Bad bearing whine when engine is started

I have a 2004 GMC 4.2 liter Envoy with 60,000 miles on it. Every time I start the engine there is a high pitched whine coming from the left rear of the engine where the starter is usually found. It sounds like a bearing going bad and is only heard after the starter has been engaged and the engine has started. The whine lasts about 20 seconds then slows to a stop like an electric motor, with a bad bearing, has been turned off. If I turn off the engine right away, the whine continues but slows to a stop in five to ten seconds. I can not isolate the noise with a hose to my ear but, it is not coming from the alternator, power steering, water pump or cooling fan. I don’t notice it if I’m in the car with the windows closed. Other than the starter, what else, in that area could cause this noise?

Maybe there is something going on with the starter bendix.

Yes indeed…That sounds like the Bendix is hanging up on the ring-gear and after the engine starts, the starter is being spun up to very high speed…The starter will be quickly destroyed if this is allowed to continue…