The only turbprop I've travelled is the ATR 72. I've noticed that the props' rev go down (for like a second, the sound also goes down) just before engaging full throttle in order to takeoff. I've included a video (video is not mine), this thing happens at 1:40. Why the RPM drops for a sec? Or is this just the sound?
Because the pilot is taxiing the airplane with the props in the beta range (turboprops turn into landsharks if you don’t do this and you end up really riding the brakes to keep the speed down), then on takeoff, the propellers move into a maximum power setting, the engine snarls and slows a bit under the increased workload.
It's because he was taxiing in DISC (discing, or flat pitch making the prop like a big disc), which is in the ground beta range, then coming out of it.
Beta range is a mode where propeller blade angle is directly controlled by the power levers, and the propeller RPM is controlled by an Np governor in the fuel controller modifying gas generator (the engine core) speed to maintain rpm on a fixed schedule, depending on where the power levers are. Beta range is similar to speed governing on a turbine helicopter, where you change pitch with collective and a governor automatically controls the fuel to keep the rotor RPM constant for you.
Beta range starts just ahead of flight idle (there is no marking for this on the power lever quadrant). The range forward of idle is "flight beta" and aft of flight idle is "ground beta". On the non-FADEC PW120 series engines there is a cam called the beta cam (obviously) in the power control linkage (on the propeller control unit on the engine) that triggers the transfer of propeller control between the prop governor/prop lever setting and the power lever/fuel controller once the prop has hit its fine pitch limit and propeller governor is no longer governing.
So to be in beta mode the prop has to be "off the governor" (with no torque and the props set to MAX RPM, the prop is trying to go finer and finer to keep the rpm up, then the blades hit the full fine pitch limit, about 24 degrees, and there's nothing more it can do) and the power lever has to be back just forward of flight idle at which point the beta cam takes over to directly regulate blade angle, from +24 degress to -11 degrees blade angle. So if you are descending with the engines at or near flight idle you are in flight beta mode.
Once in beta mode the beta cam works with a beta metering valve to regulate fine pitch oil pressure to the prop such that when the power lever is moved, the cam movement displaces the metering valve, causing the prop pitch to change until the input is nullified and blade angle is fixed at a new position. The cam's profile thus gives a specific blade angle for a given power lever position.
Anyway, what's happening there is engine's torque dropping off momentarily as the engine transfers from prop rpm governing in beta (via the fuel controller Np governor controlling torque) to normal flight mode (rpm controlled by the propeller flyweight governor as set by the prop levers, with the power levers now taking over production of torque) as the Power Levers are moved past about one inch forward of Flight Idle.
Most likely this is happening after the pilot advances the power lever -- but the power lever controls both throttle (fuel flow, in a turbine), and propeller pitch.
The propeller can change pitch pretty quickly, while the turbine takes longer to increase power (increased fuel flow must produce hotter combuster air, which must then spin up both the turbine-compressor section, and the independent shaft power turbine connected to the gear box and propeller). Usually, the engine's rotating parts will change RPM faster than the ones that spin the (relatively large) propeller, so you may hear the "whine" or "whistle" of the primary shaft spooling up before the propeller noise starts to rise, possibly even while the propeller is still slowing down from the pitch increase.