AN INADVERTENT FREQ CHANGE ON AN INSTRUCTIONAL FLT RESULTS IN CONFUSION OVER CLRNC AND HDOF BTWN 2 CLOSELY LOCATED CLASS D TWRS.

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FOLLOWING FINAL LOW APCH ON TRAINING FLT TO BFI; WE REQUESTED VFR DEP TO RNT. CTLR ADVISED US TO FLY STRAIGHT OUT. I FLEW WHILE MY STUDENT REMOVED HIS HOOD. STUDENT THEN TRIED TO ASSIST BY TUNING RADIO TO RNT ATIS AND TWR. UNKNOWN TO ME; HE TUNED THE ACTIVE RADIO; RESULTING IN A NORDO SIT; WITH BFI TWR. AFTER NOT HEARING CALLS FOR ABOUT 30 SECONDS TO 1 MIN; I CHKED THE RADIOS AND DISCOVERED WE WERE TUNED TO RNT TWR; NOT BFI TWR. QUICKLY TUNED BFI TWR ON #1 RADIO COM. AS SOON AS I PUNCHED IN THE FREQ; BFI TWR RATTLED OFF A HIGH SPD CLRNC TO ENTER A R BASE FOR RNT. BY THAT TIME WE WERE ALMOST ABEAM RNT TWR; SO THE CLRNC DID NOT MAKE SENSE. MY STUDENT KEYED THE MIKE AND SAID 'CALL SIGN; ACCEPTING THE CLRNC' WHERE HE SHOULD HAVE QUESTIONED IT. RATHER THAN ACCEPTING AN ESSENTIALLY UNFLYABLE CLRNC; I INSTRUCTED MY STUDENT TO FLY STRAIGHT OUT AND QUERY THE CTLR. BY THE TIME HE COULD QUERY; WE WERE S OF RNT. THE CTLR INSTRUCTED US TO FLY STRAIGHT OUT. THIS COULD HAVE RESULTED IN A LOSS OF SEPARATION. AS AN INSTRUCTOR; I SHOULD HAVE PAID MORE ATTN TO MY STUDENT'S TUNING OF RADIOS. CONTRIBUTING FACTORS WERE SOME MINOR FATIGUE DUE TO BEING AT THE END OF A DIFFICULT INST LESSON AND MY STUDENT'S ACCEPTANCE OF AN UNFLYABLE CLRNC DUE TO THE DELAY IN GETTING THE CLRNC BY BEING OFF FREQ.