Shimmy means shaking not humming... which a bad alignment and unbalanced tires could cause.
If you are hearing variable noise with speed it is either road noise off the tires or you could potentially have a bad wheel bearing. Could also be a problem with the rear diff.
Also I am curious to know how you could tell the tires wear perfect if you just bought the car. Just because the tires on it are good doesn't mean the alignment wasn't recently wacked out of spec (such as if someone sold a car that was lowered, put it back to stock and never had it realigned).
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