Just before engine start the air bleed is transferred from the air conditioning to the engine to assist in engine start, the aircraft becomes relatively quite so it becomes easier to notice all the surrounding sounds, the whirring sound will be the different turbine stages starting to rotate, first by the bled air and later during the process with jet fuel.
Depending on which engine is fitted on the aircraft ( typically CFM or the IAE ), you get a different "signature" sound, the 320 engine is known for its sharp whizzing sound from the moment you apply takeoff power until you reach a higher cruise level.
I hope this answers you query, now back to topic
