A B737 FLT CREW PERFORMED A RAPID DSCNT FOLLOWING A SLOW CABIN PRESSURIZATION LOSS WITH A WARNING HORN. AN EMER WAS DECLARED.

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A FEW MINS AFTER LEVELOFF AT FL340; APPROX 25NM E OF ZZZ1; THE CABIN ALT WARNING HORN SOUNDED AND THE CABIN ALT WAS OBSERVED AT 10000 FT. WE ACCOMPLISHED THE CABIN ALT WARNING HORN MEMORY ITEMS AND QRC FOLLOWED BY THE EMER DSCNT QRC AND QRH. I INITIATED THE EMER DSCNT WHILE THE FO WORKED THE PROB. THE HIGHEST THE CABIN ALT WAS OBSERVED ON DSCNT WAS APPROX 12000 FT. WE WERE INITIALLY CLRED TO FL180; THEN TO 10000 FT. WHEN THE FO WENT TO MANUAL ON THE PRESSURIZATION MODE SELECTOR; THE OUTFLOW VALVE WAS OBSERVED IN THE FULLY CLOSED POSITION. PASSING APPROX 15000 FT THE CABIN ALT WAS UNDER CTL AND COMING DOWN. PRESSURIZATION SYSTEM SEEMED TO FUNCTION NORMALLY AND WE LEVELED AT 12000 FT TO CONSERVE FUEL. WE CONTACTED DISPATCH; DISCUSSED FUEL AND POSSIBLE DIVERT; BUT IT WAS DETERMINED THAT THE NEAREST SUITABLE ARPT WITH MEDICAL PERSONNEL WAS ZZZ.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THE CABIN PRESSURIZATION LOSS WAS VERY INSIDIOUS AND BECAUSE OF AN EQUIPMENT COOLING FAN VIBRATION; THE FO INITIALLY ASKED WHAT THE HORN WAS; THINKING IT MY HAVE BEEN RELATED TO A PRIMARY FAN FAILURE. REPORTEDLY THE FLT CREW REALIZED VERY QUICKLY THAT THE FAN FAILURE HORN THAT OCCURS ON THE GND WHEN THE PRIMARY EQUIPMENT FAN FAILS IS DIFFERENT THAN THE HORN THEY WERE HEARING; ADDING ONCE THEY IDENTIFIED THE HORN; THEY QUICKLY PERFORMED THE EMER PROCS. THE RPTR INDICATED THIS ACFT WAS FOUND TO HAVE A STICKY FWD OUTFLOW VALVE AND AN AFT CARGO DOOR SEAL NOT PROPERLY SEATED.SUPPLEMENTAL INFO FROM ACN 688579: A FEW MINS AFTER LEVELOFF AT FL340; THE CABIN ALT WARNING HORN SOUNDED AND THE CABIN ALT WAS OBSERVED AT 10000 FT. WE ACCOMPLISHED THE CABIN ALT WARNING HORN MEMORY ITEMS AND QRC FOLLOWED BY THE EMER DSCNT QRC AND QRH. THE CAPT INITIATED THE EMER DSCNT WHILE I WORKED THE PROB. WE WERE INITIALLY CLRED TO FL180; THEN TO 10000 FT. WHEN I SWITCHED THE PRESSURIZATION MODE SELECTOR TO MANUAL; THE OUTFLOW VALVE WAS OBSERVED IN THE FULLY CLOSED POSITION. PASSING APPROX 15000 FT THE CABIN ALT WAS UNDER CTL AND COMING DOWN. PRESSURIZATION FUNCTIONED PROPERLY AT 12000 FT. WE CONSIDERED AN ALTERNATE; CONTACTED DISPATCH AND THE FLT DUTY OFFICER AND DECIDED ZZZ WAS THE MOST SUITABLE ARPT GIVEN THE MEDICAL RESOURCES AVAILABLE AND THAT WE HAD SUFFICIENT FUEL FOR THE DEST.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT FOR A BRIEF COGNITIVE MOMENT HE CONSIDERED THAT THE WARNING HORN COULD BE THE EQUIPMENT COOLING FAN BECAUSE THE CREW HAD HEARD THAT HORN ON THE GND TROUBLESHOOTING ANOTHER PROB. THE RPTR INDICATED HE REALIZED VERY QUICKLY THAT THIS WAS NOT THE CAUSE; ADDING THE CHKLIST LED THE CREW ON A PATH THAT ALLOWED THEM TO REGAIN PRESSURIZATION CTL. THE RPTR INDICATED WHAT CAUSED SOME ADDITIONAL QUESTION WAS THE SOUND VOLUME OF THE WARNING HORN; CONTRASTING THE SOUND OF THE TKOF WARNING HORN IN A RELATIVELY QUIET ACFT ON THE GND; THE CABIN ALT WARNING IN FLT WITH AMBIENT FLT NOISE WAS SOMEWHAT WEAK AND DID NOT COMMAND THEIR ATTENTION AS THE RPTR WOULD HAVE EXPECTED. THE RPTR INDICATED UNOFFICIALLY; THE CREW WAS TOLD THAT THE FORWARD OUTFLOW VALVE HAD FAILED.