If the good piece had this function, then I would have been delighted! I would have just googled what White noise is supposed to be...now I know and -> the alarm clock can't do that ;)

White Noise does not, but there is the "Sunset" function. There you can play certain sounds for a maximum of 60 minutes, either with or without light accompaniment. The available sounds are Soft Rain, Ocean Waves, Under Water and Summer Lake.
There is also an FM radio function, if no station is found there, it simply hisses ;) even without a time limit