Could have a bearing going out in any of the belt driven components. ie: powersteering, alternator, water pump, air conditioning compressor ,or idler pulleys . Could also be low fluid level in Power Steering or transmission.
You are hearing a whirring when accelerating first to fourth because you are accelerating too fast and the whirring noise results. If you accelerate normally then you won't hear the whirring sound.
There are a number of reasons why your car may be making a whirring sound when accelerating. You may have a lose part for example.
Possible diff. bearings
More than likely... the power steering belt.
This most likely sounds like your water pump is on its way out. HAVE IT CHECKED IMMEDIATELY.
Perhaps the impellor on the fan motor is loose or broken
a whirring noise coming from the starter
the fuel pump
Brakes
c
needs grease in transmission
During Stirring Whirring Slurring