B737-800
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Speed All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Flight Crew Requested ATC Assistance / Clarification
Weather
We were cruising at FL390 and we called the back for a break. I was the second pilot to exit the flight deck and while in the main cabin I noticed the pitch of the aircraft.  I then made a brief break and called to return to the flight deck.  Once the flight deck door opened and the A came out I noticed the thrust levers advancing to max power and the airspeed indicator slowly approaching the amber band.  I then immediately called for a lower altitude as I took my seat and once I was in my seat I looked at my First Officer and said we need lower now.  My First Officer then dialed a lower altitude on the FMC and selected descent via V/S (Vertical Speed). I then gathered all info on what we were experiencing and thought either we had an unreliable airspeed or runaway stabilizer.  As I looked back at our altitude; I realized we weren't descending and our airspeed was slowly approaching amber pole.  At that time I disconnected A/T (Autothrottle); A/P (Autopilot) and started a slow descent and requested my First Officer to call in our descent to ATC.  ATC then notified us that we needed to stop descent at FL370 due to lower aircraft.  My training kicked in and I figured if this went back we would need around 10;000 feet to recover so I then requested a vector off course.  We then were given 10 degrees left and I leveled off at FL370 continued to hand fly and one by one acquired A/P; HDG; VNAV.  Our Airspeed gained approximately 30kts and we were stable at FL370 on a heading.  ATC asked why the need to descend and I replied we encountered mountain wave and could not hold altitude. ATC then replied that we were the first to complain of mountain wave. Seconds later an aircraft at FL470 notified of +/- 1000 gain/loss and another airliner requesting lower due to mountain wave. We were then given direct to a waypoint on our flight plan and landed at destination without further incident. Be more vigilant while single pilot operations.
Air carrier Captain reported altitude and airspeed deviations as a result of mountain wave activity in cruise.