There is the valve that goes from sap into the exhaust. If that isn't opening full or some other issue I could see it making a whistle. Too coincidental of the cold start and 90-120 seconds to really be anything not sap related.

Usually the bearing fails and it will make a horrendous noise like the car is trying to hover.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)