AN INSTRUCTIONAL FLT ENTERS THE LGB CLASS D AIRSPACE WITHOUT CLRNC AFTER AN INITIAL CALL TO THE WRONG LCL CTLR ON AN INCORRECT FREQ.

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I WAS RETURNING WITH A STUDENT FROM THE LGB PRACTICE AREA; WHICH FOR LGB IS JUST OFFSHORE; EXTENDING OUT FROM THE LONG BEACH HARBOR AND BREAKWATER. WE HAD MADE OUR INITIAL CALL TO LGB TWR OVER THE QUEEN MARY; WHICH IS A RPTING POINT. LGB WAS OPERATING WITH S TFC; USING RWY 16R AND RWY 12 DUE TO SOUTHERLY WINDS. OUT OF HABIT; WE CALLED ON 119.4; THE USUAL FREQ FOR RWY 25L AND RWY 30. THE LCL CTLR ACKNOWLEDGED OUR CALL; AND ADVISED US TO CONTACT TWR ON 120.5 FOR RWY 16R. AFTER SWITCHING TO THIS FREQ; WE FOUND IT TO BE VERY BUSY. BUT SINCE WE HAD INITIALLY MADE CONTACT ON 119.4; I WASN'T TOO CONCERNED. AFTER MAYBE 15-30 SECONDS; BEING UNABLE TO CHK IN; I HAD THE STUDENT START A L TURN BACK OUT OF THE AREA AS WE HAD NOT MADE CONTACT YET ON 120.5. ONCE IN THE TURN; I GOT A CHANCE TO CALL THE TWR. I GOT A REPLY AND WAS IMMEDIATELY INFORMED OF TFC ABOVE ME; A PIPER SENECA (I THINK) WHICH WAS APPARENTLY A FEW HUNDRED FT ABOVE US. MY STUDENT AND I DID NOT SEE THE TFC; AND IMMEDIATELY BEGAN SEARCHING; AND ROCKING THE WINGS TO CHK BLIND SPOTS. I ALSO REDUCED PWR AND MADE A QUICK DSCNT DOWN TO ABOUT 1000 FT TO GET OUT OF THE WAY. FOLLOWING FARS. WE SAW THE TFC; WHICH WAS NOW NOT A FACTOR. THE TWR THEN TOLD US WHERE TO RPT IN THE TFC PATTERN. SHE CLRLY SOUNDED IRRITATED. I UNDERSTOOD AND APPRECIATED HER CONCERN. I WAS ALSO TRYING TO DO THINGS PROPERLY. AFTER FINISHING OUR LESSON; AND TAXIING CLR OF THE ACTIVE; SHE TOOK A MIN TO EXPLAIN; THAT WE HAD ACTUALLY CONTACTED HER 1.5 NM INSIDE THE CLASS D AIRSPACE; AND TO PLEASE BE AWARE OF WHERE IT BEGINS; AND WHEN THE TWR IS USING S TFC; PLEASE CALL THEM ON THE APPROPRIATE FREQ (122.5). I ACKNOWLEDGED ALL OF THIS; AND THANKED HER FOR THE INFO. AFTER FINISHING WITH MY STUDENT; I CALLED THE TWR TO SPEAK WITH THE CTLR. SHE WAS NOT AVAILABLE. I EXPLAINED THE SIT BRIEFLY; AND APOLOGIZED; AND THANKED THEM. THE CTLR I SPOKE WITH PROMISED TO PASS ON MY MESSAGE. I HAD THOUGHT THAT WHEN I INITIALLY MADE CONTACT WITH ONE LCL CTLR; THAT I WAS THEN OK TO ENTER CLASS D AIRSPACE. POSSIBLY THIS TIME IT WAS DUE TO A HIGH CTLR WORKLOAD; AND SHE DID NOT APPRECIATE MY LATE CALL. I DID NOT ANTICIPATE THINGS GOING AS THEY DID; ANOTHER IMPORTANT LESSON LEARNED. I MADE THIS POINT WITH MY STUDENT. I HAVE TO SAY THAT IT IS DIFFICULT AT TIMES; TRYING TO JUGGLE TEACHING AND OTHER DUTIES IN BUSY AIRSPACE. IT REMAINS A CHALLENGE.