TKOF ROLL. AS WE CROSSED OVER THE EXTENDED CENTERLINE OF RWY 6 NWBOUND WE SEE THE OTHER A/C ABORT ITS TKOF. BOTH OF US WHERE A LITTLE PUZZLED BECAUSE WE WEREN'T A FACTOR FOR THEIR DEPARTURE. I SWITCHED OVER TO CENTER FREQ AND AT THIS POINT REALIZED I HAD BEEN TUNED TO COMPANY RADIO NOT UNICOM. AS A RESULT; OTHER A/C NEVER HEARD OUR DEPARTURE CALL ON CTAF. WHEN THEY SAW US XING THEY WERE UNCERTAIN OF OUR INTENTIONS SO THEY DECIDED TO PLAY IT SAFE AND ABORT THE TKOF. COMPLICATIONS: WE WERE FLYING ON REDUCED REST. THIS WAS OUR LAST LEG OF THE DAY AND WE WERE VERY TIRED. BECAUSE WE HAD BEEN FLYING ALL DAY AND WERE TIRED WE WERE IN A HURRY TO GET HOME. CAPT USED POOR JUDGEMENT WHEN HE DECIDED TO RUSH PROCEDURES THROUGH FOR A QUICK TKOF/DEPARTURE. F/O (MYSELF) JOINED IN THE RUSHING BEHAVIOR AND OVERLOOKED WHICH RADIO FREQUENCY I WAS TRANSMITTING ON. ACFT RADIOS DID NOT HAVE SEPARATE SIDETONES. IN OTHER WORDS; WHEN I TRANSMITTED ON COMM 2 CAPT WHO WAS LISTENING ON CORRECT RADIO COMM 1 COULD STILL HEAR ME. THIS MADE HIM ASSUME I WAS ON CORRECT FREQ. SOLUTIONS: WHEN ON REDUCED REST TAKE THINGS ESPECIALLY SLOW. MUST REALIZE THAT A LEGALLY FATIGUED STATE MAKES MISTAKES MORE LIKELY THAN WHEN FULLY RESTED. DON'T MAKE A CONTEST OUT OF WHO CAN DEPART SOONER. SUCH A TIME FACTOR SHOULDN'T BE AN INFLUENCE ON ONE'S DECISION. (WHAT DID IT GAIN US? A LONG ASRS REPORT!) CORRECT RADIO DESIGN IF POSSIBLE; IF NOT; MAKE ALL VIEWS AWARE OF THE POTENTIAL PROBLEM.