Narrative:

During cruise flight [over the rocky mountains] at FL350 we experienced moderate mountain wave activity (+10/-20 kias). The autothrottles were engaged and actively moving from near idle to max cruise thrust settings in an attempt to maintain airspeed. We reported the mountain wave activity to ATC.we then heard approximately four loud bangs. Initially we believed someone in the cabin was doing something. We then saw the #1 engine was in a compressor stall. The #1 engine was at approx 50-55% N1 and #2 engine was at max cruise thrust. The thrust levers were both at a max cruise thrust position and both egt's were normal.as the pm (pilot monitoring) I accomplished the QRH items and the #1 engine stabilized immediately. With a stable engine we requested and were granted a descent to FL280. At this point we transferred duties and I became the PF (pilot flying) so the captain could accomplish items as the pm.the captain completed the QRH items. We elected to divert to ZZZ. ATC issued us [routing and approach instructions]. Weather was day VFR. Dispatch was advised of our malfunction; emergency status; and provided weather and overweight landing data. The captain briefed the flight attendant's (flight attendants) who advised hearing 'several loud metallic bangs from the left side of the aircraft'. An announcement was made to the passengers advising them of our situation and that we were diverting to ZZZ out of an abundance of caution. Passenger response was positive throughout the event. Pm/PF duties were transferred and the captain flew the approach and landing. I referenced the diversion [checklist] and completed all normal checklists items. An uneventful landing was completed and we cleared the runway. Crash fire rescue equipment (crash fire rescue) inspected the #1 engine and advised all was normal. We secured the #1 engine and proceeded to the gate. We requested ramp to advise ground personnel the #2 engine was running as this was non-standard.once at the gate passengers were deplaned normally via jet bridge; maintenance entries were made for the overweight landing and #1 engine stall. A debrief was accomplished with maintenance and flight ops personnel at the gate. Dispatch and the [operations manager] were briefed via phone. Finally the captain and I debriefed the event.

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Original NASA ASRS Text

Title: B737 First Officer reported encountering mountain wave activity causing an engine stall.

Narrative: During cruise flight [over the Rocky Mountains] at FL350 we experienced moderate mountain wave activity (+10/-20 kias). The autothrottles were engaged and actively moving from near idle to max cruise thrust settings in an attempt to maintain airspeed. We reported the mountain wave activity to ATC.We then heard approximately four loud bangs. Initially we believed someone in the cabin was doing something. We then saw the #1 engine was in a compressor stall. The #1 engine was at approx 50-55% N1 and #2 engine was at max cruise thrust. The thrust levers were both at a max cruise thrust position and both EGT's were normal.As the PM (Pilot Monitoring) I accomplished the QRH items and the #1 engine stabilized immediately. With a stable engine we requested and were granted a descent to FL280. At this point we transferred duties and I became the PF (Pilot Flying) so the Captain could accomplish items as the PM.The Captain completed the QRH items. We elected to divert to ZZZ. ATC issued us [routing and approach instructions]. Weather was day VFR. Dispatch was advised of our malfunction; emergency status; and provided weather and overweight landing data. The Captain briefed the FA's (Flight Attendants) who advised hearing 'several loud metallic bangs from the left side of the aircraft'. An announcement was made to the passengers advising them of our situation and that we were diverting to ZZZ out of an abundance of caution. Passenger response was positive throughout the event. PM/PF duties were transferred and the Captain flew the approach and landing. I referenced the diversion [checklist] and completed all normal checklists items. An uneventful landing was completed and we cleared the runway. CFR (Crash Fire Rescue) inspected the #1 engine and advised all was normal. We secured the #1 engine and proceeded to the gate. We requested ramp to advise ground personnel the #2 engine was running as this was non-standard.Once at the gate passengers were deplaned normally via Jet Bridge; maintenance entries were made for the overweight landing and #1 engine stall. A debrief was accomplished with maintenance and Flight Ops personnel at the gate. Dispatch and the [Operations Manager] were briefed via phone. Finally the Captain and I debriefed the event.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.