Humming/whining noise

We have a 2.6 SE A4, 1996 (right hand drive). After driving for about 20 minutes it develops a high pitched humming sound. To the driver it
sounds as if it's coming from the left, and to the passenger as if it's coming from the right, so therefore we think it's in the middle. It doesn't appear to happen when the clucth is depressed, and is most noticeable as you start moving from a standstill, although it is constant on the move. Any suggestions as to what it could be?
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