My cockatiel likes to make this short, kind sound: 'Toot'. It sounds a bit like a very short train flute.
She seems to make this sound whenever I appear from another room or come around a corner. Recently she also started saying this to my two cats whenever they appear (which btw go very well along).
I suspect it means 'Hi' or something close, but I find no information on this on the web. Is it something my cockatiel has "invented", or is it a common sound? If it's common, what does it usually mean?
I also wonder if this sound is part of what is called 'chirping'? As English is not my mother language I'm not sure of what sounds are considered chirping.
Cockatiels will imitate sounds and calls as well as use the repertoire that they have naturally. From your description, it sounds like your cockatiel has picked up a sound from her environment and is using it as an announcement or greeting. She's trying to indicate something, so try responding with the same actions several times in a row until you find the action she's trying to get you to do.
One of my male cockatiels makes the sound of the timer on my microwave (at exactly the pitch of the number 3 on the keypad) when he wants me to 'sing' microwave to him (and then he expects to have his cheeks rubbed). It took me a while to figure this out, but he trained me eventually.