Your air conditioner may need the fan replaced or a belt changed. You can check the model online for troubleshooting tips. Often times it is an easy fix and will not cause you to replace the unit.
If your air conditioner is a generally older version, you would expect this to happen. However if it is fairly new, the sound may be coming from the external furnace.
The air conditioner could be making a high pitched noise due to the factor that the lubricant in the air conditioner is on the verge of ending or has ended.
My Air Conditioner is to be serviced, It is too old. The quality and Brand is also not so renowned. There is lot of dust also. I think this might be the Reason