ACR MLG FREQ CHANGE MISSED AND UNAUTH PENETRATION OF AIRSPACE.

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ACR FLT OPOP WAS CLRED 'CHS J55 FLO J207 RDU FAK COATT1 IAD FL330.' ON CLB OUT; WE WERE RECLRED 'DIRECT VAN DIRECT FLO J207 AS FILED' AT JAX ARTCC REQUEST DUE TO TFC AND WX. OUR LAST CLRED ALT WAS FL230. ON CLB OUT AND CRUISE; WE WERE IN AND OUT OF CLOUDS IN LIGHT TO LESS THAN MODERATE CHOP. AFTER PASSING FLO ON J207 WE CONTINUED TO HEAR RADIO CONVERSATION; BUT WERE UNAWARE WE HAD FLOWN OUT OF JAX ARTCC RANGE. THE COMPANY CONTACTED US BY SELCAL AND TOLD US TO GO TO DCA ARTCC ON 132.4. SHORTLY AFTER CHKING IN; WE WERE TOLD BY DCA ARTCC THAT WE HAD FLOWN THROUGH R5311C (12000 TO FL290) AT FL230. R5311C WAS 'HOT' AT THE TIME. WE NEVER HEARD OR ACKNOWLEDGED A FREQ CHANGE FROM JAX ARTCC AFTER LEVEL OFF AT FL230. JAX ARTCC TAPE INDICATES THEY SAID 'COMPANY OPOP; GO TO 124.07.' SOMEONE ANSWERED '24.07 OPOP;' NOT '124.07; COMPANY OPOP.' IN 22 YRS OF COMMERCIAL FLYING AS A F/O AND CAPT; I HAVE ALWAYS USED MY COMPANY CALL SIGN WHEN TALKING TO ATC; AND AS A CAPT I ALWAYS BRIEF MY F/O'S TO DO THE SAME SO THAT ATC KNOWS WHO THEY'RE TALKING TO. HAD SOMEONE NOT ANSWERED FOR US; JAX ARTCC WOULD HAVE COME BACK AT US WITH THE NEW FREQ. HAD WE ANSWERED; THERE IS NO REASON WHY WE WOULD NOT HAVE CHANGED TO THE NEW FREQ. HAD WE NOT ESTABLISHED RADIO CONTACT; WE WOULD HAVE COME BACK TO THE OLD FREQ. I MAINTAIN WE DID NOT HEAR OR ACKNOWLEDGE A FREQ CHANGE FROM JAX ARTCC TO GO TO 124.07. SUPPLEMENTAL INFO FROM ACN 94058. NEITHER THE CAPT NOR I RECALL ANSWERING A RADIO CALL FROM JAX CENTER FOR A FREQ CHANGE. I HAVE FLOWN UP J207 N OF FLO TENS OF TIMES IN THE LAST FEW YEARS. RESTR AREA 5311 HAD NEVER BEFORE COME INTO PLAY; AND THUS HAD ALMOST BECOME INVISIBLE ON THE CHART. I THINK WE ALL RELY TOO MUCH ON ATC TO KEEP US OUT OF RESTR AIRSPACE. VIEWING THE CHART IS TOO OFTEN LIMITED TO SEEKING OUT THE OUTBND AND INBND RADIALS W/O PAYING MUCH ATTN TO WHAT IS IN BETWEEN; ESPECIALLY OVER ROUTES WE HAVE FLOWN DOZENS OF TIMES.