B757-200 FLT CREW ENCOUNTERS MODERATE TURB AND MOUNTAIN WAVE ACTIVITY.

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WITH THE SEATBELT SIGN OFF IN SMOOTH CONDITIONS; I FELT THE ACFT START A SIGHT BUFFET; AS IF IT WAS THE ONSET OF TURB. I CHKED THE AIRSPD INDICATOR AND IT WAS REGISTERING .84 MACH AND RAPIDLY INCREASING. WE WERE FLT PLANNED AT .79 MACH. I DISCONNECTED THE AUTOTHROTTLES AND PULLED THE THROTTLES BACK. THE AIRSPD WAS CONTINUING TO INCREASE AT A RAPID RATE AND APCHING THE BARBER POLE WITH INCREASED AIRFRAME BUFFET. THE FO SUGGESTED USING THE SPD BRAKES BUT I FELT THAT THE RATE AT WHICH THE AIRSPD WAS INCREASING; INCREASING THE PITCH WOULD PRODUCE THE QUICKEST RESPONSE. I DISCONNECTED THE AUTOPLT TO INCREASE THE PITCH BUT THE AIRSPD INCREASED BEYOND THE BARBER POLE. THE AURAL OVERSPD WARNING WAS SOUNDING. THE AIRFRAME BUFFETING WAS APCHING MODERATE. WE MADE A RADIO CALL TO ATC ADVISING THEM OF THE SEVERE MOUNTAIN WAVE AND THAT WE WERE UNABLE TO MAINTAIN ALT AND CLBING. IN THE CLB I ATTEMPTED TO USE AS MUCH CTL FORCE AS I WOULD FOR A TFC RA ALERT; TRYING NOT TO BE ABRUPT WITH THE CTLS AT THIS HIGH ALT. THE SEATBELT SIGN WAS TURNED ON AND ANNOUNCEMENT MADE. THE AIRSPD CLBED TO MACH .87 BEFORE DECREASING. AS SOON AS WE STARTED THE CLB; WE ENCOUNTERED MODERATE TURB. WE CLBED TO APPROX FL400 AT WHICH TIME THE AIRSPD THEN STARTED A RAPID DECREASE AND A DSCNT WAS MADE BACK TO FL390. THE AIRSPD DECREASED TO MACH .73 AT THE SLOWEST POINT. ALTHOUGH STILL ENCOUNTERING MODERATE TURB AT FL390; THE FLT BECAME STABLE ONCE AGAIN. WE REQUESTED A DSCNT TO FL370 FOR SMOOTHER CONDITIONS. IT WAS STILL ROUGH THERE; SO WE CONTINUED FURTHER TO FL350 WHERE WE REMAINED. WE CALLED THE FLT ATTENDANTS INQUIRING ABOUT INJURIES WHILE IN THE DSCNT TO A SMOOTHER ALT. I WAS INFORMED THAT THE FLT ATTENDANT IN THE AFT GALLEY HAD FALLEN AND INJURED HER WRIST. DETAILS WERE TO FOLLOW AS TO THE EXTENT OF THE INJURY. WE RPTED THE SEVERE MOUNTAIN WAVE AND MODERATE TURB TO DISPATCH VIA ACARS. A CODE WAS SENT TO MAINT FOR THE OVERSPD. WE ESTABLISHED RADIO CONTACT WITH DISPATCH REGARDING THE INJURY TO THE FLT ATTENDANT. BY THAT TIME I WAS INFORMED THAT THE FLT ATTENDANT WAS IN A LOT OF PAIN WITH A POSSIBLE BROKEN WRIST. SHE WAS BEING ATTENDED TO BY AN ER TRAUMA UNIT NURSE ON FLT. THE NURSE'S RECOMMENDATION WAS TO GET HER TO A MEDICAL FACILITY TO BE TREATED. A DIVERSION TO ZZZ1 WAS COORD WITH DISPATCH DUE TO THE FACT THAT ZZZ2 WAS IN HOLDING FOR MICROBURSTS AT THE ARPT. SHORTLY BEFORE LNDG; I WAS ADVISED BY THE PURSER THAT THE INJURED FLT ATTENDANT HAD SUSTAINED INJURIES ALSO TO HER HIP; KNEE AND ANKLE AND WAS NOT ABLE TO STAND UP TO MOVE TO A SEAT FOR LNDG. SHE REMAINED ON THE FLOOR OF THE AFT GALLEY FOR LNDG SURROUNDED BY PILLOWS AND BLANKETS. THE ER NURSE REMAINED WITH HER. EMER PERSONNEL MET THE ACFT AND TOOK THE FLT ATTENDANT TO A LCL HOSPITAL. THE EVENT HAPPENED VERY SUDDENLY AND WITHOUT WARNING. MOST OF THE FLT WAS SMOOTH AND THE SEATBELT SIGN WAS OFF. THE WX BRIEFING HAD PROVIDED US WITH CAT ALERT OF 015F FOR RISK OF MODERATE TURB FL200-FL380. WE DID HEAR RPTS OF ACFT AT THE LOWER ALTS RPTING LIGHT TURB AND MODERATE CHOP; BUT FL390 WAS SMOOTH. WE DID ENCOUNTER LIGHT CHOP AND DID HAVE THE SEATBELT SIGN ON FOR A PERIOD OF TIME. THE CHOP DID NOT REQUIRE US TO SEAT THE FLT ATTENDANTS. WHEN ASKED; ATC SAID IT WOULD SMOOTH OUT AT THE FRONT RANGE. THE SEATBELT SIGN WAS TURNED OFF WE TOOK A BATHROOM BREAK AND IT REMAINED SMOOTH UNTIL THE INCIDENT. THERE WERE NO RPTS FROM ATC; DISPATCH OR OTHER ACFT AHEAD OF US REGARDING THE MOUNTAIN WAVE OR TURB.