Re: Youtube situation is now almost comical...
FM radio broadcasting was invented in 1933 says Wikipedia. The Big Bang, from which the oldest radio white noise originates, took place about 13.8 billion years ago. Either way, it is surely out of copyright by now. At worst, we have to look for the origin of FM radio receiver powered by battery, whose output degenerates to white noise as it runs out.
Science fiction reference: https://en.wikipedia.org/wiki/The_Stardroppers
An obvious allegory of the subversive social menace of teenagers passively littered all over the place listening to portable transistor radio with earpiece playing unworldly alien sounds like The Beatles and Who? and Purple Hayes and Terry Wogan And The Pirates. If any of that makes sense for 1962.