INST PLT TRAINEE; WITH INSTRUCTOR; FAILED TO FOLLOW CLRNC TRACK DUE TO LOOKING AT THE WRONG VOR RADIO COURSE INDICATION.

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I TOOK OFF FROM FARMINGDALE; NY (FRG); GOING TO ATLANTIC CITY MUNI-BADER FIELD; ON AN IFR TRAINING FLT. MY STUDENT HAD PRESET THE NAV RADIOS DURING THE RUN-UP ACCORDING TO OUR CLRNC WHICH READ: CLRED TO ATLANTIC CITY BADER; MAINTAIN RWY HEADING; VECTORS TO JFK; V229; ACY DIRECT. ALT AND SQUAWK ARE IRRELEVANT. AFTER TKOF WE WERE VECTORED AS EXPECTED UNTIL CLRED JFK DIRECT. WE HAD TURNED OUR RADIO #1 (COLLINS) IN THE 'TO' MODE DISPLAY AND FLEW THE NUMBER IT SHOWED SINCE IT SEEMED TO MAKE SENSE. THE VOR HAD BEEN IDENTED SHORTLY AFTER TKOF. AFTER A FEW MINS NY APCH QUESTIONED OUR HEADING AND WE CHKED THE HEADING INDICATOR AGAINST THE COMPASS AND FOUND A MINIMAL ERROR OF 5 DEGS. THEY THEN GAVE US A CORRECTION OF 20-30 DEG TO THE L. AT THAT POINT I CHKED ALL THE RADIOS AND FOUND OUT THAT OUR VOR #1 WHICH WE WERE USING WAS SET ON LGA AND THE #2 WAS SET ON JFK. OBVIOUSLY; BECAUSE OF THE PROX OF THE VORS ON THE MAP MY STUDENT ENTERED THE WRONG ONE AND WHEN IDENTING HE CHKED THE #2 (I WAS LISTENING). SINCE #1 WAS IN THE 'TO' DISPLAY MODE (COLLINS) IT DID NOT SHOW THE FREQ AND WE WERE NOT USING THE #2 WHICH WAS ON THE RIGHT FREQ BUT THE OBS WAS ON 221 (V229). BECAUSE OF THE WORKLOAD; FLYING IN NY AIRSPACE; I SHOULD HAVE BETTER SUPERVISED MY STUDENT; OR EVEN DONE SOME OF THE WORK. ALTHOUGH I FIND IT VERY CONVENIENT TO HAVE A DIRECT READING OF THE TO AND FROM INDICATION I THINK IT IS NOT SAFE TO KEEP IT FOR ANY LENGTH OF TIME IN THE 'TO' OR 'FROM' MODE WITHOUT ANY FREQ DISPLAY. THESE RADIOS ARE OLD AND WILL NOT BE MODIFIED BUT I THINK THAT THE FREQ SHOULD BE DISPLAYED ALL THE TIME OR MOST OF THE TIME. I (ALMOST) ALWAYS TEACH THE USE OF THE SECOND VOR TO CHK THAT THE #1 IS OK; UNLESS IT IS NEEDED FOR ANOTHER PURPOSE. WE WERE NOT USING #2 EXCEPT IT WAS SET FOR V229 (OUR RTE AFTER JFK). CONSIDERING THE SPD OF THE AIRPLANE WE SHOULD HAVE USED BOTH VORS ON THE SAME SETTINGS AND ONCE ABOVE JFK WE WOULD HAVE HAD PLENTY OF TIME TO TURN THE OBS TO 221. NOTHING HAPPENED THANKS TO THE RADAR BUT WITHOUT IT WE MIGHT HAVE BEEN FLYING INTO AN OBSTACLE. LESSON LEARNED; BETTER CHK THE RADIOS. COCKPIT MGMNT IS USEFUL.