G’day Gents,
I have, over the years, flown several different airliners with all the major engine brands and model of jet engines and some of them buzz or hum from light off to idle and some do not.
Now this is a memory stretch but I recall a tech instructor once explaining the hum/buzz after the engine lights off as an instability in the compressor airflow as the engine accelerates to idle.
Apparently the engine fueling schedule during start is controlled to ensure the engine is accelerating just on the stable side of the surge line and humming. Cross the surge line and you get a compressor stall and all sorts of problems, some engines are fitted with surge bleed valves to relieve compressor pressure during start to prevent a surge. Some engines modulate the engine anti ice valve to achieve the same result.
Once stable idle is achieved the hum/buzz no longer occurs. Of course there are many noises associated with engine start and operation but the above is how it was explained to me many years ago.
Mind you it could all be rubbish as I said it was a long time ago.
Cheers,
BH.