I have recently bought a 330i with 118k miles. On accelerating through the gears, there is a distinct whirring sound, particularly between 2000 - 3000 rpm in second and third gear (the noise is drowned out by engine and road noise at higher speeds). Other than that it runs just as smoothly as my wife's 330, which has only done 70k.
My first hought was transmission - does it simply need new gearbox oil? The car has a reasonable service history but as far as I know the oil has never been replaced.
However, I'm also wondering if the timing chain or tensioner could be worn.
Any thoughts on how to identify the problem would be appreciated, thanks.