"My phone makes a different sound today."
Translation:Min telefon siger en anderledes lyd i dag.
Is it normal to use "at sige" for general sounds like this? Or is this a specific case?
That is normal. 'at sige' can mean both 'to say' (also animals) and 'to make a sound'
'to make (a) noise' is 'at larme' or 'at støje'
'at tale' and 'at snakke' mean 'to talk/speak' and are reserved to humans only