INSTRUCTOR PLT DURING A TRAINING FLT LWOC AND COMMENCED TAXIING WITHOUT CLRNC DUE TO A MALFUNCTIONING COM RADIO.

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CLRED FOR A VISUAL APCH FOR RWY 22 AT DCA. GIVEN A FREQ CHANGE TO TWR. CONTACTED TWR AND WAS TOLD (WE WERE TOLD WE WERE #2 FOR THE ARPT) TO SQUARE THE BASE TURN TO PROVIDE SPACING FOR B737 LNDG RWY 19. WE RESPONDED AND SQUARED FOR A 1 MI FINAL BEING CAREFUL TO AVOID P56 NE OF THE ARPT. WE DID NOT RECEIVE ANY OTHER XMISSIONS UNTIL WE HAD LANDED AND CLRED THE RWY AT TXWY H. AFTER CLRING; I HEARD TWR ASK IF WE WERE STILL ON FREQ. I RESPONDED THAT WE WERE AND THEN HEARD TWR CALL SEVERAL OTHER ACFT CLRING THEM FOR TKOF AND LNDG. AT THAT POINT I NOTICED FLASHING GREEN LIGHT GUN SIGNALS COMING FROM THE TWR. I SWITCHED TO GND AND WAS UNABLE TO CONTACT THEM ON EITHER COM #1 OR COM #2. I TRIED TWR ON COM #1 AND COM #2 AND WAS UNABLE TO CONTACT THEM. WE CROSSED RWY 19 AND STARTED TO TAXI TOWARD GA PARKING AND THEN I TRIED GND ON COM #1 AGAIN AND WE WERE ABLE TO MAKE CONTACT WITH THEM. AFTER PARKING; I SPOKE WITH THE TWR CTLR AND HE STATED THAT NOT ONLY DID WE NOT CONTACT THEM PROPERLY AFTER LNDG; BUT THAT WE HAD LWOC AND WERE TOLD TO GO AROUND 3 TIMES. I EXPLAINED THAT WE DID NOT RECEIVE THE XMISSIONS. HE STATED THAT THE B737 WAS ABLE TO HOLD SHORT OF OUR RWY SO A SERIOUS PROB HAD BEEN AVOIDED. AFTER REVIEWING THE AIM AND FAR 91.185; I FEEL THAT OUR DECISION TO CONTINUE AND LAND WAS APPROPRIATE. HOWEVER; EARLIER RECOGNITION OF THE RADIO PROB COULD HAVE HELPED IN RESOLVING THIS BEFORE A POTENTIAL FOR A RWY INCURSION HAD DEVELOPED.