Ok, here it goes, I bought my second handed 2004 impreza 2.5 TS (manual transmission) with about 190,000 km on it about a month ago.

A couple of weeks later I noticed that there is a high pitched whining noise when I am driving, the noise sounds kinda like wind noise when the window was not fully closed, so I made sure all windows were fully shut and I can still hear it. The noise is more pronounced at about 40-60 km/h, it will go away at lower and higher speed, it is only related to vehicle speed.

Also, I noticed that the tire on rear drive side is more worn than all the other three tires. 3/32 Vs. 7/32.

I thought the worn tire might be caused by bad tire alignment, so I went to tire shop and get them aligned, which was not out of spec. The people in the tire shop also told me mis-matched tire will damage my differential.

I did some research and find out that the high pitched noise is from worn centre differential which is the result of mis-matched tires.

So, here are my questions:

Can somebody confirm my diagnose based on my information?

The previous owner isn't sure that all four tires had the same wear/thread depth when he put them on. Assume that all four tire had the same wear to begin with, what will cause the rear drive side tire wear faster than all other three, other than alignment?

Will rear differential be damaged as well? How can I confirm if it is good/damaged?

Do I really have to replace/fix centre differential if I put a set of new tires on? If I do not fix the centre differential will it cause more problem further down the road, even with a new set of tires? Will it cause abnormal/uneven tire wear? Will it get worse than what it is now? If I have to get centre diff fixed, what is the cheapest way to do it? Do I have to do a full centre diff swamp? I really do not planning on spend tons of money on it, I kinda expect the vehicle to last for 3 to 5 years at least.

Thanks for all the advices in advance.

Yes I would say that you are correct in that it was probably the tires that damaged the diff and not the other way around no farther then it has been.

 

As far as fixing the centre diff, new tires won't hurt it, seriously dout that it will keep it from getting worse also, generally when a bearing starts to go it will die completely down the road somewhere.  So at some point it will need to be fixed, hard to say how soon though.

 

As far as getting it fixed I don't really have much knowledge on the part.

Get new tires first.

 

Also change the fluid in the rear diff. The only real killer of gear oil is heat, and there will be quite a bit of extra heat generated by the speed difference left-right because of the tires. This can cause wear in the rear diff as well as the center diff.

You might also consider changing the transmission oil as well.